Papers

Within the open quantum system formalism, using the Markovian process, we investigate the quantum speed limit time (QSLT) of a uniformly accelerated Unruh-DeWitt detector, interacting with the massless real scaler field. Three specific scenarios are being studied – the field is in Minkowski spacetime (i) without any reflecting boundary but at a finite temperature, (ii) presence of single boundary with the detector is accelerating parallel to the plane of it, and (iii) presence of two boundaries with the detector is moving between them along the parallel direction. Interestingly, the behavior of QSLT appears to be very distinctive around a particular value of $a$. For the first scenario QSLT shows very noticeable change around a specific $a$ and the required value of $a$ corresponding to this change decreases with the increase of field temperature. In the other two scenarios, QSLT starts to fluctuate after a critical value of $a$. If we further increase $a$, more vigorous fluctuation emerges. The value of $a$ required for the starting of the oscillation is much less for the double boundary case compared to the single boundary. Taking into account specific values of the distance between the boundaries and the detector's frequency, we estimate that the critical value of $a$ can be as low as $\sim 10^5 \text{m}/\text{s}^2$ for the double boundary situation. We argue that such a distinctive feature in QSLT can be a fruitful tool to diagnose the Unruh effect.

We present a spacetime that describes a rotating and charged black hole immersed in an external magnetic field. This exact solution to the Einstein-Maxwell equations has a surprisingly simple form which reduces to standard Kerr-Newman metric, and to the uniform Bertotti-Robinson magnetic universe. We show that the Kerr-BR solution presented in [Phys. Rev. Lett. 135, 181401 (2025)] has a special charge, and we identify a genuine Kerr black hole without any charge, in the magnetic field. In the weak-field limit it gives the Wald solution. We analyze main physical properties of the new family, namely singularities, horizons, regularity of axes, charges, entropy and temperature.

Newtonian mechanics is usually written on a spacetime of fixed geometry. Here we build that geometry, introducing a propagator and a bilinear form only as the description demands. Within this reconstruction the Principle of Inertia emerges as a theorem rather than an independent postulate. Inertial motion is blind to the scale of the form and to the torsion the propagator defines, and that blindness is a geometric precursor of the universality of free fall, before gravity enters. Newton's Second Law is a compatibility between two derivatives along a curve. The force exceeds the mass times the lowered acceleration by an exact term, and the law survives arbitrary torsion. Requiring force-free motion to be inertial along curves parametrised by arc length restricts the torsion to be totally antisymmetric. The remaining torsion is a three-form which we postulate the particle carries along its worldline. Its contraction with the velocity annihilates that velocity, so the supplementary condition of spinning-particle mechanics holds identically, and we propose that contraction as a classical spin. The algebra is familiar from relativistic spin hydrodynamics; the assignment, to the best of our knowledge, has not been proposed elsewhere. Since inertial motion resolves neither the mass nor the spin, the predictive content lies in the transport law we postulate, which turns the spin against a parallel-transported frame at a rate fixed by the acceleration alone and by no coupling constant. That rate becomes a laboratory number only once the arc-length parameter is identified with a clock, which we leave open. The dynamics asks non-degeneracy of the form, so this spacetime is not Newton–Cartan's Galilean one, and gravitation lies outside the construction. We prove every mathematical result, make three constitutive postulates and one physical conjecture.

We investigate the inflationary dynamics of a spectator massive vector field with a non-minimal curvature coupling in de Sitter (dS) and quasi-de Sitter (qdS) backgrounds, focusing on the transverse and longitudinal sectors. By solving the mode equations with Bunch-Davies initial conditions, we compute the spectral energy densities and quantify the deviations between the exact dS approximation and the slow-roll-corrected qdS evolution. We find that the coupling parameter xi significantly affects the evolution of the effective mass, the mass-crossing condition, and the behavior of the longitudinal mode. In particular, increasing xi suppresses the vector fluctuations and reduces transient tachyonic effects. We further follow the evolution of the modes into the radiation-dominated era, showing how the inflationary initial conditions determine the subsequent spectral energy densities. Our results identify the parameter regime in which the dS approximation provides an accurate description and determine when slow-roll corrections become relevant.

