Papers

When spatial sections of spacetime are topologically nontrivial, the symmetry arguments usually used to choose the Bunch-Davies vacuum are no longer guaranteed to apply. We study this problem for a scalar field on de Sitter spacetime with toroidal spatial sections. The Hadamard conditions, which ensure the same short-distance structure as in flat space, are local and naturally insensitive to the compactification. By contrast, we find that the infrared sector is affected by the toroidal identifications that break global de Sitter invariance, thereby removing the usual argument for discarding zero-mode contributions. We treat the remaining zero-mode freedom as an effective topology-induced source and analyze its effects on an inflationary de Sitter expansion within a semiclassical setting. We show that, for a massless scalar, the zero-mode sector can contain a contribution to the stress-energy tensor with equation of state $P=-\rho$, behaving as a cosmological constant. Thus, the source driving an early-Universe de Sitter phase need not be determined solely by local terms in the action, but can also depend on the infrared structure of the quantum state. Nontrivial topology, as a concrete realization of de Sitter symmetry violation, turns the otherwise-unfixed infrared freedom in vacuum selection to a contribution directly relevant to the semiclassical expansion. This contribution could potentially be applicable to the current accelerated expansion of the Universe.

The ${L}_\Lambda w_{1+\infty}$ algebra is the cosmological-constant deformation of the celestial $Lw_{1+\infty}$ symmetry algebra of gravity, providing an infinite-dimensional extension of the three-dimensional conformal algebra at the AdS$_4$ boundary. We construct the Hamiltonian charges associated with these symmetries from boundary ambitwistor-space data, using LeBrun's Heaven on Earth correspondence, and translate them to spacetime via the Penrose transform. We relate the resulting expressions to light-ray operators in the boundary CFT$_3$, including ANEC operators, their conformal descendants, and their commutators.

We find the shape of the modes containing most of the entanglement between two disjoint spherical regions in the vacuum of a free massless real scalar field in 1+3 Minkowski spacetime. Using the Klco-Beck-Savage method we approximate the field and momentum profile of the vacuum most entangled modes (MEMs) between two spheres. We define a non-perturbative mode-swap entanglement harvesting protocol where two spacelike separated probes extract the maximal amount of entanglement between two regions. Our results are a first step in the direction of understanding the local entanglement structure of quantum fields, pinpointing the exact degrees of freedom that encode accessible quantum correlations in QFT.

We construct traversable wormhole solutions in the linear teleparallel model $f(T) = \alpha T + \beta$, adopting Padé approximants of order [1/0] and [0/1] as shape functions together with the redshift function $\Phi(r) = -M/r$, and derive the corresponding source terms from the modified field equations. We assess the physical viability of both configurations through the energy conditions, Tolman–Oppenheimer–Volkoff equilibrium, the volume integral quantifier, thin-shell junction matching to an exterior Schwarzschild vacuum, embedding diagrams, proper radial distance, the gravitational energy and the active mass. We then examine the observational signatures of each geometry by analysing equatorial null geodesics and the photon-sphere structure, computing shadow maps and radial intensity profiles, ray-tracing relativistic images of a geometrically thin accretion disc, and integrating timelike rosette orbits. Finally, we study the dynamical stability of both wormholes through a third-order WKB quasinormal-mode analysis across scalar, electromagnetic, and axial gravitational perturbations, cross-checked against time-domain evolution and the eikonal photon-sphere correspondence, and examine the parameter dependence of the mode spectrum together with the possibility of trapped-mode echoes.

