We present for the first time the exact solution of the massive Klein-Gordon equation in the Schwarzschild star (perfect-fluid, uniform-density, spherically-symmetric star), including the non-minimal curvature-scalar coupling. The solution is expressed in terms of the general Heun function. A geometry-induced algebraic coordinate transformation reveals a hidden Fuchsian structure that underlies the exact solvability. Known leading- and next-to-leading-order results are recovered in the low-compactness limit. In the Buchdahl limit, we derive a regularity condition for static modes and describe analytically the divergence in amplitude and oscillation wave vector of dynamic modes as they approach the pressure singularity at the center of the star.

We investigate top-down derivations of effective descriptions for radiation from gravitational systems such as binaries. With a specified cutoff prescription, one can derive worldline effective field theories, but the cutoff dependence also complicates their description. We investigate a related effective approach, based on parameterizing dynamics in terms of an action on the boundaries of cavities encompassing individual bodies. We give examples of such cavity descriptions for black holes and for simple models for modifications of their behavior. We also show how cavity effective descriptions connect to observable quantities -- detailed wave profiles, and importantly, accumulated phase shift of emitted signals. A primary motivation is to have a systematic approach to inferring effects of modification of classical black hole behavior, such as those motivated by the need for black hole evolution to be consistent with quantum mechanics, or by other models for new BH behavior, on gravitational wave signals; the latter phase shifts have in particular been argued to provide sensitivity to small new effects from the inspiral phase. To illustrate basic principles and methods, this paper largely focuses on examples with scalar radiation, but we outline extension of the analysis to gravitational wave contexts.

We investigate the fully relativistic dynamical tidal response of neutron stars up to second order in the frequency. Combining the worldline effective field theory for extended gravitating bodies with perturbation theory of relativistic stellar models, we derive the tidal deformation induced by an external time-dependent field, including a universal logarithmic running term. In the effective theory, we work in dimensional regularization and, through a consistent matching procedure, obtain for the first time the complete leading-order dynamical tidal corrections to both the conservative dynamics and the gravitational-wave signal of compact binaries, including the scheme-dependent finite terms in addition to the running. We show that, in the relativistic regime, dynamical effects cannot be fully captured by mode excitations alone. The magnitude of the additional contribution depends on the stellar compactness, the equation of state, and the running term. Dynamical Love numbers are significantly enhanced with respect to their static counterparts for relatively small compactness. As a result, although they formally enter the gravitational-wave phase at 8th post-Newtonian order, dynamical tidal effects yield a non-negligible contribution during the late inspiral. Using a Fisher-matrix analysis, we show that third-generation detectors such as the Einstein Telescope could measure dynamical Love numbers for a range of neutron-star masses and equations of state. Conversely, neglecting these effects can lead to significant biases in the inference of static Love numbers, and hence on the nuclear equation of state. Our results highlight the importance of dynamical tidal effects for high-precision gravitational-wave modeling with future detectors.

We study a $q$-deformed extension of Brans-Dicke gravity in a spatially flat Friedmann-Lemaître-Robertson-Walker space-time. The deformation enters through a coupling function that modifies the effective gravitational strength and leads to generalized Friedmann equations. In the matter-free sector, we obtain exact analytic solutions for the scale factor and the Brans-Dicke scalar field, and recast the scalar contribution as an effective fluid. We show that the corresponding equation-of-state parameter and the deceleration parameter are constants and depend only on the Brans-Dicke coupling $ω$ and the deformation function, allowing the scalar sector to mimic radiation-, matter-, or dark-energy-like behavior for a restricted region of parameter space.

It has been observed that the Universe is permeated by the cosmic photon background, ranging from radio waves to gamma rays. We investigate the conversion of the photon background into gravitons in the presence of background magnetic fields in the Milky Way Galaxy and in blazar jets. We find that the resulting graviton background is dominated by the contribution generated in blazar jets. Importantly, this graviton background constitutes a graviton floor for high-frequency gravitational wave detectors searching for new physics, analogous to the neutrino floor.