Recently we have demonstrated that black hole radiation can be smoothly extended to the zero-temperature limit. Here we analyse entropy variations at the zero temperature limit and evaluate the validity of the Generalized Second Law (GSL). Typically one verifies that the entropy gain in the exterior region compensates for the entropy loss of the black hole due to evaporation. However an anomalous feature emerges at the zero temperature limit. The fact that the emission is restricted to the modes $\omega <m\Omega$, renders the variation of the horizon area of a Kerr black hole positive definite. Simultaneously the von Neumann entropy of the exterior region increases both for bosonic and fermionic modes. The dual entropy gain at the zero temperature limit marks a robust conservation of the GSL. We demonstrate that the dual increase also applies to Kerr-Taub-NUT black holes whose entropy is neither directly proportional to the horizon area nor analytically integrable.

It is widely repeated in the popular literature and elsewhere that the singularity at the center of a black hole is a point. It is not true. Two observers who free-fall into a spherical black hole along two different angular trajectories at the same time $t$ do not encounter each other at the central singularity; rather, they lose causal contact with each other already well away from the singularity. Counterintuitively, in general relativity two points can be spatially close yet causally distant. The singularity is a surface, not a point. The story for rotating black holes is more complicated, but the same conclusion holds. For a rotating black hole, the singular surface almost certainly resides at its inner horizon, where even the tiniest classical or quantum perturbations ignite the exponential mass inflation instability, precipitating collapse to a spacelike singular surface. There are implications for quantum gravity. We argue that, whatever the ultimate theory of quantum gravity may be, the quantum states of a black hole probably reside at its effectively 2-dimensional singular surface, which coevolves unitarily with, and in thermodynamic equilibrium with, the hot atmosphere of trapped Hawking radiation that the black hole generates within its event horizon.

We investigate the dynamical instability and gravitational collapse of charged, spherically symmetric anisotropic matter configurations within $f(R,\mathcal{L}_{m})$ gravity. The analysis focuses on the combined effects of anisotropic pressure, perturbations, electric charge, and modified-gravity source terms on the stability of compact objects. A specific equation of state is adopted to relate the static and perturbed variables through the adiabatic index. Using a perturbation scheme, we derive the modified hydrostatic equilibrium and collapse equations and obtain instability constraints in both Newtonian and post-Newtonian regimes. The results show that the stability of the system is governed by the competition between inward gravitational attraction and outward pressure support. In addition, the dark source terms generated by the non-minimal matter-geometry coupling modify the collapse conditions and can enhance the stability of the charged fluid. These findings provide a useful framework for understanding the evolution and collapse of dense self-gravitating compact objects in non-minimally coupled gravity.

We construct a new family of static, electrically charged, cylindrically symmetric black-string solutions of four-dimensional Einstein–Yang–Mills theory with a negative cosmological constant, supported by a genuinely non-Abelian $SU(2)$ vortex field. The coexistence of electric and vortex sectors renders the standard single-function Lemos metric inconsistent with the Einstein equations, requiring a three-function metric compatible with the anisotropic Yang–Mills stress tensor. Regular near-horizon and asymptotic AdS expansions provide boundary data for numerical integration of the complete field equations. Two limiting sectors are recovered: vanishing electric horizon datum yields the neutral Lemos black string with zero Yang–Mills field strength, while switching off the vortex component gives the embedded $U(1)\subset SU(2)$ charged Lemos–Zanchin solution. Perturbations about the latter show that genuinely non-Abelian hair appears at linear order through the commutator field strength, whereas its backreaction on the electric profile and geometry begins at quadratic order. The horizon equations yield the analytic local non-degeneracy bound $R_1^{\rm crit}=s_0\alpha\sqrt{3/(4\pi G)}$. The asymptotic geometry exhibits a quadratic correction absorbable into an effective Abelian charge and a cubic coefficient giving the first irreducible asymptotic signature of the non-Abelian hair. The entropy obeys the Bekenstein–Hawking area law, while the temperature difference from the embedded Abelian solution arises through the asymptotic lapse normalization. The fully backreacted numerical solutions are nonlinear realizations of this transverse non-Abelian deformation.