We investigate the optical and dynamical properties of a rotating black hole in scalar–tensor–vector gravity (STVG) surrounded by perfect fluid dark matter (PFDM). Starting from the static STVG–PFDM geometry, we consider a Kerr-like rotating extension characterized by the spin parameter $a$, the STVG coupling $\alpha$, and the PFDM parameter $\lambda$. We first examine the horizon structure and a radial effective mass function, then analyze null geodesics and unstable spherical photon orbits. We use these results to construct the black-hole shadow and study its size, distortion, and dependence on model parameters and observer inclination. We then compare the predicted angular shadow diameter with the Event Horizon Telescope observations of M87$^*$ and Sgr~A$^*$ in the $(a,\alpha)$ parameter space for representative values of the PFDM parameter. The comparison shows that the PFDM contribution can shift the parameter-space region compatible with the observed shadow diameter, while the shadow size is generally less sensitive to spin than to deformation. We further estimate the Hawking energy-emission spectrum in the high-frequency geometric-optics approximation, using the shadow radius as an effective absorption scale. Finally, we study the quasinormal-mode spectrum in the eikonal limit through the correspondence between unstable photon orbits and ringdown frequencies. The numerical results recover the expected Schwarzschild limit and show a clear separation between the prograde and retrograde modes as the spin increases. The combined analysis provides a consistent optical, energy emission, and ringdown characterization of the rotating STVG–PFDM geometry.

Astronomers increasingly fit their models with gradient-based methods, such as Hamiltonian Monte Carlo, which need the derivatives of the model with respect to its parameters. In many analyses a prediction requires solving a small system of ordinary differential equations (ODEs) for thousands to millions of parameter sets, and this ensemble of integrations often sets the cost of the analysis. We introduce to the astronomical community GRADSOLVE, a JAX library that moves this computation to graphics processing units (GPUs): it integrates each member of the ensemble in its own GPU thread with its own step size and returns the derivatives with respect to the parameters in the same pass. We measure the speed-up it provides in three examples from different fields of astronomy, stellar orbits in the Galactic potential, the expansion history of a dark-energy cosmology and the spin precession of binary black holes, with every code held to the same accuracy requirement. For a million trajectories GRADSOLVE runs 8.5 to 1500 times faster than the serial CPU code of each example running on all 128 cores of a CPU, and several orders of magnitude faster than on one core. On the same GPU it is also 11 to 15 times faster than DIFFRAX, the state-of-the-art ODE library in JAX, in all three examples. With GRADSOLVE a million such integrations take seconds or less on one GPU, so gradient-based analyses that need ensembles of this size become routine. The code is publicly available at https://github.com/ECLIPSE-AI4Science/gradsolve.

We study $O(4)$ symmetric Euclidean wormholes in four-dimensional gravity with a massless scalar linearly coupled to the Gauss-Bonnet invariant. At nonzero coupling, the Einstein wormhole becomes a regular complex saddle that satisfies the Kontsevich-Segal-Witten criterion until its branch ends at a finite coupling. In asymptotically flat space, the Gauss-Bonnet term modifies the scalar displacement and the on-shell action for finite wormholes, but the size dependent parts of both corrections vanish in the large throat limit. The original imaginary distance threshold therefore remains unchanged. A negative cosmological constant already lowers the Einstein large throat imaginary distance relative to its flat space value. When the Gauss-Bonnet coupling is also present, the scalar is no longer a modulus as it develops a logarithmic running and its trajectory has infinite length. Subtracting the logarithmic asymptotic behavior leaves a finite regulated displacement. Its large throat value is shifted upward from the Einstein AdS result by the Gauss-Bonnet interaction and determines the leading large charge behavior of the renormalized fixed charge action.

The role of surface gravity in neutron stars (NSs) is considerable in the radiation mechanisms of the surrounding plasma magnetosphere near the star surface, as they are highly magnetized, compact gravitating objects with compactness $M/R \simeq 0.2$. In this context, they serve as a celestial laboratory for testing gravity theories that dominate the stars' exteriors through plasma magnetospheric radiation. In this paper, we examine how dynamical Chern-Simons (dCS) gravity modifies pulsar electrodynamics in the slow-rotation, weak-coupling regime; the leading-order correction affects only the off-diagonal metric component $g_{t\phi}$, while the diagonal components remain as in General Relativity (GR). We first solve the Maxwell equations in the dCS framework for the electromagnetic field components and obtain analytical solutions for the electric and magnetic fields. We show that the magnetic field components are the same as in GR, while the electric field components are modified in dCS. We then derive analytic expressions for the induced electric charge density, known as the Goldreich-Julian (GJ) charge density, which sources the induced electric field arising from the magnetic field and the star's rotation. In dCS, it is larger than in the GR case, whereas the accelerating electric field parallel to the magnetic field lines is weaker. Next, we consider the deathline condition for switching off electron and positron radiation via inverse Compton scattering in the star's polar cap zone and show that the line shifts upward in the $P-\dot{P}$ diagram, explaining the physics of shorter-lived pulsars. Lastly, we study charged-particle acceleration in the polar cap region and show that electrons reach higher energies over shorter distances than in the GR case.