Kiselev solution is a metric that describes black holes immersed in a quintessence-like dark energy background. By introducing a dynamic state parameter $w_q$, the Kiselev solution is supposed to help comprehend the effect of quintessential matter on black holes. In this work, we study the evaporation behaviors of Kiselev black holes. By varying the state parameter $w_q$, we find that the decreasing state parameter lowers the non-final stage temperature and markedly prolongs the evaporation lifetime. We also find that the ultra-slow evaporation mechanism of Kiselev black holes differs vastly from the perfect fluid dark matter (PFDM) black holes and Horndeski black holes, which share the analogous ultra-long lifetime. These results illuminate the effects of dynamic dark energy background on black hole evaporation, provide a potential laboratory to constrain the value of $w_q$, and may complement cosmological and astrophysical observations, e.g., the DESI's preference for thawing dark energy and the observation of exploding black holes based on ultra-slow evaporation.

We investigate the impact of higher-curvature corrections on photon propagation within an effective field theory framework and explore their observational consequences in strong gravitational fields. In particular, we consider polarization-dependent modifications to photon trajectories induced by higher-order curvature terms and analyze their effects in static and spherically symmetric spacetimes, focusing on Schwarzschild and Reissner-Nordström backgrounds. Using the geometrical optics approximation, we derive the effective metric governing photon propagation and study the resulting shifts in the photon sphere. Based on this modified propagation, we compute the quasinormal modes in the eikonal limit and examine their dependence on the polarization modes. We further analyze gravitational lensing observables, focusing on the deflection angle, incorporating the polarization-dependent corrections. Our results clarify how contributions from beyond-general-relativity effects manifest in both quasinormal mode spectra and strong gravitational lensing observables. These findings further suggest the possibility of placing meaningful constraints on effective field theories.

We extend the analysis of photon surfaces in spherical dust collapse to the general, non-marginally bound case, i.e.\ allowing the \textit{energy function} $k(x)$ of the Lema\^ıtre--Tolman--Bondi (LTB) model to be non-zero. Starting from the dynamical-systems formulation developed in our previous work for the marginally bound case (arXiv:2509.01368), we derive the photon surface equations for the LTB metric with $k(x)\neq 0$, and we recast the geometric condition for a timelike hypersurface to be a photon surface as a non-autonomous first-order dynamical system. Even though the LTB evolution equation does not integrate in closed form when $k(x)\neq 0$, the implicit solutions available in the literature, together with comparison theorems for ordinary differential equations, are sufficient to show that the only physically acceptable extension of the exterior photon sphere $r=3M$ into the collapsing dust cloud is a null hypersurface, generated by outgoing radial null geodesics. Combining this fact with the known results on the causal structure of the general LTB model, we then establish that the photon surface reaches the central singularity if and only if the singularity is naked, thereby extending to the general case the picture already known in the marginally bound regime. The structural dichotomy between the naked and covered end states is also discussed in connection with possible observational signatures in the early-time evolution of black-hole shadows.

We study static, spherically symmetric stellar configurations in an extended class of Energy--Momentum Squared Gravity using the covariant \(1+1+2\) semi-tetrad formalism. For perfect physical fluids, we show that the nonlinear matter corrections can be reinterpreted as an effective perfect fluid, so that the stellar equilibrium equations retain the standard Tolman--Oppenheimer--Volkoff form when written in terms of effective variables. The resulting covariant structure equations are formulated in both metric and dimensionless variables and, whenever an effective closure relation exists, reduce to an autonomous planar dynamical system. This provides a global qualitative description of the stellar phase space in terms of finite and asymptotic critical points. Specializing to linear physical equations of state, we recover the general relativistic benchmark and identify sectors that are exactly, asymptotically, or piecewise equivalent to general relativity, as well as sectors -- particularly dust configurations -- for which the planar reduction breaks down and the full three-dimensional covariant flow must be considered. We further recover the standard metric Tolman--Oppenheimer--Volkoff equation in terms of effective variables and show that, although the exterior spacetime remains Schwarzschild, the natural matching condition at the stellar surface is \(p_{\rm eff}(R)=0\), which need not coincide with \(p(R)=0\) for self-bound matter.