We prove that black-hole isospectrality between linearly independent solutions follows whenever radiative metric and matter perturbations are reconstructed from complex master variables obeying a closed, complex-linear system with complex-linear boundary conditions. If a phase rotation maps one parity sector to the other, then the even- and odd-parity QNM spectra coincide, and the perturbations are parity isospectral. A broad class of chiral-aligned theories satisfies these criteria. As an application, we demonstrate that subextremal Kerr–de Sitter black holes are parity isospectral.

The observed diversity of galaxy centers motivates the possibility that the local dark matter composition may vary among galaxies. In conventional multicomponent dark matter scenarios, however, large stochastic variations in the relative abundances are not generically expected, with the cold component typically remaining dominant. We perform $N$-body simulations with a subdominant ultralight dark matter component carrying significant large-amplitude small-scale isocurvature perturbations. We find that although nonlinear evolution largely homogenizes its fraction on galactic scales,ultralight dark matter can still be enhanced and even dominate the centers of small halos because large initial ultralight dark matter fluctuations seed early potential wells that later form halo centers. The ultralight-dominated region can extend beyond $0.01R_{\rm vir}$ and account for more than half of the central dark matter density, even for a cosmological ultralight dark matter fraction below $O(10\%)$. This central segregation provides a possible route to stochastic cusp–core diversity, potentially explaining the observed diversity of galaxy centers.

We develop a phase-space description of classical scattering in which the matter sector of the Dyson S-matrix is partially Weyl transformed while the radiation sector remains operator valued. The resulting S-matrix symbol provides a common origin for several classical observables: we show that the inclusive waveform, the classical displacement in phase-space (i.e. the impulse and position shift), and the angular momentum arise as different projections of the same object. We show that the partially Weyl-transformed $S$-matrix admits an exponential organisation in terms of an elastic phase and connected radiation kernels, while its inclusive one-point projection admits a coherent representative with waveshape $\alpha_I$ describing classical radiation, extending our recent proposal. Furthermore, we show explicitly how nonlinear gravitational memory can be derived from an inclusive coherent waveshape. The dependence of the waveshape on the hard scattering data naturally leads to a quantum geometry, including an induced Berry connection on the space of waveforms, whose contribution to the phase-space displacement captures both radiation-reaction and static-field effects. We illustrate this structure by deriving static contributions to the position shift and field angular momentum in both scalar QED and gravity.

Every traversable wormhole reported so far in static (2+1) gravity coupled to nonlinear electrodynamics has come from a power-Maxwell Lagrangian L propto |F|^k restricted to k=1/2, always forcing the cosmological constant to a fixed sign or zero. We show these restrictions are artefacts of that single choice, not physical requirements, and give a complete classification of static traversable wormholes in this theory. Of the three mutually exclusive electromagnetic configurations compatible with the symmetry, the radial electric branch admits no throat for any Lagrangian or Lambda. In each remaining branch, azimuthal electric and magnetic, the field equations admit exactly two regimes: either the redshift function is fixed, leaving the shape function b(r) completely free with Lambda absorbed without constraint; or the redshift is generic, in which case b(r) becomes fixed instead. We solve both regimes in closed form in both branches, and show that fixing the Lagrangian to any single power k forces Lambda nonzero and determines b(r) up to finitely many constants: this freedom requires the Lagrangian to be genuinely unrestricted. One azimuthal-electric family reproduces the static BTZ mass function, turning the vacuum black hole into a wormhole once sourced by the nonlinear field. Applied to the unique conformal power-Maxwell theory, k=3/4, previously known only as a radial-branch charged black hole, the same Lagrangian yields genuine wormholes in the azimuthal and magnetic branches, showing the electromagnetic configuration, not the Lagrangian, decides between a horizon and a throat; Born-Infeld electrodynamics admits no throat in any branch.