We investigate topological defects produced by a chiral phase transition in a fermionic ultraviolet completion of dynamical Chern-Simons (dCS) gravity. The model contains a complex scalar field with a chiral Yukawa coupling to fermions. Below the chiral symmetry breaking scale, integrating out the gapped bulk modes produces a gravitational Chern-Simons coupling which, we argue, modifies cosmic string solutions from the phase transition. The resulting corrected string metric is supported by a generalization of the Callan-Harvey fermionic zero mode solution, in which the null current generated by these zero modes provides a mechanism for parity violation. In the weak-coupling and weak-gravity regime, we derive the leading order-reduced dCS correction to this exterior metric. We also discuss the effective action description for generic string configurations in dCS gravity. The gravitational Pontryagin term provides the anomaly inflow required to cancel the gravitational anomaly of the chiral worldsheet theory.

Entropy has emerged as a key concept at the intersection of gravity, quantum theory, and cosmology, revealing deep connections between geometry, information, and thermodynamics. The realization that black holes are thermodynamic systems, characterized by an entropy proportional to their horizon area, has provided evidence that spacetime itself may possess a microscopic structure. Since then, entropy has acquired a central role across quantum field theory, holography, quantum gravity, and cosmology. In this review, we present a unified account of entropy in gravitational and cosmological contexts. We first survey entropy in gravitational systems, focusing on black-hole thermodynamics, entropy bounds, the holographic principle, entanglement entropy, and the area law, together with the main corrections and generalizations arising from quantum field theory, generalized uncertainty principles, modified statistics, and extended theories of gravity. We then discuss three conceptually distinct ways in which entropy is employed in cosmology. The first is through the spacetime-thermodynamics conjecture, in which gravitational dynamics emerge from thermodynamic relations applied to cosmological horizons, and generalized entropy forms consequently lead to modified cosmological evolution. The second is the holographic approach, in which entropy bounds constrain the vacuum energy of the Universe, giving rise to the holographic dark energy scenario and its various extensions. The third is entropic gravity, where gravity is interpreted as an emergent phenomenon of entropic origin, leading to interesting cosmological phenomenology. By reviewing the theoretical foundations and cosmological implications of these entropic frameworks, we aim to clarify the role of entropy, discuss open issues and outline directions toward a deeper thermodynamic and informational understanding of gravity and cosmology.

Time-frequency methods are well suited to the analysis of data from the Laser Interferometer Space Antenna (LISA), including nonstationary noise and data gaps. Another motivation is that the sparse time-frequency support of binary signals allows for fast waveform generation, which is the focus of this work. Amongst the many possible time-frequency representations, the orthogonal Wilson-Daubechies-Meyer transformation has a frequency translation symmetry that allows for a banded heterodyne transformation of chirping signals. When combined with the sparse evaluation of the LISA time-delay-interferometry (TDI) response using “TDI on the fly,” the time-frequency representation has a small memory footprint and highly parallel operations. Full-observation, full-cadence waveforms are avoided: templates are assembled from sparse carrier tracks and local packet calculations, with short direct endpoint segments where the slow-track approximation fails. A family of fast template-generation algorithms is described for three important source classes: galactic binaries, massive black-hole binaries, and extreme mass-ratio inspirals (EMRIs). The same construction applies to the slowly evolving portions of all three signals; the principal differences arise at frequency turnovers, merger, and plunge. The calculation may be organized carrier by carrier, or the polarization waveforms may be transformed first and the detector response applied to their combined time-frequency representation. The latter construction is referred to as “TDI Tapestry.”