Cubic Galileon cosmological models provide a well-motivated framework for investigating late-time cosmic acceleration beyond the standard $Λ$CDM paradigm. In this work, we study observational constraints on cubic Galileon models within the teleparallel gravity framework, where deviations from the standard teleparallel equivalent of general relativity are encoded through the model parameter $b_1$. We consider two scalar-field potentials, namely quadratic and exponential potentials, and analyze four representative scenarios: quadratic and exponential potentials with $b_1$ treated as a free parameter, together with the corresponding cases in which $b_1=2$ is fixed. Using the $\text{Pantheon}^+$ Type Ia supernova sample, cosmic chronometer measurements, SH0ES information, and baryon acoustic oscillation data, we constrain the cosmological and model parameters and compare the observational viability of the different scenarios. We find that the considered teleparallel cubic Galileon models can accommodate the late-time expansion history, although the statistical preference depends on the choice of potential and on whether $b_1$ is fixed or varied. In particular, the fixed-$b_1$ model with a quadratic potential provides the most competitive fit among the Galileon scenarios when BAO data are included, showing a lower $χ^2_{\min}$ than $Λ$CDM and comparable support according to the AIC criterion. However, the BIC criterion continues to favor the minimal $Λ$CDM model because of the larger parameter space of the extended models. These results suggest that teleparallel cubic Galileon cosmologies remain phenomenologically viable, while a stronger claim regarding the Hubble tension requires further consistency tests.

In Plebanski's formulation the coupling of matter is less direct than in the metric formulation since the energy-momentum tensor $T_{μν}$ is symmetric, while the Plebanski variables are naturally valued in the self-dual/anti-self-dual Hodge decomposition of 2-forms. An explicit construction of the Plebanski matter source $T^i$ is obtained by lifting the trace-free energy-momentum tensor $\hat T_{μν}$ into the $(1,1)$ component of the algebraic curvature space using the Kulkarni-Nomizu product, and then extracting its chiral components. This construction reproduces the definition for $T^i$ in terms of the self-dual basis $Σ^i$ and $\hat T_{μν}$ introduced by Krasnov. We also verify that the matter-coupled chiral field equations imply the usual conservation law $\nabla_μT^{μν}=0$ through the chiral Bianchi identity $d^A F^i=0$. As an application, the construction is applied to a spherically symmetric electromagnetic stress-energy tensor, where the anti-self-dual part of the matter-coupled Plebanski field equations yields the Reissner-Nordström-de Sitter solution. The result gives a systematic prescription for translating metric matter sources into the anti-self-dual source terms required by the Plebanski field equations.

We study regular black hole solutions sourced by an anisotropic energy momentum tensor. It is well known that the geometry of the interior of a spherically symmetric regular black hole approaches the dS metric. Having decomposed the energy momentum tensor into its isotropic and anisotropic components, we assume a hydrodynamic equation of state, $P= P(ρ)$, for the pressure, and look for spherically symmetric, regular black hole solutions. We consider different forms of $ P(ρ)$ which yield the previously known regular black hole solutions, as well as various new metrics. We show that the profile of $ P(ρ)$ has a root and a maximum as it approaches $0^+$ at large distances. Consequently, the square of the sound speed of perturbations, $c_s^2$, changes sign at the point where $P$ reaches its maximum, indicating a potential hydrodynamic instability. In addition, imposing the subluminal bound on $c_s$ puts strong constraints on the model parameters, excluding models in which the energy density has an exponential fall off. We establish a universal hierarchy among the relative positions at which the strong energy condition is violated, at which $P$ has its root, and at which $P$ attains its maximum.

Born-Infeld New Massive Gravity (BINMG) completes New Massive Gravity to all orders in curvature through the determinant of the metric shifted by the Einstein tensor. We recast it with an independent auxiliary metric $q_{μν}$, whose algebraic equation of motion $q_{μν}=g_{μν}+\fracσ{m^2}G_{μν}(g)$ recovers the determinant action exactly on the regular branch and resums the infinite curvature series into a single relation. In the densitized variable $P^{μν}=\sqrt{-q}\,q^{μν}$ the three-dimensional action is polynomial, with all derivative dependence carried by the coupling $P^{μν}G_{μν}(g)$. The formulation makes known properties follow with substantially less algebra: the unique vacuum follows in one line, and the quadratic action yields a single Pauli-Fierz massive spin-2 field with the Fierz-Pauli tuning generated rather than imposed. On locally AdS backgrounds the conserved charges, BTZ mass and angular momentum, central charge, and entropy reduce to the Einstein results times a common factor. The formulation also isolates the nonlinear degree-of-freedom problem in the right variables, leaving the full Dirac count to separate work.

