Papers

We study idealized levitated protocols that create spatial superpositions of massive test particles. For each protocol, we compare the dimensionless contrast-loss exponent of mass-proportional continuous spontaneous localization (CSL) with the Diósi–Penrose (DP) self-energy exponent $E_G\tau/\hbar$. We first prove that the point-particle CSL separation kernel has an exact random-unitary realization: Gaussian momentum kicks arriving at Poisson-distributed times produce the same unconditional decay of spatial coherence, although a pure state conditioned on the complete kick record remains pure. The separation kernel alone therefore specifies an operational decoherence law, not the occurrence of objective collapse. We then show that the ratio of the CSL and DP exponents is independent of particle mass and interrogation time. In the point-particle model it depends only on branch separation and an effective distance; for the standard GRW reference parameters, its resolved-superposition crossover is $x_*\approx1.91\,\mathrm{nm}$. For rigid spherical bodies with an arbitrary normalized radial mass profile, total mass, overall density scale, and interrogation time again cancel, leaving a dimensionless geometry factor. The results distinguish three requirements for a decisive experiment: detectable absolute effects, a controlled comparison of CSL and DP scales, and observables capable of discriminating physically different dynamics that share the same ensemble decoherence kernel.

Modern physics has achieved extraordinary empirical success while retaining much of the absolute, unobservable structure introduced by Newton, largely without questioning its necessity. We investigate how far this structure can be eliminated by adopting a relational ontology guided by Leibniz's principle of sufficient reason. Removing absolute position, orientation, time and, finally, scale leads naturally to a formulation of the gravitational $N$-body problem where only dimensionless ratios are physically meaningful. Within this framework, the scale-invariant variety $V$ becomes a central quantity, providing a measure of structure, a natural ordering of shapes, and an emergent gravitational arrow of time. We argue that the resulting formulation unifies classes of Newtonian solutions previously regarded as distinct, uncovering a possible new symmetry, suggests a notion of explanation based on timeless spatial correlations rather than temporal evolution, and points towards a more economical ontology. Although developed in the context of Newtonian gravity, the principles proposed here may also offer a new perspective on general relativity and quantum mechanics.

We study the gravitational effective action induced, at first order in the deformation parameter, by non-local $T\bar T$-like deformations of quantum field theories. Using a heat-kernel formulation, we extract the local geometric terms generated by stress-tensor two-point functions, and apply the construction to free fermions, massive Maxwell theory, and second-order Yang-Mills theory. While the resulting coefficients are generally model dependent, conformal field theories contain a universal sector fixed by the central charge $C_T$. After regularization and renormalization, this sector yields finite, scheme-independent contributions organized into a finite set of curvature invariants. We further analyze trace-trace deformations, for which the relevant contact terms are determined by the Weyl anomaly, and derive the corresponding finite gravitational action for a general class of minimal non-local kernels. These results provide a quantum effective-action realization of induced gravity in which universal conformal data determine calculable contributions to the emergent geometric response.

We construct a novel Kerr-like black hole solution embedded in a general double power law dark matter environment by applying the Newman–Janis algorithm to a Schwarzschild-like seed geometry. This framework provides a unified rotating spacetime for arbitrary double power law density profiles and reveals how dark matter modifies the horizon structure, extremal spin, and curvature properties of rotating black holes. Remarkably, we find that the rotation–halo interplay can eliminate essential curvature singularities for Dehnen-type profiles with $\gamma\leq2$, despite the singular nature of the corresponding static configurations. We then investigate the spectroscopic signatures of the dark matter environment through massive scalar perturbations in the Dehnen $(1,4,\gamma)$ halo. Using an analytical low-frequency matching method, we derive the quasibound state spectrum, the onset condition for scalar cloud formation, and superradiant amplification factor, showing that the halo parameters $\rho_0 r_0^3$ and $\gamma$ leave characteristic imprints on the scalar spectrum. Increasing the halo density or the cusp strengthens the binding of quasibound states and enhances their decay, shifts the scalar cloud threshold, and suppresses superradiant amplification effectivity by narrowing the allowed frequency window and lowering the amplification factor peak. Finally, we analyze rotational energy extraction from thermal scalar fields and demonstrate that the efficiency is controlled by the interplay between the thermal spectrum and the superradiant instability, with lower temperatures and less cuspy density profiles yielding more efficient energy extraction.