We derive an analytic black-hole family in three-dimensional scalar–tensor Einstein–Gauss–Bonnet gravity with positive coupling. A single implicit equation determines the static circular metric and a scalar linear in time. We show that these solutions exhaust regular nonextremal exteriors with the stated AdS boundary conditions and a fixed nonzero coefficient of time in the scalar. The coupled metric and scalar perturbations have one propagating degree of freedom. On one branch, its kinetic coefficient is positive, its equation is hyperbolic throughout the exterior, and its bulk spatial energy is positive for perturbations of compact support. Scalar signals can cross the metric horizon outward, so exterior evolution needs information from the interior. For linear perturbations with the original metric and scalar boundary values fixed, nonzero compact initial master displacements with zero velocity can evolve only until their first contact with the AdS boundary. We derive this restriction from the original metric and scalar equations.

Improved sensitivity of the LIGO-Virgo-KAGRA detectors has enabled the accumulation of a large gravitational-wave event catalog, providing an opportunity for catalog-wide residual analyses to assess waveform-model performance. We study GWTC-4 and GWTC-5 events with signal-to-noise ratio $>12$ in at least one detector, applying three goodness-of-fit tests to the normalized Q-transform energies of whitened residuals obtained by subtracting the IMRPhenomXPHM and SEOBNRv5PHM waveform models. Across the catalog, the residuals are consistent with Gaussian noise, with no evidence of systematic deviations in either multi-detector events or valid single-detector events. For events exhibiting strong model dependence in parameter estimation, variations between waveform models likewise do not produce persistent residual structures. These results demonstrate that parameter-estimation biases associated with waveform modeling do not necessarily manifest as detectable features in the residuals. Residual analyses therefore provide a complementary diagnostic in data space for validating gravitational-wave waveform models within the detector sensitivity.

The detection of gravitational waves (GWs) from compact binary coalescences (CBCs) using matched filtering is computationally demanding because detector data must be correlated with many template waveforms spanning a high-dimensional intrinsic parameter space. In our previous work, we showed that a convolutional neural network (CNN) can classify noisy signals against pure noise and constrain the intrinsic parameter space of a true non-spinning binary black hole (BBH) signal, enabling a narrower matched-filter search region and reducing computational cost. Here, we extend this framework to aligned-spin BBH systems and investigate how different parameter-space representations affect CNN-based patch identification. Using IMRPhenomD waveforms over the aligned-spin BBH parameter space and Advanced LIGO design sensitivity, we show that a CNN trained solely on the aligned-spin template bank achieves more than 99.8% signal-noise classification accuracy on independently generated uniformly sampled BBH signals, indicating that additional uniformly sampled training data are unnecessary. We partition the template bank into four approximately balanced patches using a Principal Component Analysis (PCA)-based quantile scheme and evaluate five parameter-space representations for patch identification. The chirp mass-duration representation achieves the highest average accuracy (93.2%), followed by chirp mass (91.6%) and component masses (90.5%). The post-Newtonian coordinates tau_0-tau_3 and theta_0-theta_3-theta_3s yield substantially lower accuracies. These results show that the existing template bank is sufficient for training and high-accuracy signal detection, while the choice of parameter-space representation is critical for constraining the parameters of the true signal.

In this work, we investigate the dynamics of a scalar particle in a black-hole spacetime surrounded by a cosmological constant and an anisotropic fluid. By solving the Klein–Gordon equation through a power series approach, we obtain quasibound states and the corresponding energy quasispectrum. We find that the quasispectrum can exhibit both real and imaginary components, depending on the model parameters, with the real component existing only under specific conditions. The numerical analysis shows that decreasing the cosmological constant and the anisotropic fluid parameter enhances the energy and increases the radiation in the region outside the event horizon, whereas stronger contributions from these surrounding fields tend to suppress the emitted radiation. We also analyze several asymptotic limits and recover the corresponding results for the Kiselev, de Sitter, and Schwarzschild black holes, providing consistency checks for our solutions. These results highlight the role of the surrounding matter distribution and cosmological contribution in modifying the dynamics and radiation of scalar fields in black hole spacetimes.