The Wilson-Daubechies-Meyer (WDM) time-frequency transform has been widely used in gravitational-wave astronomy, yet a self-contained, mathematically explicit reference for practitioners remains lacking. This is especially true for those wishing to adopt the transform in modern Python and JAX inference workflows. We present wdm_transform, an open-source Python package implementing the WDM wavelet-packet time-frequency transform, and document its mathematical foundations, statistical properties, and practical implementation for gravitational-wave data analysis. The package supplies NumPy and JAX backends, both transforms (forward and inverse) validated to floating-point precision, with the JAX backend enabling GPU-accelerated transforms of million-point data streams in tens of milliseconds. As a worked example, we verify that the WDM-domain likelihood reproduces frequency-domain posteriors for a resolved LISA galactic binary under a shared stationary noise model, confirming numerical equivalence of the two representations in that controlled setting. This work paves the way for systematic optimisation of WDM tilings, a particularly promising direction for the non-stationary noise, stochastic backgrounds, and data gaps anticipated in future detectors, and for direct comparisons with alternative time-frequency representations needed to meet the challenges of future gravitational-wave data analysis.

We study high-frequency electromagnetic propagation in the rotating García--Díaz solution of Einstein gravity coupled to NLED. In this system, light is not governed only by the null cone of the spacetime metric, because the NLED field also behaves as an optical medium whose constitutive response determines the physical optical cones. Starting from the mixed electromagnetic potentials, we project the field $F$ and the excitation $P$ on a principal tetrad and obtain the aligned scalars $E$, $B$, $D$ and $H$. These scalars allow us to reconstruct the regular local constitutive branch connected with Maxwell theory through the map $(D,B)\mapsto(E,H)$. We then insert the resulting response matrix into the Fresnel characteristic problem. At the perturbative order considered here, the Fresnel quartic factorizes into two quadratic branches, each defining an effective optical metric. Both optical metrics admit Carter-type separation of the Hamilton--Jacobi equation and possess their own radial and angular potentials, critical constants and unstable critical families. By projecting these families onto the celestial sphere of a finite-distance observer, we obtain two critical contours, $Γ_+$ and $Γ_-$, which coincide in the Maxwell limit and split when the nonlinear constitutive response is active. We quantify this birefringent splitting through the maximum angular separation, the relative diameter shift and the normalized birefringent width. Numerical scans over the nonlinear coupling, spin and observer inclination show that the splitting is generated by the constitutive response, redistributed by rotation and stable under local projection changes within the perturbative domain. This provides a direct geometrical link between the local NLED response and a polarization-dependent critical structure on the observer screen.

In PRL 129, 110401 it was shown that it is theoretically possible to have operationally detectable causal loops without violating the principle of no superluminal signalling (NSS) in (1+1)-Minkowski spacetime. Whether or not such causal loops are also possible in $d > 1$ spatial dimensions, has remained a key open question. We resolve this question by showing that in a wide class of "conical" spacetimes, including Minkowski with d > 1, NSS does rule out all operationally detectable causal loops, in classical, quantum and post-quantum theories. This establishes that the relationship between the relativistic principles of NSS and no causal loops depends inherently on the geometry of spacetime.