Previously, it was shown that the interplay between the gravitational memory effect and the thermodynamics of an ensemble of spinning objects gives rise to a hysteresis effect, which can be termed Gravo-Thermo memory. This effect can be studied either through a statistical approach or via kinetic theory. Here, we present a general kinetic theory model for the general case of a fluid composed of spinning extended objects in the presence of gravity.

It has been shown that static black hole event horizons cannot exist in time-dependent backgrounds without becoming naked singularities. In light of this, we are left with the question “how does a black hole horizon evolve in an expanding universe?” Here we offer a solution to this puzzle by showing in full generality that regular black hole apparent horizons tend to become comoving, thus confirming the necessity of a cosmological coupling and raising intriguing possibilities for the early growth of black holes.

Astrophysical binaries formed by a stellar-mass compact object and a massive black hole are among the most promising sources for future space-based gravitational-wave detectors. These extreme mass-ratio inspiral (EMRI) systems are tracked coherently over more than $10^{5}$ orbits, encoding detailed information about strong-field gravity. Translating a detection into physical parameters requires models of comparable precision. One outstanding difficulty is the treatment of transient orbital resonances. In this work we address the problem at the level of the Koopman operator, where the waveform is promoted to an observable and the evolution over one radial cycle is a linear operator. Removing the fast timescale without a singularity at a crossing is then a matter of choosing a function of that operator. We demonstrate the approach on a Kerr geodesic driven through the 3:2 crossing by a modelled forcing term. There the coefficient of the standard near-identity transformation diverges, while the finite-window generator attains its analytic bound to better than one part in $10^{6}$. Averaging over twice the crossing duration recovers the resonant jump with its predicted magnitude and phase dependence.

Ultralight scalar dark matter can make space-based gravitational-wave detectors respond through both the scalar charge of freely falling test masses and scalar-induced changes of local solid length scales. Existing space-detector forecasts usually model the former as a center-of-mass force, while ground-based interferometer studies show that scalar fields can also act through material and optical-path transduction. We ask which part of a local material response survives after one-way Doppler measurements are assembled into delayed time-delay-interferometry observables. To this end, we formulate center-of-mass motion and endpoint-size breathing in a common link-response notation for LISA-, Taiji-, and TianQin-like detectors. The main result is a projection rule: in the equal-arm, identical-endpoint, common-field limit, endpoint breathing enters Michelson-$X$ as a common-mode link perturbation and is removed from the retained channel. Its leading leakage is controlled by finite scalar wave vector, unequal or time-dependent arms, nonidentical endpoint response, or auxiliary readouts, and carries extra geometric and delay suppressions beyond the local size response. We then give reproducible noise, sensitivity, and network-combination formulas, and quote multi-mission improvements only under explicit independent-stream and scalar-coherence assumptions. The result provides a controlled baseline for deciding when test-mass breathing can be neglected and when instrument-specific material response must be modeled.

In a recent paper \cite{Chu:2026dhx}, the quantum stability of the fuzzy sphere was established at large but finite $N$, where a tadpole was also identified for the scaling fluctuation mode of the matrix geometry. Here we show that this tadpole generates a positive area-conjugate microscopic response, which in isolation energetically favors contraction of the fuzzy sphere. However, when the horizon is coupled to gravity, the tadpole requires the bulk geometry to adjust according to the junction condition of general relativity. Taking the exterior geometry to be Schwarzschild, we show that the junction condition requires a positive interior cosmological constant. Imposing a static, spherically symmetric, regular vacuum interior then selects pure de Sitter space. The matching further determines a soldering relation between the interior de Sitter time and the exterior Schwarzschild time, with a relative lapse growing as $C = O(N)$. We also propose a matrix realization of the de Sitter interior in which fuzzy-sphere representation sizes determine the angular geometry while condensates of off-diagonal link fields determine the emergent radial metric. This provides a concrete consistency test for spacetime emergence from the matrix degrees of freedom. Potential cosmological implications are discussed.