We study black hole formation resulting from the collapse of a homogeneous and isotropic dust ball within a framework built upon loop quantum cosmology. Using loop dynamics formulated for Lemaitre-Tolman-Bondi spacetimes—which reduce to the asymmetric loop quantum cosmological bounce scenario—we analyze the dust ball undergoing power-law contraction followed by a de Sitter-like expansion. We discover an emergence of a physical shock at the dust ball surface, characterized by a continuous induced metric and a discontinuous extrinsic curvature arising from a dynamical mismatch between the expanding interior and the contracting exterior vacuum shells. Furthermore, we explicitly derive two variants of Schwarzschild-like line elements for the vacuum sector, and we demonstrate that the resulting spacetime is geodesically complete featuring a rich causal structure. This establishes, for the first time, fully dynamical regular black hole formation within a framework consistent with loop quantum cosmology.

We investigate gravitational and Kerr-Newman extensions of an information-theoretic black-hole entropy that satisfies the Nernst formulation of the third law of thermodynamics. The entropy is identified with the Kullback-Leibler divergence between a mass-dependent Bernoulli ensemble and an unbiased reference ensemble, and therefore measures relative information rather than the logarithm of the number of black-hole microstates. We show perturbatively that its temperature and entropy can be reproduced by an infrared deformation of General Relativity. To linear order in the deformation couplings, the surface-gravity temperature and the Wald entropy agree with the information-theoretic results. In an explicit realization, the matching generates a positive effective cosmological term whose smallness is related to the large microscopic parameter $N$. We also propose an extension to Kerr-Newman black holes based on the irreducible mass. This construction preserves the connection with the horizon area and the semiclassical limit, while distinguishing geometrical extremality from the universal statistical-freezing endpoint, which is independent of angular momentum and charge.

Although the Bekenstein-Hawking area law is consistent with the first and second laws of black hole thermodynamics, it appears to be in conflict with the third law, which in the Nernst formulation states that the entropy should either vanish or approach a universal constant in the zero-temperature limit. We argue that this tension reflects a limitation of the semiclassical area law rather than a fundamental feature of black hole thermodynamics. On this basis, we obtain an entropy formula that is consistent with the third law, and approaches Bekenstein-Hawking entropy in the high-temperature limit. The resulting entropy admits a simple microscopic interpretation, and it can be written as the Kullback-Leibler divergence between a mass-biased Bernoulli distribution and the uniform distribution on N microscopic bits. From this perspective, the thermodynamic black hole entropy admits an information-theoretic representation as an entropy deficit, namely as the relative entropy between the black hole ensemble and a maximally mixed reference ensemble. The Bekenstein-Hawking area law then emerges as the leading term in an $1/N$ expansion, while a universal mass scale $M_0=\sqrt{N}\,M_P$, interpreted as an absolute upper bound on the black hole mass, controls the bias of the underlying microscopic ensemble. The subleading terms represent finite-information corrections to the classical area law.

The tidal response of neutron stars during binary inspiral encodes the equation of state (EOS) of dense matter in the gravitational-wave signal. Quantifying the signal-to-noise ratio (SNR) required to distinguish competing EOS models with third-generation detectors is therefore essential. We perform Bayesian nested-sampling parameter estimation on simulated binary neutron star signals observed by an Einstein Telescope plus two Cosmic Explorer detector network and compute the evidence difference between correct- and incorrect-EOS recovery models over a broad range of SNR. Across two tidal-deformability contrasts, a swap of the true and recovery EOS, and two binary mass points, we find a common scaling, $\Delta\log Z = A\,\mathrm{SNR}^{n}$ with $n \simeq 1.74$–$1.95$, where the EOS contrast and binary properties determine only the prefactor $A$. This behavior follows from an Occam-factor argument, yielding $\Delta\log Z \propto (\Delta\tilde{\Lambda}\,\mathrm{SNR})^{2}$. Calibrating this relation on three configurations predicts, before the run, the SNR required for decisive EOS discrimination in the fourth to within $0.3\%$. These results establish a quantitative framework for assessing the EOS-discrimination reach of third-generation gravitational-wave detector networks.

Objective facts in quantum Darwinism are values recorded redundantly in many independently accessible fragments of the environment. Redundancy does not create additional logical information, so its thermodynamic meaning has remained unclear. We show that it creates an exact work asymmetry between controllers with different access architectures. For a record cloud $F$ and a partition $\mathcal{P}$ into blocks that cannot be jointly controlled, the reversible isothermal erasure penalty relative to a global controller is $k_{\mathrm{B}}T$ times the partition total correlation. If the source event $X$ is supplied as catalytic classical side information, subtracting the corresponding penalty gives the source-loss law $\mathcal{F}_{\mathcal{P}}^{T}=k_{\mathrm{B}}T\left[\sum_{B\in\mathcal{P}}I(X{:}F_B)-I(X{:}F)\right]$. We call this the thermodynamic factuality charge. It ranges from $-k_{\mathrm{B}}T H(X)$ for perfect secret sharing to $(|\mathcal{P}|-1)k_{\mathrm{B}}T H(X)$ for perfect broadcast objectivity. Its normalized form defines a thermodynamic record number between $0$ and $|\mathcal{P}|$. We derive Landauer–Darwin bounds, endpoint-rigidity certificates, exact growth and partition-refinement laws, spectrum-broadcast saturation, and closed formulas for noisy classical and quantum collision models. The theory does not modify quantum mechanics or posit objective collapse; it identifies the thermodynamic resource generated by redundant records under restricted control.