The explicit formulas for the spherical solutions of the Dirac equation in the expanding universe are given. The initial value of the solution can be, in particular, a wave function of the hydrogen-like atom or a spherical wave in the Minkowski space, that then propagates in the Friedmann-Lemaître-Robertson-Walker space-time, which is expanding with the de~Sitter scale

We show that higher-curvature Lovelock terms do not restore local cosmic censorship in spherical dust collapse, but instead promote the local visibility of central shell-focusing singularities. On the collapse branch with positive highest-order Lovelock coefficient \(c_N\), the highest nonvanishing Lovelock order \(N\) controls both the near-singularity collapse and the formation of trapped surfaces. In noncritical dimensions, \(D-1-2N>0\), the apparent-horizon curve approaches the singularity curve with trapping exponent \(β_N=(D-1)/(D-1-2N)\). Comparing this scale with the first nonvanishing correction \(r^\ell\) to the singularity curve gives the local-visibility condition \(\ell<β_N\), provided the singularity curve opens outward. Thus increasing \(N\) enlarges the class of inhomogeneous initial data producing outgoing radial null rays from the central singularity. In the critical odd-dimensional branch, \(D=2N+1\), no apparent horizon forms sufficiently close to the center, so any outward opening of the singularity curve gives local visibility. The locally visible singularities are Królak-strong along the emerging null rays, with Tipler strength reached at threshold. For bound and unbound collapse, the noncritical exponents are unchanged: the energy function modifies the opening of the singularity curve, while in the critical branch it enters the leading terminal collapse velocity.

Past and recent observations suggest that many planetary mass or dwarf planet objects may exist in the outer Solar System. Gravitational perturbations may occasionally bring some of them into the inner Solar System. The early, rare collision between the early Earth and a Mars sized body is generally invoked to explain the formation of the Moon. More probable than a direct impact, are grazing or near Earth flybys of similar objects. Such passages may have left strong tidal signatures: giant waves, large volcanic episodes, sea regressions, coherent meteor showers, and major climatic perturbations. These mechanisms could have contributed to several major biological mass extinctions over the past $600$ million years, as suggested by peculiar correlations in the geological record. Similar events may have occurred several times during the earlier history of Earth. Accretion of mini planets by largest planets and in particular by the Sun may also have occurred many more times over the last four billion years. Possibly producing additional temperature variations on planets and Earth.

Could two worlds localised on neighbouring branes communicate through gravity alone? We investigate this question in a minimal higher-dimensional framework in which Standard Model fields are confined to our brane while gravity propagates through the bulk. From the brane-to-brane graviton propagator we derive the retarded transfer kernel of the inter-brane link and identify the transition from evanescent to propagating Kaluza-Klein modes. The central idea is to give the Kaluza-Klein tower a new role: not only as a spectrum of massive gravitational states, but as a set of communication carriers. Below the first KK threshold the channel is effectively four-dimensional and is mediated only by the massless graviton. Above threshold, massive KK modes open as additional propagating subchannels, and information may be encoded in their occupation pattern, relative phases, and arrival-time structure as well as in ordinary signal variables. The compactification determines the KK masses, wavefunctions, brane overlap factors, and propagation phases, which together define a multi-input multi-output (MIMO) channel matrix. In the resolved-mode limit, the tower yields approximate parallel subchannels, to which standard information-theoretic notions such as capacity bounds, water-filling, effective rank, and sparse occupancy codes apply. The production and detection of such signals are highly model-dependent and not assumed to be feasible with known technology. Nevertheless, the channel structure is well defined: a neighbouring brane-world could be separated from us by a microscopic distance in the compact space while remaining hidden because the only shared interaction is gravity. The first observable signature may not be a deliberate message, but the spectral and modal structure of the Kaluza-Klein tower itself, revealing partial information about the geometry of a nearby hidden world.

Recent preprints by Key et al. reported the discovery of a short-lived brightening of a star (nicknamed "Phoebe") located in the Large Magellanic Cloud that was interpreted as a short-timescale gravitational microlensing event produced by a lunar-mass primordial black hole (PBH) in the Milky Way dark matter halo. Here, we present an independent re-analysis of the publicly available DECam observations of this object, incorporating additional data from 2020 and 2021. The object underwent at least three distinct, low-amplitude brightenings (one of which was misinterpreted as a short-timescale microlensing event) in addition to long-term variations of its mean magnitude. These characteristics indicate that Phoebe is an ordinary variable star rather than a microlensing event. This finding resolves the apparent tension with the results from earlier microlensing experiments that rule out the hypothesis that a substantial fraction of dark matter is composed of lunar- and planetary-mass PBHs.