Static black holes in conformal Weyl gravity differ from their Einstein counterparts in a simple but important way: the Mannheim–Kazanas geometry is encoded in a Bach-flat lapse function whose radial dependence is richer than that of Schwarzschild–de Sitter. We study the de Sitter branch of this solution in the Schwarzschild gauge, keeping the characteristic linear term together with the quadratic de Sitter term. In the branch continuously connected to the positive-mass Schwarzschild–de Sitter spacetime, a regular static region between a black-hole horizon and a cosmological horizon exists precisely when \[ -\frac{1}{3}<\beta\gamma<\frac{2}{3}, \qquad 0<\kappa<\frac{1+3\beta\gamma}{27\beta^{2}}. \] In this window the singularity at the origin is hidden, the two positive horizons obey $0<r_b<3\beta<r_c$, and the limiting endpoint is the Nariai geometry. The thermodynamic interpretation is subtler than the root structure: the two horizons generally have different temperatures, and the static patch has no asymptotic region that would select a unique normalization of time. We therefore compare the Killing, Bousso–Hawking normalized, Tolman local, and effective two-horizon temperature conventions, and we compute the corresponding Wald entropy for the pure Weyl-squared action. The result is a local horizon thermodynamic description that keeps the geometric facts separate from the ensemble-dependent choices needed for any global first law.

We formulate a global optical-area method for shadows of static, spherically symmetric black holes. For the metric \(ds^{2}=-A(r)dt^{2}+B(r)dr^{2}+C(r)d\Omega^{2}\), spherical sections of the optical geometry have area \(\mathcal{A}_{\rm opt}=4\pi C/A\). A null ray with impact parameter \(b\) can cross a spherical section only if \(b^{2}\leq C/A\). The capture threshold is fixed by the infimum of \(C/A\) on the connected interval between the observer and the black hole horizon. When attained at an interior point, the infimum gives \(b_{\rm sh}^{2}=\min(C/A)\), while a static observer outside the controlling minimum, on the inward-sky branch, measures \(\sin^{2}\alpha_{\rm sh}=\mathcal{A}_{*}/ \mathcal{A}_{\rm opt}(r_{\rm o})\). The usual photon-sphere equation follows when the minimum occurs at a smooth interior point. Exponential instability additionally requires the minimum to be nondegenerate. The local optical-radius and photon-sphere formulas are established results. Our contribution is to organize them into an observer-to-horizon global selection rule that compares all stationary candidates and relevant endpoint limits. The radial function \(B(r)\) does not affect the shadow angle, although it enters the coordinate-time instability rate, whose numerical value also depends on the normalization of the static time coordinate. We derive compact first- and second-order formulas for deformed metrics, demonstrate candidate comparison with a synthetic two-minimum profile, and apply the construction to Reissner–Nordström, Bardeen, charged dilaton, and Kottler black holes. An explicit transformation of the charged-dilaton example from a nonareal to an areal radial coordinate verifies radial-coordinate invariance, while the Kottler example probes a nonasymptotically flat static region.