We solve cyclic finite-dimensional quantum histories for arbitrary time-dependent unitary steps, without assuming that one step has finite order. The propagation Hamiltonian is a unitary connection Laplacian on a cycle; its complete gauge invariant is the monodromy $M=U_{L-1}\cdots U_0$. Its spectrum is $\lambda_{a,k}=1-\cos((2\pi k-\theta_a)/L)$, where $e^{i\theta_a}\in\mathrm{spec}(M)$. Thus the exact history sector is isomorphic to $\mathrm{Fix}(M)$, while frustration, the gap above a nonempty zero-energy sector, the determinant, and the finite-temperature trace are obtained in closed form. Ordinary spectral data recover the multiset of monodromy phase cosines but not phase orientation; low energy certifies proximity to an exact relational history. We then define the predictive quotient of a sharp finite clock relative to an accessible operator system as the unique coarsest event alphabet preserving all conditional statistics on a history sector. A finite-error theorem shows that threshold clustering recovers this quotient when the minimum diamond separation of inequivalent event channels exceeds four times the estimation error, and proves an optimal record-count bound. With full matrix access and homogeneous step $U$, the minimal number of clock events is the projective order of $U$. We distinguish the normalizer of the clock algebra from transformations preserving the coherent history code and classify oriented exact sharp clock changes by $U(r)\times\mathbb{Z}_L$ on a rank-$r$ history sector; without orientation the cyclic factor becomes dihedral. Reversible changes of full-information clock fibers are necessarily unitary, so irreversible coarse-graining is not exact clock covariance. Minimal realizations of a complete history Gram kernel are uniquely unitarily equivalent, with a finite-data Procrustes bound. Independent finite-matrix code verifies the main results.

In this paper we construct the canonical harmonic coordinates of the Kerr metric within the multipolar post-Minkowskian (MPM) formalism to the fourth post-Minkowskian (4PM) order. Based on the well known Geroch–Hansen moments of Kerr metric and Gürsel's theorem, we derive the exact canonical MPM moments $\mathrm{M}_L,\mathrm{S}_L$, which are free of any gauge moments. With these moments, we iteratively compute the gothic metric perturbation $h^{\mu\nu}_{\mathrm{can}}$ up to 4PM order and compute the 4PM canonical metric $g_{\mu\nu}^{\mathrm{can}}$. The resulting spatial and time components of these metrics are even functions of the spin parameter $a$ while the mixed components are odd. This parity property distinguishes the canonical coordinates from other harmonic coordinates. To contrast this minimal-gauge construction, we also extract the 1PM source moments of the Kerr metric in the Jiang–Lin coordinates. We find that the Jiang–Lin representation possesses non-vanishing gauge moments starting from the 1PM order, whereas in the canonical representation gauge moments vanish to all orders. This comparison highlights the canonical coordinates as the most gauge-pure representation of the Kerr metric in the MPM framework. The complete canonical metric for the Schwarzschild case is also computed to all PM orders. A recent independent construction by Damgaard et al. using momentum-space recursion yields 4PM equivalent results expressed as a power series in $a$, providing a cross-validation of our closed-form 4PM canonical metric. The coordinate transformation linking the canonical Kerr coordinates to previously known harmonic Kerr coordinates remains an open problem.