We investigate a nonrelativistic approximation to general relativity that does not require the metric coefficients to be weak perturbations of the Minkowski metric. Instead, we assume a differential hierarchy in which the contributions to the curvature containing second derivatives of the metric dominate over those quadratic in its first derivatives, while the metric-dependent coefficients multiplying the retained terms are kept fully nonlinear. Since this separation is not covariant, we formulate the approximation in harmonic coordinates, where it corresponds to retaining the principal part of the reduced Einstein equations. We show that the truncated Einstein tensor satisfies the contracted Bianchi identities up to the order neglected in the derivative hierarchy, ensuring compatibility with energy–momentum conservation at the retained order. The standard Newtonian equations are recovered in the weak-field regime, whereas outside it the dynamics retains a nonlinear dependence on the lapse and spatial metric. In particular, null geodesics probe the spatial geometry at leading order, suggesting gravitational lensing as a natural setting in which observable departures from the standard weak-field description may arise. We illustrate the construction with a static spatially isotropic configuration and discuss the scope and limitations of the approximation.

We investigate stellar oscillations driven by the time-dependent gravitational potential of ultralight dark matter (ULDM) in the de Broglie regime. The response is controlled by the ratio of the ULDM coherence time to the stellar mode damping time. When the field decoheres faster than the damping time, ULDM acts as a stochastic source that excites modes below a characteristic de Broglie frequency, while higher-frequency modes are suppressed. In the opposite, long-coherence regime, individual modes can be resonantly driven. Focusing on solar oscillations, we find a signal far below current sensitivity, and estimate that other stars are similarly unlikely to provide observable signals.

Dynamical black hole scalarization describes the process by which a “no-hair" black hole transitions to a scalarized hairy state. This transition significantly alters the spacetime geometry, including the structure of stable circular orbits of the test particles, which are critical for astrophysical observations and tests of gravity. In this work, we employ numerical relativity simulations to model the time-dependent evolution of a vacuum black hole undergoing scalarization. By evolving timelike geodesic equations within the dynamically changing spacetime background, we investigate how the scalarization process impacts initially stable circular orbits. Our results reveal that the growth of the scalar hair destroys the circular nature of these orbits, forcing them to either become eccentric or plunge into the black hole. This orbital destabilization arises from the rapid change of spacetime curvature induced by the scalar field. Our findings provide novel insights into the interplay between scalar fields and black hole dynamics, with significant implications for gravitational-wave signatures, accretion disk stability, and observational tests of extended theories of gravity.

We investigate quark stars (QSs) described by three quark matter (QM)equations of state (EoSs) and analyse their radial and quasiradial oscillation modes within the slowly rotating relativistic approximation. The considered EoSs describe massless quarks, massive quarks, and massive quarks with a temperature-dependent gluon mass. Our analysis of radial modes shows that the mode separation depends on the stellar mass and radius for a given compactness, as well as on the stellar temperature. The considered QS models satisfy the slowly rotating relativistic condition of Hartle, Thorne and Chitre formalism, allowing rotation to be treated as a small perturbation of the non-rotating configuration. We find that, although more massive and larger stars can exhibit greater surface eccentricity and quadrupole deformation, their stronger self-gravity results in a lower tendency to deform than less massive and smaller stars. For all models, the variation in mass distribution increases towards the stellar surface, while the variations in pressure, energy density, and number density remain small near the center and become more pronounced towards the surface. More compact stars exhibit stronger twisting of the local inertial frame but weaker frame dragging for a given angular velocity. Rotation shifts the oscillation modes from their non-rotating values and leads to different vibrational decay times at different angular velocities. The fundamental modes considered here exhibit frequencies below $2$ kHz and show non-continuous behaviour across the investigated rotational configurations.