In this work, we investigate the cosmological reconstruction of $f(Q, T)$ gravity, where $Q$ is the non-metricity scalar and $T$ is the trace of the energy-momentum tensor. We consider the functional form $f(Q,T)=f(Q)+\lambda T$ and reconstruct explicit forms of $f(Q)$ corresponding to the $\Lambda$CDM expansion history in Friedmann-Lemaître-Robertson-Walker (FLRW) universe. By employing the matter conservation equation and expressing the cosmological quantities in terms of $Q$, the reconstruction problem is formulated as a first-order linear differential equation for $f(Q)$. Analytical solutions for $f(Q)$ are obtained for various matter configurations, including dust-like matter, a perfect fluid with equation-of-state parameter $\omega=-1/3$, and a nonisentropic perfect fluid with a time-dependent barotropic index. Additionally, an e-folding formulation of the reconstruction is considered to examine the cosmological evolution in terms of the e-folding parameter. The resulting forms of $f(Q)$ confirm that the $\Lambda$CDM expansion history can be successfully realized within the $f(Q,T)$ framework across diverse matter sectors.

We determine the complete solution set of the conformally flat isotropic pure Lovelock field equations for every order $N\ge2$ and every admissible dimension $d\ge2N+1$. Conformal flatness and pressure isotropy combine into a single identity that factorises exactly, splitting the solutions into two branches. The first is the constant-density Schwarzschild interior, which persists at every order with both metric potentials keeping their Einstein form. The second has no Einstein counterpart and is governed by the single dimension–order parameter $k=(d-2N)/[4(1-N)]$; we obtain its physically admissible orbit in explicit closed parametric form, both potentials included. A phase-space analysis on the projective line shows that no solution of this branch has a pressure-free boundary at finite radius, so only the Schwarzschild branch can describe a bounded star. The second instead loses all memory of its central data and relaxes onto a pure Lovelock isothermal sphere with $\rho\propto r^{-2N}$, a higher-curvature analogue of the singular isothermal halo, which we show to be the attractor of the whole family, approached at the closed-form rate $\lambda_*=-(d-2)/(d-2N)$ and with limiting equation of state fixed by $(d,N)$ alone. We prove that $p/\rho$ increases monotonically outward there, and that of the two regular-centre orientations only one is admissible. Since $k$ is rational the spatial potential is algebraic of degree $u+v$, where $2k=-u/v$; radical inversion is guaranteed for degree at most four, while four representative cases have full symmetric Galois group.

We examine analytically the restricted 3-body problem in general relativity for a set of extremally charged black holes. We apply the method of Ferrell and Eardley, which consists in perturbing the Majumdar-Papapetrou solution that describes a static set of such black holes. We extend the method from a pair of black holes to a triplet. We compare the motion of a test particle and a small black hole in the field of a rotating black-hole binary and discover a repulsive self-force acting upon the third black hole.

X-ray reflection spectroscopy is an established probe of black hole (BH) spin and accretion geometry, and many studies have examined its systematic uncertainties. In this work, we explore a possible environmental effect associated with compact dark matter (DM) halos. We adopt numerical BH-DM spacetimes and perform general-relativistic ray-tracing calculations to generate broadened Fe\, K$\alpha$ line profiles. For the configurations studied here, compact DM halos shift the lines toward lower observed energies relative to their Kerr counterparts. We fit the simulated profiles with standard Kerr models and find that the inferred spin and inclination can differ from their input values; in some cases, the spin is overestimated. These results suggest that compact DM halos may introduce an additional uncertainty in reflection-based measurements. Conversely, reflection models that include the environment could ultimately help constrain key halo parameters, such as its mass and characteristic scale, complementing gravitational-wave probes.

We investigate the relativistic dynamics of network nonlocality in general $n$-local networks with chain and star topologies using the Unruh-DeWitt detector model. We show that the relativistic degradation of network nonlocality is strongly governed by the underlying topology. While chain networks suffer an irreversible sudden death of non-$n$-locality under relativistic motion, star networks exhibit remarkable resilience against relativistic decoherence. Most strikingly, a minimal star network with three peripheral nodes exhibits a remarkable sudden death-sudden birth transition of network nonlocality as the acceleration increases. This reentrant behavior reveals a dual role of the Unruh effect: it can both suppress and protect network nonlocality, offering a new perspective on the relativistic effects of acceleration on quantum networks. For larger star networks ($n>3$), non-$n$-local correlations persist over the entire acceleration regime. These insights provide valuable conceptual guidance for the structural optimization and design of acceleration-resilient architectures for future relativistic quantum communication and sensing protocols.