We derive and test kinematic upper bounds on charged energy extraction in the purely electric branch of a static $f(R,T)$ black hole family sourced by an Euler–Heisenberg type nonlinear electromagnetic sector. The analysis is restricted to external, minimally coupled probe particles on the fixed background. In this electric solution the field remains Coulombic up to an additive gauge constant; the nonlinear electromagnetic and matter-coupling coefficients therefore affect extraction indirectly through the metric, the event-horizon position, and the global causal structure. We obtain a general local bound retaining nonzero angular momentum and radial velocity of the negative energy fragment, and identify the commonly used zero angular momentum turning-point choice as an upper envelope rather than a generic decay configuration. A co-moving split supplies a locally four momentum-conserving benchmark. We classify horizons with the double root conditions $\mathcal F=\mathcal F'=0$, distinguish asymptotically flat, de Sitter, and anti-de Sitter branches, and impose the corresponding global outward-accessibility criterion. In the de Sitter static patch the electrostatic energy is referenced to the cosmological horizon, so the relevant scale is $Q(1/r_+-1/r_c)$ rather than $Q/r_+$. Reproducible scans compare Reissner–Nordström, Einstein–Euler–Heisenberg type, $f(R,T)$–Maxwell, and full $f(R,T)$–Euler–Heisenberg type backgrounds. The results show that the branch-referenced horizon potential controls the local upper envelope, whereas the asymptotic structure determines whether an outward trajectory can reach infinity, a cosmological horizon, or only a finite outer turning point.

We develop a quantitative framework for charge assisted Penrose extraction in Reissner–Nordström Anti-de Sitter black holes surrounded by a Kiselev type anisotropic dark energy sector. The generalized electrostatic ergosphere is defined by the balance between redshift and electrostatic work. Under explicitly stated monotonicity assumptions on the lapse and electrostatic potential, we prove uniqueness of the exterior ergosphere boundary and of the turning point of negative energy trajectories. We derive a local upper bound on the escaping energy, formulate a finite radius reception criterion appropriate to AdS asymptotics, and map the allowed extraction domains in terms of the mass, charge, cosmological constant, Kiselev normalization, and state parameter. We also introduce first order adiabatic discharge and accretion laws for slowly varying mass and charge, clarifying the regime in which the evolving horizon and ergosphere can be tracked consistently. The results provide controlled analytic and numerical diagnostics for charged Penrose extraction in RN–AdS backgrounds with a dark energy environment, while clearly separating local kinematic bounds from backreaction, radiative losses, and near extremal stability effects.

An axion driven toward a thermal minimum need not remain a coherent condensate. We derive the coupled attenuation of the field mean and production of stochastic momentum modes in an expanding plasma. A single momentum dependent optical depth partitions every mode between coherent power and Bose occupation, placing standard misalignment, partial relaxation, and stochastic production in one dynamical relation. Finite spatial and temporal response suppresses high momentum production, so the stochastic relic has lower mean momentum and a shorter free streaming length than an equilibrium population at fixed mass and bath temperature. A weakly coupled realization produces the dark matter abundance, reduces inherited coherent isocurvature, and confines production correlations to scales removed by collisionless propagation. Thermal relaxation therefore determines the composition, momentum distribution, and transported structure of axion dark matter.

We introduce a measure of information loss for any quantum process that may be modeled by a prepare-evolve-measure scenario: Alice prepares an ensemble of states that gets sent via a quantum channel to Bob, who then measures the output. As a quantum channel models open system dynamics, our measure of information loss quantifies Bob's inability to retrodict with certainty which state Alice sent through the channel. By minimizing this measure over all possible pure state ensemble decompositions of a fixed state $\rho$, and over all POVMs on the output of a channel $\mathcal{E}$, we arrive at an intrinsic notion of information loss for any state-channel pair $(\rho,\mathcal{E})$. We show that the vanishing of information loss with respect to all states supported on a fixed codespace $\mathcal{H}_{\text{code}}$ is equivalent to a condition we term universal pristineness, which ensures that orthogonal pure states in $\mathcal{H}_{\text{code}}$ get sent via the channel $\mathcal{E}$ to possibly mixed states whose supports are orthogonal. Moreover, we prove universal pristineness is equivalent to the Knill-Laflamme conditions in quantum error correction, which are necessary and sufficient for the existence of a perfect recovery channel for all states supported on $\mathcal{H}_{\text{code}}$. As an application, we apply our framework to the Hayden-Preskill model of black hole evaporation, demonstrating that the evaporation channel becomes asymptotically universally pristine, thereby providing a purely channel-theoretic formulation of Page-time information retrieval.

We study the reflected entropy and the Markov gap for modes of a free bosonic field shared by inertial observers (Alice, Charlie) and a uniformly accelerated one (Bob), for a bipartite Bell state and the tripartite Werner (W) and Greenberger–Horne–Zeilinger (GHZ) states. The bosonic Bogoliubov transformation spans an infinite-dimensional Fock space with an unbounded squeezing parameter unlike the fermionic case. By identifying a conserved charge, we block-diagonalize the reduced density matrices into exact two-dimensional sectors, yielding closed or semi-analytic forms for all three states. Although bosonic entanglement is known to vanish asymptotically, the Alice–Bob reflected entropy instead saturates at a nonzero floor, retaining the surviving classical correlation, and converges to the value Alice shares with Bob's causally disconnected partner. Crucially, only the inter-wedge reflected entropy diverges, linearly in the squeezing parameter—the sharp distinction from the fermionic case, where it stays bounded—while the Markov gaps saturate. The construction transfers verbatim to a Schwarzschild black hole, where the saturation values become mass-independent constants.