Existing general-relativistic magnetohydrodynamics (GRMHD) codes offer complementary capabilities, but these capabilities remain distributed across different frameworks. To unify them, we introduce PANGU–Parthenon-Based Astrophysics for Numerical Relativity and GRMHD in a Unified Framework–a modular computational framework that integrates a shared solver across physical regimes, flexible spacetime geometry, and extensible computational infrastructure within a single architecture. In the first paper of this series, we present and validate the fixed-spacetime GRMHD component of PANGU. The shared solver combines finite-volume Godunov methods with constrained transport on uniform and block-structured, statically refined meshes, and covers hydrodynamics and magnetohydrodynamics in Newtonian, special-relativistic, and general-relativistic regimes. PANGU provides a flexible geometry interface supporting coordinate selection and either on-the-fly or precomputed evaluation of prescribed stationary spacetimes, demonstrated here in Kerr spacetime with Cartesian Kerr-Schild and modified Kerr-Schild coordinates; additional components can be incorporated without restructuring the core solver. Verification covers all three regimes on uniform and statically refined meshes: smooth Newtonian and special-relativistic problems approach second order against their analytic solutions, with deliberately matched double-precision trajectories agreeing with AthenaK to roundoff; in fixed-spacetime GRMHD, the stationary analytic solutions are preserved to second order, and the turbulent accretion reproduces the same flow and flux scales as BHAC. Together, these results establish the fixed-spacetime matter-sector foundation for the broader PANGU framework. Numerical-relativity and coupled dynamical-spacetime GRMHD capabilities will be presented in subsequent work.

In this paper, we generalize the covariant phase space formalism conjugate to field dependent vectors to include internal gauge transformations when gauge fields are present. In our formalism, the symmetry generators are combination of diffeomorphisms plus internal gauge transformations and depend on the field configuration. When the field dependence of the symmetry generators is considered in the covariant phase space formalism, the first law of black hole thermodynamics is a direct result for generally invariant gravitational theories. To check the validity of our formalism, we investigate the conserved charges and the first laws of thermodynamics for a torus-like black hole in Einstein-Maxwell theory and a charged Einstein-Euler-Heisenberg AdS black hole in Einstein-Euler-Heisenberg nonlinear electrodynamics.

We investigate the black-hole quasinormal mode redshifts induced by a galactic dark-matter halo with nonvanishing radial pressure. The halo is described by an anisotropic fluid with a generalized density profile and a constant radial equation-of-state parameter $w$. We construct the corresponding static, spherically symmetric spacetime and study the resulting corrections to the unstable light ring and quasinormal-mode spectrum. For dilute halos and $w\neq -1$, the light-ring angular frequency and Lyapunov exponent acquire the same leading-order gravitational redshift, implying a universal shift of the real and imaginary parts of the quasinormal frequencies. The magnitude of this effect depends on both the halo structure and the radial pressure. This universal redshift relation holds not only in the case of $w=0$ that has been discovered in the literature but also in a much wider scenario, supporting its importance in black hole spectroscopy. On the other hand, the case $w=-1$ is qualitatively different: the factor that corresponds to the leading common redshift vanishes, the corrections are further suppressed by the hierarchy between the black-hole and halo scales, and the universal relation is broken, with the dominant contribution controlled by the inner halo profile. Our numerical computations of scalar-field quasinormal mode spectra confirm the analytic eikonal results.

We report a new source of systematic bias in the Bayesian Templated Background Search (TBS) for the astrophysical stochastic gravitational-wave background. This bias arises from the statistical uncertainty in nested sampling evidence estimates at the segment level and persists even when the likelihood model accurately characterizes the data. Using an analytically tractable model and a frequency-domain mock data analysis with an astrophysically motivated binary black hole population, we show that this uncertainty coherently inflates the inferred duty cycle by up to an order of magnitude when millions of segments are accumulated. We propose a simple and efficient correction and demonstrate its effectiveness across all tested configurations. We also find that a search prior restricted to high optimal signal-to-noise ratio (SNR) misattributes intermediate-strength signals, while extending the prior to support weaker signals amplifies the evidence uncertainty. Both the correction and careful search prior design are essential for robust inference as TBS analyses scale to upcoming observing runs.

This paper investigates a self-consistent effective-one-body (EOB) theory developed to describe the dynamics of spinning binary systems. We systematically derive, using field-theoretic principles, all expressions and quantities entering Hamilton's equations, which govern the dynamical evolution of the system. Based on the effective rotating metric up to fifth post-Minkowskian (PM) order recently obtained by us, we construct the Hamiltonian and the stress-energy tensor. We then derive a decoupled, separable Teukolsky-like equation with a source term for the Newman–Penrose Weyl scalar $\psi_4^B$ and present its formal solution. Finally, using this solution, we obtain the energy flux, radiation-reaction force, and gravitational waveforms for the “plus” and “cross” polarizations generated by spinning binaries. The EOB theory applies to systems with arbitrary mass ratio, which filling the gap between comparable mass ratios and extreme mass ratios.