The detection of a stochastic gravitational-wave background (SGWB) is a primary science objective for the Laser Interferometer Space Antenna (LISA). However, extracting these signals is difficult because both the signal and the instrumental noise are stochastic and overlapping in the millihertz band. In this work, we present a Bayesian framework for the joint estimation of LISA noise and SGWB signals. Our approach models the LISA instrumental noise using flexible log-penalized splines, employing a roughness penalty to prevent overfitting while maintaining computational efficiency. For the SGWB, we compare a power-law model with a spline-based model and study how the choice of signal model and noise prior affects signal recovery and detection. Using simulated LISA data, we find that the power-law model gives tighter estimates when the signal follows the assumed shape. However, it fails to recover a localized spectral feature that is not described by a power law, causing the signal to be absorbed by the instrumental-noise spline. The fully spline-based model is less restrictive and successfully recovers such features. We also find that stronger prior information about the test-mass noise helps reduce the degeneracy between the noise and SGWB models at low frequencies, improving signal detection. These results reflect a single trade-off: added model flexibility reduces sensitivity when the assumed signal shape is correct, and prevents bias when it is not.

A Bell violation by material probes certifies nonlocal behavior, but it does not identify which internal subsystem carried or was measured to produce that behavior. We determine the additional information required to attribute such a violation to a gravitational field. For any setting-independent field-to-probe channel completed before the Bell settings are chosen, an entanglement-breaking channel makes all induced field measurements jointly measurable. A static Newtonian phase pickup belongs to this class, even with arbitrary adaptive probe control. Applied to a recent four-mass proposal, the claimed field-only measurements obey the stronger CHSH bound \(\sqrt2\), whereas the Bell-active operation is the source-to-probe instrument that includes the coherent source herald. At the published parameters, the observed flagged behavior is at least \(0.1630\) from the claimed field-detector family, exceeding its \(0.0898\) distance from Bell locality. We then incorporate a common field slice, gravitational constraints, dressing, detector backreaction, and coherent references into a robust certification theorem. The result isolates the minimum missing information: field-only factorization and a local measurement- incompatibility witness on each wing. More precise phase data cannot replace either requirement.

We develop a double-null framework for Cauchy-horizon dynamics in metric $f(R)$ gravity that separates ordinary mass inflation from scalaron cancellation and genuine escape from the blueshift instability. Starting from the exact spherical Hawking-mass transport equation, we show that a regular nondegenerate Cauchy horizon undergoes mass inflation whenever the effective longitudinal source is eventually nonnegative, uniformly dominates the mixed channel, and has a divergent blueshift-weighted integral. Hence bounded mass requires sufficiently strong blueshift-integrable suppression of this source or an independent competing channel. We then analyze the weaker branch in which the scalaron cancels only the leading Price-tail contribution. Under non-cancelling transverse and trace asymptotics, this forces $|R|\to\infty$ and an asymptotically linear high-curvature theory, $f(R)/R\to F_->0$, where $F_-\equiv\lim_{v\to\infty}f_R$. The curvature coefficient is fixed explicitly by the transverse asymptotics. For regular model classes with a finite high-curvature $f_{RR}$ limit one obtains $f_{RR}\to0$. More sharply, every eventually viable branch with $f_{RR}>0$ is forced to $R\to-\infty$ and $\Lambda_\infty>-1$; the standard scalaron mass parameter then diverges, while an additional differentiable rate condition yields $m_{\rm sc}^2\sim F/(3f_{RR})\to+\infty$. In the Einstein frame the scalaron null kinetic contribution is nonnegative, so the Jordan-frame cancellation cannot be interpreted as negative scalaron null energy. The result is a local rigidity classification rather than a global theorem of strong cosmic censorship.