3-forms are interesting fields to study in the cosmological context for numerous reasons, such as being candidates for explaining inflation and dark energy. The background evolution of a 3-form field is similar to but distinguishable from a scalar field in an expanding universe, and its tensorial structure allows for unique couplings that cannot be experienced by canonical scalars. In this work, we explore the possibility that 3-form dark energy can explain cosmic birefringence. We consider two EFT-inspired couplings between the 3-form and the photon, and compute the birefringence angle $\beta$. We find that a dimension-6 gauge-invariant operator necessitates an extremely large coupling to explain $\beta\sim0.3^\circ$, the value suggested by observations of recent cosmic microwave background radiation. Conversely, a dimension-4 operator can accommodate $\beta\sim0.3^\circ$ at the expense exciting the longitudinal mode of the photon. Interestingly, demanding a self-consistent decoupling limit implies the photon mass lies within a few orders of magnitude of $H_0$. We also derive `universal' profiles for $\beta(z)$, finding the $\beta$ from the dimension-4 operator is insensitive to the form of the 3-form potential but is sensitive to the initial conditions. Contrarily, the dimension-6 operator is highly sensitive to the form of the potential. We finally compare the universal profiles to that of axion-like particle (ALP) dark energy and an ultralight massive 3-form, the latter obtained from numerically integrated cosmological histories consistent with $\Lambda$CDM up to low redshift. Our results show that birefringence from 3-form dark energy can both mimic that from an ALP or be distinguishable, depending on the field configuration in the early universe.

The timing residuals produced by gravitational-wave signals can be described as an incoherent (pulsar term) contribution and a coherent (Earth term) map on the sky, which PTAs measure at the locations of the timed pulsars. The observed Earth term map and the variance induced by the pulsar term contain all of the information about any GW signal available to a PTA (assuming pulsar distances are unknown). Furthermore, any type of signal produces on average the same angular correlation function, the Hellings and Downs curve, which decays steeply with multipole as $C_\ell \propto 1/[(\ell+2)(\ell+1)\ell(\ell-1)]$. This suggests that the signal is inherently low-dimensional and therefore only a small number of parameters are needed to fully characterize it. We present an expression for the PTA likelihood that makes the dependence on the Earth term map and pulsar term variance explicit, and show that only a few spherical harmonic coefficients are needed to capture most of the information about the signal. To quantify this in a realistic setting, we compute the Fisher matrix of the amplitude of a stochastic background or a deterministic point source assuming the noise properties and sky locations of the pulsars in the NANOGrav 15yr dataset. We find that $\ell_{\rm max}=2$ of the Earth term map and the monopole of the pulsar term variance retain $\sim 95\%$ of the information about the signal. For a point source, including the dipole of the pulsar term variance is important to achieve a similar fraction.

In the last few decades, singularity-free black holes (BHs) obtained in the framework of Loop Quantum Gravity (LQG) have gained attention in the literature. These compact objects replace the classical singularity with a transition hypersurface called the bounce radius and stand out as potential scenarios for exploring the imprints of LQG in BH physics. Although scalar perturbations in the vicinity of LQG-based BHs are currently being studied, the absorption spectrum has not yet been analyzed in detail. In this work, we present an in-depth investigation of the absorption properties of massless test scalar fields by a charged LQG BH, aiming to better understand the role played by the quantum and charge parameters of the BH spacetime. Using a numerical approach, we compute the absorption cross section (ACS) of the massless scalar wave for arbitrary values of the frequency of the incident wave. We find that the behavior of the ACS as we increase the quantum parameter indicates that the peaks and troughs of the total ACS exhibit opposite behaviors, i.e., the curve related to the highest peak corresponds to the deepest troughs. Moreover, we show that the ACS decreases as we consider higher values of the BH charge-to-mass ratio. This is in stark contrast to the behavior of the absorption spectrum as we vary the quantum parameter. We also draw comparisons with the Reissner-Nordstrom (RN) BH, exploring the situations where LQG and RN BHs can have the same absorption properties. Furthermore, we find excellent agreement between our numerical results and the well-known classical and semiclassical approximations for the total ACS in their corresponding limits. For completeness, we also investigate the greybody factors. Our results can be viewed as a first step toward a better understanding of the absorption properties of LQG-inspired BHs.