Standard weak-lensing calculations treat lensing as a linear remapping of the matter field along the line of sight. We instead formulate lensing as a stochastic field theory for the Sachs optical scalars, driven by random Ricci-focusing and Weyl-shearing fields. The resulting path integral generates a diagrammatic expansion for arbitrary $n$-point correlation functions of lensing observables, organised into linear response, nonlinear propagation, and driving-field cumulants. The conventional calculation emerges as the lowest-order, linear-propagation limit. Beyond it, nonlinear Sachs evolution couples to driving-field non-Gaussianity, mixing the matter cumulant hierarchy into the lensing hierarchy. A selection rule governs the couplings: an $n$-point observable receives a direct contribution from the $n$-point driving-field cumulant, and its leading hierarchy-mixing correction from the $(n+1)$-point cumulant via one nonlinear Sachs interaction, with higher cumulants entering only at higher order. The two-point function, for instance, is corrected by squeezed three-point cumulants of Ricci focusing and Weyl shearing, letting small-scale modes source larger scales and feeding the lensing $E$- and $B$-modes equally. Rather than a restrictive approximation scheme, the formalism is a paradigm shift: a unified framework naturally accommodating path corrections, higher-order matter statistics, stochasticity, and small-scale effects.

When stochastic field dynamics are cast into a path-integral formulation, perturbation theory becomes systematic but the resulting expansion quickly grows combinatorially large. The setting targeted here includes multi-component, multi-dimensional fields with matrix propagators, tensor-valued couplings, and non-Gaussian driving noise specified by arbitrary $n$-point cumulants. Wick pairings grow factorially, and component indices must be routed through the tensor-valued vertices. The useful output is not a raw contraction list, but a diagram table: one entry per topology, with multiplicities, coupling sums, signs, and causal constraints resolved. We present sft-wick, an open-source Python package that constructs these diagram tables and computes their integrals numerically. Given an action and an observable, it enumerates topologically distinct Feynman diagrams, derives their algebraic coefficients, and evaluates the resulting diagram integrals from user-supplied response and cumulant functions. The core algorithm enumerates spatial topologies before routing component indices, avoiding contraction-by-contraction Wick expansion. Response-field constraints, including vanishing response-response contractions, the ito prescription, and the absence of causal response loops, are enforced during enumeration. Predictions are validated against direct Langevin simulation, agreeing to within the simulation's statistical noise.

We formulate reheating as a constrained variational problem in the space of equation-of-state histories, rather than attempting to describe it through microscopic models. We introduce a regularized functional framework that identifies reheating histories which extremize a given cosmological observable under minimal physical assumptions. As illustrative applications, we consider prompt gravitational waves, induced gravitational waves, and primordial black holes. We find that different observables select qualitatively different regions of reheating-history space. These examples demonstrate that cosmological observables define distinct extremal directions in reheating-history space and can therefore be used to systematically explore the space of post-inflationary expansion histories.

The gravitational effects of seismic waves, so-called Newtonian noise, will likely limit the low-frequency sensitivity of future ground-based gravitational wave detectors, such as the Einstein Telescope. It has been proposed to mitigate this noise source by predicting it from measurements of the surrounding seismic displacement field using an array of seismometers. In this paper, we investigate the Newtonian noise prediction abilities of neural networks based on synthetic data from such seismometer arrays and compare the results with the Wiener filter as benchmark. We developed a simulation that generates density fluctuations of random plane waves and Gaussian wave packets, and that calculates the resulting Newtonian noise and displacement field. We investigate the performance on approximately stationary wave fields and single dominating long- and short-term events. For the first case, we observe comparable performance of neural networks and the Wiener filter with the networks performing slightly better. For the second case, however, we find that convolutional neural networks and graph neural networks can outperform the Wiener filter by factors of 15-80, depending on the frequency and the array configuration, and that they can reduce the corresponding Newtonian noise amplitude spectral density by factors of 10-30.

