General Relativity and Quantum Cosmology Papers

ALT `Adding colour” to the gravitational-wave sky by probing unexplored frequency bands has the potential to unveil new and unexpected phenomena in the Universe. The microhertz band, between pulsar timing arrays and LISA, is a particularly attractive target: it should host the extension of the signal recently found by pulsar timing arrays (if it is generated by a family of sources of gravitational waves), and it may harbour signals from the early Universe, primordial black holes or dark matter. In these proceedings, we review how the orbits of gravitationally bound systems act as resonant detectors of microhertz gravitational waves and ultra-light dark matter. We then describe GUEST (Gravitational Universe Exploration with Satellite Tracking), a mission concept recently proposed to the ESA F-class call, consisting of two dense passive spheres covered with retroreflectors, placed in highly eccentric Earth orbits and tracked by a global laser-ranging network.

ALT We extend the horizon wave-function (HWF) formalism to a spherically symmetric, charged, spinless quantum source in D + 1 dimensional spacetime geometry and construct the HWFs associated with inner- as well as outer-horizons of the Tangherlini–Reissner–Nordström (TRN) black hole. The corresponding black hole formation probabilities, P_BH±, are also calculated and their sensitivities due to various source parameters including charge, mass, and D are analysed as well. Our analysis reveals that the ratio of inner- to outer-horizon probabilities, P_BH⁻/P_BH⁺, changes drastically from being unity as the source departs away from being in the extremal limit defined by α (→ 1 for extremal case). Furthermore, black hole formation probabilities are found to be highly suppressed for higher values of D, particularly for the source mass, m ≲ Λ_D, e.g., for α=0.5, the ratio, P_BH⁺(D = 5)/P_BH⁺(D=10) turn out to be approximately associated with D spatial-dimensions.

ALT The interplay between black hole thermodynamics and topology provides a strong, coordinate-independent framework for discovering the underlying structure of black hole phase transitions as well as their universal features. We explore the thermodynamic topology of the anisotropic Kerr-Newman-AdS black hole using Duan's φ-mapping theory and a complex residue approach. By creating the generalized off-shell free energy, we propose a thermodynamic vector field in the parameter space with zero points corresponding to equilibrium black hole states. The winding numbers associated with these defects are utilized to calculate the black hole's global topological number. We begin with an analysis of the entire anisotropic Kerr-Newman-AdS black hole, followed by two limiting examples. Setting the anisotropic parameter K = 0 produces the Kerr-Newman-AdS black hole, while eliminating the AdS contribution produces the Kerr-Newman black hole. The anisotropic Kerr-Newman-AdS and Kerr-Newman-AdS black ho

ALT The horizon shear of a near-extremal Kerr black hole perturbed by an eccentric extreme mass ratio inspiral shows low amplitude, high frequency oscillations (”wiggles") after periapsis passage. Previous works are unable to tie the frequency of the wiggles to the orbit, and argue they cannot be quasinormal modes (QNMs). We show that they are Kerr QNMs belonging to the damped-mode branch — that is, modes whose decay rate stays finite as the spin approaches extremality. For an equatorial prograde orbit with p = 3M and e = 0.85 and spins ranging from a/M = 0.999 to a/M = 0.99999, fits to the time-domain shear identify the fundamental (ℓ,m) = (2,1) and (3,2) modes as the dominant and first subdominant excitations. Fitting each multipole separately gives frequencies to within two standard deviations of the Kerr values and provides evidence for the excitation of the fundamental (3,1), (4,1) and (4,2) modes, though these are not resolvable in the full signal. We further argue that the same wigg