Short tensor modes can generate a white noise contribution to the local scalar $K=8\pi G\rho/3-\theta^2/9$, but this does not induce an infrared-enhanced adiabatic curvature spectrum. For a conserved causal source, analyticity of the longitudinal velocity correlator requires $P_V=\mathcal O(k^2)$, hence $P_{\mathcal R}=\mathcal O(k^0)$ and $\Delta_{\mathcal R}^2=\mathcal O(k^3)$, excluding the $\Delta_{\mathcal R}^2\propto k^{-1}$ relic. We also construct a conserved conversion of radiation into gravitational waves: the white field resides in a compensated entropy mode, and the fluid response cancels the slowly decaying $a^{-2}$ relic. Adiabatic bounds on such sources are therefore source- and matching-dependent.

Higher-curvature terms modify the action but do not necessarily generate new vacuum geometries on the branch perturbatively connected to GR. We develop a first-order framework for static, spherical vacuum black holes in 4D metric theories with $\mathcal L_{\mathrm{grav}}=R/2+\lambda\Psi(R,X,Y)$, $X=R_{\mu\nu}R^{\mu\nu}$, and $Y=R_{\mu\nu\rho\sigma}R^{\mu\nu\rho\sigma}$. On the coupling-analytic branch, purely Ricci-based terms $\Psi(R,X)$, analytic in curvature with $\Psi(0,0)=0$, do not deform a Ricci-flat background under adopted regularity and boundary assumptions. Riemann-dependent terms can, since Kretschmann scalar is nonzero. In areal-radius gauge, we derive model-independent first-order expressions for the horizon shift, ISCO, epicyclic frequencies, periapsis advance, photon sphere, critical shadow impact parameter, Wald entropy, and Hawking temperature. For $\Psi_\eta=\ell_\lambda^{-2+4\eta}\mathcal G^\eta$, treating noninteger powers as phenomenological parametrizations of nonlinear curvature, we obtain a closed first-order Schwarzschild-connected solution. Perturbations decay for $\eta>1/2$, while fixed-ADM interpretation requires $\eta>2/3$; at $\eta=2/3$, sourced $1/r$ term mixes with asymptotic mass mode. For positive effective coupling, the horizon, ISCO, photon sphere, and critical shadow impact parameter increase for $2/3<\eta<1$ and decrease for $\eta>1$. On the fixed-ADM branch, mass, Wald entropy, and Hawking temperature satisfy $dM=T_H,dS_{\rm W}$ to first order at fixed couplings. At $\eta=1$, the linear 4D Gauss–Bonnet term leaves local geometry and geodesic observables unchanged but adds a constant topological entropy shift. Finally, an Event Horizon Telescope-inspired shadow-size criterion gives a conservative first-order sensitivity estimate for the effective dimensionless coupling, a geometric consistency test rather than a complete observational constraint.

In this work, we investigate the worldline deviation of spinning test particles in a weak gravitational wave (GW) spacetime. Within the pole-dipole approximation and the Tulczyjew spin supplementary condition, we consider the modified deviation equation, which contains the standard geodesic deviation term and an additional contribution generated by the Mathisson-Papapetrou-Dixon (MPD) force. We demonstrate how the deviation equation can be solved under viable approximations to yield a new expression for the change in the deviation vector in terms of the perturbation $h_{ij}$, its time derivative, the spin vector components and the longitudinal and transverse components of the deviation. The spin-curvature coupling is shown to play a crucial role in controlling the change in deviation. We then use this result to investigate the changes in the form and expressions of the net GW signal as well as our understanding of GW memory, in the presence of spin. We conclude with our attempts on the measurability of this spin-induced effect vis-a-vis present GW observations.