We present the canonical quantization of Weyl-invariant gravity in a specific conformal gauge. Fixing the scale factor as $a(\eta) = 1/(H_0\eta)$ yields an effective geometric cosmological term $\mathcal{M}(\eta) = \alpha/\eta^2$ on the left-hand side of the Einstein equations, guaranteeing an equation of state $w = -1$ by construction. The Bianchi identity requires a compensator scalar field; we show that this compensator is the conformal mode of the metric, a gauge artifact that does not propagate ghost instabilities in the full quantum theory. We develop the complete ADM Hamiltonian formulation and prove that the constraint algebra closes in standard first-class form. Canonical quantization yields a well-defined Wheeler-DeWitt equation where the $\mathcal{M}(\eta)$ term acts as a potential barrier dynamically suppressing the quantum creation of small-scale universes. The physical reduced Hamiltonian is demonstrated to be bounded from below, time evolution is strictly unitary in the physical Hilbert space, and microcausality is preserved. In the pure vacuum regime, the model admits an exact analytical solution with $\Omega_{\text{DE}} = 1$, resolving the cosmic coincidence problem without fine-tuned parameters. In the matter-dominated era, the comoving horizon scales as $R_H \propto \eta$, so our result $\mathcal{M} \propto \eta^{-2} \propto R_H^{-2}$ reproduces the central Compton Mass Dark Energy (CMaDE) hypothesis from first principles and establishes $n = -2$ as the theoretical benchmark for the Conformal Holographic Dark Energy (CHDE) parametrization $\mathcal{M} \propto \eta^n$. From a pure conformal symmetry principle, the model delivers an effective geometric cosmological term that drives the accelerated expansion with $w = -1$, providing the missing action principle for CMaDE.

We show, analytically, that a static sine-Gordon soliton cannot exist in 1 + 1 non-dynamical de Sitter spacetime if $\alpha := (m/H)^2 < 2$, where $m$ is the mass parameter of the sine-Gordon theory and $H$ is the Hubble constant. Conversely, we also show that static sine-Gordon solitons exist in 1 + 1 non-dynamical de Sitter spacetime if $\alpha > 2$. The above threshold is explained—qualitatively and to within an O(1) factor—using a heuristic argument involving the interplay of tensile force in the Lorentzian sine-Gordon soliton and the tidal force in de Sitter spacetime. A similar heuristic argument, which remains to be confirmed analytically, also suggests the existence of a threshold, $ (m_V/H)^2 \sim O(1)$, below which the tidal forces are too strong to permit the existence of a static `t Hooft–Polyakov monopole in non-dynamical 3 + 1 de Sitter spacetime; $m_V$ is the mass of the vector boson. Linde has suggested that new inflation could have triggered secondary inflation at the core of a GUT (Grand Unified Theory) monopole even if the Hubble constant at or after the GUT phase transition was significantly smaller than the mass of the $X$ boson. We present a heuristic argument, which suggests that the $SO(3)$ `t Hooft–Polyakov monopole does not allow secondary inflation at its core when the inflationary background is weak. Based on the above, as yet analytically unconfirmed, heuristic argument for the $SO(3)$ `t Hooft–Polyakov monopole, we conjecture that secondary inflation at the core of a GUT monopole is infeasible.

Motivated by problems in instanton continuation, we establish geometro-topological selection rules for continuing a Riemannian region into a Lorentzian region through a smooth transverse change of signature. Given a collar-gluing $M=\overline{M_R} \cup_{\mathcal{H}}\overline{M_L}$ of a smooth manifold $M$ along a hypersurface $\mathcal{H}$, we show that an admissible signature-changing metric of the form $\widetilde g=g-fV^\flat\otimes V^\flat$ with $g$ a Riemannian metric, having Riemannian signature on $M_R$ and Lorentzian signature on $M_L$, exists if and only if a relative Euler class obstruction on $\overline{M_L}$ vanishes. This obstruction combines ordinary Euler characteristics $\chi$ in a manner that depends on which components of $\mathcal{H}$ represent big bangs and which represent big crunches. It also restricts the choice of $M_R$; for example, if $M$ is closed and $\dim M$ is even, then it requires$\chi(\overline{M_R})=\chi(M)$. We also determine and classify the possible compactness types of $\overline{M_R}$, $\mathcal{H}$, and $\overline{M_L}$ occurring in such a collar-gluing construction, and construct explicit signature-changing metrics in each case. Topology change can be entirely contained within the Riemannian region when $M$ is the interior of a compact manifold with boundary.