LISA-band gravitational waves from massive binary black holes can be diffractively lensed by low-mass dark matter halos and subhalos, so their frequency-dependent amplification can probe the inner density profile. We isolate the generic finite-core part of this signal by comparing fixed-mass Navarro-Frenk-White (NFW) and cored-NFW lenses and propagating both profiles to the complex wave-optics amplification factor. A finite core smooths the time-delay response and reshapes the diffraction peak; an NFW template with a lower concentration can mimic part of the effect, but structured complex residuals remain after time and phase alignment. The residual peaks for intermediate cores, $r_c/r_s\simeq0.25$--$0.3$. An SIDM-inspired isothermal-core profile gives the same qualitative response, showing that the signal is not an artifact of one cored parameterization. For a fiducial LISA source, an appreciable mismatch requires favorable near alignment and $M_{\rm vir}\gtrsim 10^7M_\odot$. The result is a finite-core baseline for isolated line-of-sight halos and for subhalos perturbing strongly lensed macro-images.

In energy-momentum squared gravity (EMSG), the spacetime inside a neutron star is sourced by effective thermodynamic variables that need not coincide with the physical fluid pressure and energy density. It is therefore an open question whether the trace anomaly of dense matter -- the QCD measure of how strongly conformal symmetry is broken -- still organizes interior profiles and curvature in the same way it does in general relativity (GR). We adopt a clear matter-geometry separation: the trace anomaly is computed from the fluid sector alone, while spacetime curvature scalars are built from the variables that actually source the modified Tolman-Oppenheimer-Volkoff equations. For five relativistic mean-field equations of state, the radial trace-anomaly profiles increase monotonically from core to surface in all accepted EMSG models, as in GR, but split systematically with the EMSG coupling strength; the splitting grows with stellar compactness. Despite this deformation, curvature invariants still fall onto organized bands when plotted against the trace anomaly, extending the GR thermodynamic-geometric correspondence. The Ricci contraction shows the tightest organization, whereas the Ricci scalar remains the most equation-of-state sensitive. EMSG effects are modest for observationally accessible stars but largest in stiff, ultracompact configurations, indicating that the trace anomaly remains a useful thermodynamic label for interior geometry even when gravity couples nonlinearly to matter.

We demonstrate that, for a large black hole of radius $a$, Hawking radiation terminates around the scrambling time $u_{\text{scr}} \equiv 2a \log(a/\ell)$ due to the nonlocal, exponential suppression of trans-Planckian interactions inherent in string field theory (SFT). Modifying a massless scalar field's interaction with a dynamical black hole background via the smearing operator $e^{\ell^2\Box}$ (where $\ell$ denotes the string length scale), we calculate the time-dependent number expectation value $\langle \hat{N}(u) \rangle$ of outgoing Hawking particles at retarded time $u$. While the standard Planck spectrum at the Hawking temperature is reproduced at early times ($u \ll u_{\text{scr}}$), the particle number approaches zero shortly after the scrambling time. This early shutoff reflects the property that the collapsing shell becomes effectively invisible to trans-Planckian modes, offering an alternative resolution to the black hole information paradox via a macroscopic remnant.

The black hole information paradox challenges us to do something that is seemingly impossible: find a violation of the semiclassical approximation in a region where all curvatures are low. The vecro hypothesis proposes a structure of the gravitational vacuum that can accomplish this task. In this article we explain the hypothesis, and give a lattice model to describe the essence of its idea. The Hamiltonian of the model is completely local, but the vacuum exhibits correlations among planck scale fluctuations which fall off relatively slowly with distance. These extended-scale correlations are able to `feel around' the region where a closed trapped surface is about to form, and to react by nucleating fuzzball structure that destroys semiclassical spacetime.

We investigate the first-order phase transition that terminates thermal inflation and evaluate the associated stochastic gravitational-wave signals. The transition is first characterized through semi-analytic calculations of the bounce action, which are compared with numerical results obtained using CosmoTransitions. We then study its real-time evolution in a three-dimensional Langevin lattice simulation that incorporates Hubble expansion and the corresponding temperature evolution throughout the transition. The lattice dynamics are consistent with the bounce-action estimates: the transition proceeds through localized bubble nucleation and subsequent bubble growth, rather than through a phase-mixing instability. Using the resulting transition parameters, we estimate the gravitational-wave spectra generated by bubble collisions and acoustic motions in the plasma. The predicted stochastic background lies within the projected sensitivity ranges of future gravitational-wave observatories, including BBO and DECIGO.