We study the leading adiabatic response of magnetic GHS black holes in massless Einstein-Maxwell-dilaton theory to a prescribed exterior modulus varying slowly in advanced time. In ingoing Eddington-Finkelstein coordinates with the exact areal radius, we derive the time-dependent spherical equations and expand about a slowly evolving instantaneous static GHS representative, keeping its horizon distinct from the exact dynamical marginal horizon. The magnetic GHS family realizes the canonical-slice and Fredholm framework developed in the companion paper. Its integrability yields in closed form the canonical tangent, the finite-rank source profile, a horizon-regular solution of the auxiliary inhomogeneous equation, and a globally regular generator of the sliced-operator kernel. For the leading Robin functional arising in the massless large-radius overlap, we evaluate the Fredholm denominator analytically and prove that it is strictly positive on the charged non-extremal branch. This remains true where the conventional normalization of the kernel generator degenerates, showing that these loci are normalization singularities rather than degeneracies of the kernel mode. Within the controlled large-radius overlap regime, this positivity proves existence and uniqueness of the completed leading-order quasi-static near-zone problem. We then solve the forced radial equation explicitly. The scalar lag is the sum of a universal forced profile and a sliced homogeneous mode whose amplitude is fixed by the exterior matching datum. The mass lag follows algebraically from the radial constraint, and the lapse lag from a single elementary quadrature. The exact marginal horizon is recovered from the lag-corrected solution. The result gives the complete leading quasi-static near-zone response, exact in its radial dependence, for every admissible exterior datum within the specified massless overlap model.

We study static extremal black holes in Einstein gravity coupled to a dilaton and two Maxwell fields with independent dilaton couplings $a$ and $b$. When $b=-1/a$ in four dimensions, a time-symmetric initial-value construction allows us to determine the masses and interaction energies of multi-black-hole configurations. On this special locus, the long-range force between any two extremal black holes vanishes. For arbitrary $a$ and $b$, a constant dilaton-shift symmetry, together with homogeneity and the extremality condition, yields a first-order ordinary differential equation that determines the extremal mass as a function of the two electric charges. This equation allows us to analyze the force between non-identical extremal black holes without having to know the explicit black-hole geometry. In all analytically controlled regimes that we examine, the locus $b=-1/a$ separates attractive behavior for $b>-1/a$ from repulsive behavior for $b<-1/a$. We extend the analysis to arbitrary spacetime dimensions, where the corresponding force-cancellation condition is $ab=-2(d-2)/(d-1)$. Finally, we test this sign pattern using the exact $A_2$, $B_2$ and $G_2$ Toda black holes. In the $G_2$ case, a potentially problematic branch is excluded because it contains naked singularities outside the horizon, suggesting an intriguing connection between regularity and the sign of long-range forces.

The leading adiabatic response of a static black hole to a slowly evolving asymptotic modulus separates into a geometric problem and a functional-analytic one: the former identifies the tangent direction on the manifold of static solutions actually followed by the black hole, and the latter determines whether the resulting deformation admits a unique solution. We show that both can be characterized by explicit scalar criteria. Differentiating a smooth family of static solutions defines an intrinsic covector on its tangent space. When the family is parameterized by the asymptotic modulus and the static horizon-mass parameter, the kernel of this covector identifies a canonical tangent direction that coincides with the one selected by a slowly varying exterior modulus. Promoting the static family to a slowly evolving instantaneous representative does not solve the exact field equations; the resulting discrepancy defines a lag field governed, after elimination of the metric perturbations, by a single reduced radial operator. A representation convention separates the exact dynamical horizon from that of the instantaneous representative. A local slice then removes the remaining tangential ambiguity and induces a finite-rank perturbation of the reduced operator. The Fredholm index is preserved, and, whenever the finite-rank update is nontrivial, the canonical tangent zero mode is displaced from the kernel of the reduced operator. Under the transversality and Fredholm hypotheses, existence and uniqueness of the completed leading-order adiabatic boundary-value problem reduce to a single scalar matching condition on the resulting kernel generator. The construction depends only on a smooth non-extremal static solution manifold and the Fredholm properties of the reduced operator. A companion paper specializes the framework to the magnetic GHS family.