We study the static matter constraint associated with a conical deficit that varies along a string near a wormhole throat. A positive scalar-dependent factor multiplying the complete Abelian-Higgs Lagrangian couples a finite-width vortex to a canonical kink. At critical coupling, we obtain the leading longitudinally varying vortex tension. The flat-kink fluctuation operator has an even translational mode and an odd shape mode of mass $\sqrt{3}/L_\chi$. Reflection symmetry excludes the translational mode from the leading sourced response. We formulate the response with nonzero dressed-string boundary conditions at the longitudinal ends and derive a finite-range transverse halo. In the overlap $w\ll\rho\ll L_\chi$, its mixed stress satisfies $2\pi C\,\delta T^{\chi\,\rho}{}_l=\partial_l\mu_v^{(0)}$ to leading order, where $2\pi C$ is the azimuthal circumference. Together with the local weak-gravity deficit relation, this supplies the leading mixed Einstein constraint of a restricted varying cone. At fixed longitudinal position the sourced halo instead decays beyond $L_\chi$. Consequently, it cannot sustain that restricted cone throughout an outer overlap unless another source contributes the missing mixed stress. This obstruction is conditional on the response of the wormhole-supporting sector and is not a no-go result for general axisymmetric metrics. A finite-width calculation checks the linear-response crossover. We specify the perturbative domain and explain why a rotating extension requires an independent solution of Gauss's law. No complete backreacted wormhole solution or stability result is claimed.

Dense stellar environments such as globular clusters and young massive clusters produce both compact-object mergers detectable in gravitational waves and tidal disruption events observable electromagnetically. We investigate compact-object mergers, tidal disruption events, and micro-tidal disruption events ($\mu$TDEs) in these environments using rapid Monte Carlo star-cluster simulations with the Rapster code, extended with a unified treatment of neutron-star (NS) and black-hole (BH) spin evolution under disk accretion across the NS-to-BH transition, as well as new dynamical channels for disruptions by single compact objects and by BH-BH binaries. Simulating $10^5$ clusters across ten model variations and two formation histories, we find a BH-BH merger-rate density peaking at $z\approx2$-$3$ at several tens ${\rm Gpc}^{-3}\,{\rm yr}^{-1}$, consistent with the local LVK rate, while the cumulative number of $\mu$TDEs exceeds that of mergers by a factor of a few. Since we include only dynamically formed binaries, $\approx90\%$ of $\mu$TDEs proceed through single compact-object-star encounters, and our rates are conservative lower limits. Prograde accretion during $\mu$TDEs spins up compact objects, providing a purely dynamical, randomly oriented pathway for producing high-spin BHs, and can drive accretion-induced collapse of NSs to BHs that populate the lower mass gap.

We present a two-step construction to violate the classical third law of black hole thermodynamics for charged black holes in four dimensions. A near-extremal black hole with an $\mathrm{AdS}_2\times X$ throat is first prepared and then driven to extremality in finite time by a charged shell. This construction suggests that the second step is universal for near-extremal black holes, and can be used to construct violations of the third law for Kerr black holes. The same description allows us to study the process in quantum gravity. The classical collapse condition selects a BF-violating matter sector, for which we construct a holographic dictionary and derive the quantum transition amplitude. Quantum effects replace the classical extremal endpoint by a probability distribution that vanishes at extremality and peaks at positive energy. This obstruction is consistent with the absence of non-supersymmetric extremal black hole states in quantum gravity. We show that driving the peak close enough to extremality for quantum gravity to become important requires a preparation time that scales with the black hole entropy.