We compute the optical appearance of a maximally extended (eternal) Schwarzschild black hole surrounded by a geometrically thin accretion disk. Unlike astrophysical black holes formed by gravitational collapse, the eternal solution contains a white hole (WH) region connected to a past singularity. Following Markov's hypothesis of a limiting density of matter, we replace the past singularity with a spacelike "surface of last scattering" at $r=r_{\rm m}$ and assume that it emits black-body radiation with temperature $T$. Past-directed rays that cross the past horizon terminate on this surface, resulting in a bright spot at the center of the shadow of an eternal black hole. The radial profile of the spot is set by the gravitational frequency shift, with a blueshifted center when the spacelike surface is sufficiently close to the singularity. We use ray tracing to generate an image of the disk and the spot, and we derive a closed-form interferometric signature of the spot. Its visibility is a pure exponential in the baseline length, in contrast to the power-law envelopes of the disk and the photon ring. We constrain the product $r_{\rm m} T$ from the observed 230 GHz fluxes of M87* and Sgr A*. We also consider a Planck-star scenario in which the value of $r_{\rm m}$ is determined on dimensional grounds, and show that it is out of reach of any current or planned facilities. Nevertheless, the darkness of the observed shadows remains a test of whether these black holes are eternal.

Near-extremal black holes can amplify higher-derivative corrections to general relativity, making them sharp probes of the perturbative control of gravitational effective field theory. We study this question in quadratic gravity with a dynamical scalar degree of freedom, focusing on dynamical Chern-Simons and scalar Gauss-Bonnet gravity. Using pseudospectral methods, we construct rapidly rotating exterior solutions at fixed surface gravity and fixed horizon angular velocity, and follow this controlled family toward extremality. In dynamical Chern-Simons gravity, the sequence approaches an asymptotically flat extremal exterior whose near-horizon limit agrees with the dynamical-Chern-Simons-deformed near-horizon extremal Kerr geometry and inherits its enhanced $SO(2,1)\times U(1)$ symmetry. In scalar Gauss-Bonnet gravity, the same limiting procedure behaves differently: the scalar develops an unavoidable logarithmic singularity at the horizon, the exterior metric develops a small boundary layer near the horizon, and the scalar-Gauss-Bonnet-deformed near-horizon extremal solution is not connected to a regular asymptotically flat exterior. We then use curvature invariants and tidal forces to diagnose the breakdown of the perturbative effective-field-theory expansion. We find that scalar curvature invariants can remain finite at the horizon even when tidal forces measured by infalling observers diverge as inverse powers of the surface gravity. These results separate distinct notions of effective-field-theory breakdown near extremality and provide a perturbative validity estimate that can be compared with current bounds on the dynamical Chern-Simons and scalar-Gauss-Bonnet couplings.

Mapping anisotropies in the gravitational-wave background (GWB) requires choosing a basis to represent the sky intensity, such as pixel and spherical harmonic bases. Each introduces a truncation—e.g., a number of pixels or a maximum multipole l_max—often set by a naive counting argument that relate the number of measurable modes to the number of independent cross-correlations, N_pair, in a pulsar timing array (PTA). However, such truncations can lead to reconstruction artefacts, as they do not reflect the true information content of the PTA response. Increasing the value of truncation parameters spans the observable space better but reveals poorly constrained modes, making the inverse problem ill-conditioned and requiring regularization. A natural approach is to restrict the reconstruction to a well-measured subspace via principal maps, defined by the dominant eigenmodes of the detector response (or Fisher) matrix. However, these maps are not a fundamental parameterization of the sky, but rather, are derived from an underlying representation—such as a pixelization or a spherical harmonic expansion. While their explicit form depends on basis choice, they can span the same subspace when the underlying representation is sufficiently complete. Here, we show that reconstructed anisotropy maps via different bases are equivalent, provided they retain the same information content, i.e., span the same principal subspace. As illustrative cases, we consider a toy model for PTA configuration and several GWB anisotropy shapes: point source, an extended source with deterministic anisotropy, and a statistical isotropic background, along with its summary statistic—the angular power spectrum. Although the reconstructions are equivalent, their computational costs can differ. We conclude with brief comments on the construction of principal maps for ground-based interferometers.

Seismic Newtonian noise, arising from fluctuating gravitational forces on detector test masses due to ambient seismic activity, represents a fundamental sensitivity limit for low-frequency gravitational-wave observatories such as the Einstein Telescope. Effective mitigation of Newtonian noise requires detailed knowledge of the statistical correlations between the Newtonian acceleration perturbation at the test mass and the seismic displacement field measured by surrounding sensor arrays. In this work, the gravitoelastic correlation tensors (the cross-correlations between the Newtonian acceleration perturbation and the seismic displacement field) are derived and numerically validated for Rayleigh waves and body waves in half-space and full-space media, considering test masses located above and below ground, with and without a spherical cavity. The analytical solutions provide exact and asymptotic benchmarks for validating a Cartesian numerical integration framework, which reproduces the corresponding gravitoelastic tensors across Rayleigh-wave and body-wave models, establishing a unified tool for Newtonian-noise modeling and sensor-array design in future gravitational-wave detectors.

We revisit the generalized Glauber theorem motivated by recent applications to dark-matter axion searches and graviton production. For Hamiltonian containing up to quadratic terms in annihilation and creation operators coupled to classical sources, the time-evolution operator can be factorized into displacement, squeezing, and rotation operators. We derive the differential equations governing time evolution of their parameters, reducing the quantum dynamics to c-number equations that can be solved analytically or numerically. To compare another form of the time-evolution operator, Dyson series, we demonstrate the essential role of time ordering. This formalism based on generalized Glauber theorem provides a unified description of particle production from classical backgrounds. Axion-photon conversion in microwave haloscopes is recovered as the linear-interaction limit, while squeezed graviton production from black-hole mergers follows naturally from quadratic interactions. Extending the theorem to thermal initial states yields a realistic quantum description of microwave cavities used in axion experiments. We show that higher-order photon statistics exhibit nontrivial behavior, providing a rigorous foundation for Monte Carlo simulations of quantum-enhanced axion searches beyond heuristic noise estimates.

We investigate quintessential inflation in a nonminimally coupled scalar-tensor theory, parameterizing the post-inflationary radiation abundance independently of the reheating mechanism. The nonadiabatic inflation-kination transition generates a stochastic gravitational-wave background whose contribution to $\Delta N_{\textrm{eff}}$ imposes a lower limit on the reheating temperature. Because this temperature dictates the duration of kination and the available scalar-field excursion, it directly constrains the present-day dark-energy equation of state. While a single-exponential coupling achieves the required post-inflationary potential drop, the same constant slope does not provide viable late-time acceleration. A double-exponential deformation resolves this tension by decoupling the average slope governing the total potential drop from the asymptotic slope driving cosmic acceleration. Full numerical solutions confirm this picture, yielding a thawing quintessence regime with $w_{\varphi,0}\simeq (-0.90, -0.95)$ for our benchmarks. Our results demonstrate that future dark-energy measurements can directly probe the post-inflationary reheating history of the Universe.

Static tidal Love numbers of four-dimensional Schwarzschild black holes vanish in general relativity, whereas higher-curvature interactions can generate a nontrivial response. We investigate the parity-even cubic Weyl correction directly in metric variables and derive the electric, static response for every integer multipole $\ell \geq 2$. Organizing the angular reduction through $L=\ell(\ell+1)$, we obtain exact radial actions and show that perturbative order reduction converts the three metric equations into a constrained two-dimensional first-order system. Eliminating one field yields a scalar equation whose homogeneous operator is precisely the general-relativistic static tidal operator. A Frobenius and Green-function analysis gives the gauge-invariant Zerilli–Moncrief running coefficient $\beta_{\ell}^{\rm ZM}=\epsilon_{\rm e}\,7L^{2}(L-2)^{2}(L-4)(L-6)/12$ and identifies the factor $L-6$ as the reason why the quadrupole is the unique physical electric multipole without logarithmic running. We solve the quadrupole exactly, obtaining the fixed-integer branch ratio $-2400\,\epsilon_{\rm e}$ and explaining why it differs from the analytically continued canonical Love number $k_{2}^{E}=448\,\epsilon_{\rm e}$. For the octupole, we construct the complete horizon-regular global metric solution and exhibit the cancellation of horizon logarithms between the two Green-function channels. Finally, we derive the normalization map to the canonical electric beta functions and the corresponding running of finite-size worldline coefficients. The canonical result agrees with the modified-Teukolsky calculation, while the metric-action approach reveals the radial mechanism behind the exceptional quadrupole and provides the full metric reconstruction.

We investigate dynamical, time-evolving dark-energy models exhibiting phantom behaviour within Einstein gravity by analysing the evolution of matter perturbations. In particular, we consider five dark-energy parameterisations that predict a slowing down of the current cosmic acceleration. We examine the evolution of the growth index and its first derivative, as well as the combination parameter and the statefinder diagnostics, and compare their behaviour with that of the concordance $\Lambda$CDM model. For the parameter choices considered, the present-day values of the growth index and its first derivative are found to be compatible with ranges reported in previous phenomenological studies. The combination parameter is also found to differ from its $\Lambda$CDM value, while the statefinder parameters provide additional means of distinguishing the considered dynamical dark-energy scenarios from the concordance model. Our results illustrate the phenomenological signatures associated with these models and identify observables that may be useful for future observational tests. We stress, however, that the present analysis does not constitute a statistical model comparison or establish an observational preference for any of the considered dynamical dark-energy models over $\Lambda$CDM.