ALT We investigate axial quasinormal modes of black holes embedded in Hernquist halos, using an established analytic static geometry with an inner vacuum cavity extending to 4M_BH and solving for frame dragging to first order in rotation. We compute the fundamental and first overtone branches for mass ratios ε≡ M_BH/Mₕₐₗₒ of 0.1 and 0.01, and halo compactness C≡ Mₕₐₗₒ/a₀ in the range 10⁻⁴≤C≤0.3. The cavity geometry gives a local Kerr estimate in which redshift rescales the vacuum frequencies, horizon angular momentum sets the rotational splitting, and uniform frame dragging adds a real frequency shift. At zero spin, the cavity redshift reproduces the complex ℓ=2 frequencies with relative residuals below 0.04% for the fundamental and 0.31% for the first overtone. Its leading weak compactness behavior, 1-C, explains the weak mass ratio dependence in dilute halos; at larger compactness, the exact redshift accounts for most of the separation between the two mass ratio sequences. At fixed total

ALT We formulate the static, spherically symmetric vacuum equations of power-law metric f(R) gravity as a covariant autonomous system using the (1+1+2) formalism. The finite critical sets include the scale-invariant Clifton–Barrow solution, a Minkowski endpoint shared by the Schwarzschild family, and degenerate boundaries of the normalized chart. The Clifton–Barrow equilibrium is an outward-radial attractor over a positive interval of the power-law parameter, whereas the Schwarzschild endpoint is a saddle of the polynomially extended system. Poincaré compactification, supplemented by secondary and weighted charts, resolves several asymptotic regimes. In particular, normally attracting sheets at large normalized curvature occur in the positive-curvature sector and are separated from the negative-curvature Clifton–Barrow equilibrium. Metric reconstruction also identifies a selected scalar-flat family with a regular throat, one asymptotically flat end, and a curvature-singular end. These resu

ALT Space-based gravitational-wave detectors compare laser phases exchanged between distant spacecraft. Offset phase locking keeps beatnotes in the phasemeter band, while time-delay interferometry suppresses laser frequency noise. A disturbance of one reference can degrade the functions that depend on it, making robustness an additional criterion for choosing a phase-reference architecture. We introduce a quantitative comparison based on established cascade equations and percolation measures, with directed reference graphs and Erdős–Rényi support layers. Under uniform disturbances, the robustness score is determined by the reference-depth distribution. Under nonuniform disturbances and partial dependence, the connected-support criterion can select a different configuration from both the published depth and local-lock criteria and a reference-path baseline. The phase-locking comparisons favor configurations that limit accumulated degradation and supply downstream lasers from references reta

ALT We extend the analysis of local horizon remnants in quadratic non-metricity gravity to a specific matter trace theory with the functional form f(Q) = Q + alpha Q² + 16 pi lambda T. Here, the matter trace is defined by contracting the energy-momentum tensor with the metric from the original matter action. In the absence of explicit lambda-corrections, the theory inherits the vacuum logarithmic-connection hairy branch. To obtain a non-zero trace, we introduce polynomial non-linear electrodynamics and construct an exact magnetic branch in coincident Cartesian Kerr-Schild coordinates. The non-metricity scalar of this branch vanishes, while its matter trace is proportional to the inverse eighth power of the distance. Its metric component function is given by 1 - 2M/r + q²/r² + C/r⁶, where the correction term C equals xi(1 - 4 lambda)q⁴ / 10. Consequently, the quadratic non-metricity coupling is sterile on this branch. We derive the metric and matter equations, the Euclidean temperature, the

ALT We build an acoustic black hole in a lattice model: a draining vortex evolved by the local collide-and-stream rule of a lattice-Boltzmann model, with no acoustic metric imposed, the geometry being measured from the steady state. A horizon emerges, first located from the measured Mach profile and then confirmed by phonon ray tracing on the measured metric, and the ringdown after a perturbation follows approximately the quasinormal frequencies of the draining bathtub. The residual departures are traced to the cell-scale structure of the horizon, which is not an ideal absorber. We model it in two ways: as a reflective horizon on the ideal bathtub, with two free parameters (the modulus and phase of the reflectivity), and as the sonic point of the realised flow absorbing in its own frame, with no adjustable parameter. The second describes the horizon and the non-rotating spectrum best. Superradiance has two ingredients: the emergent geometry, which amplifies in a loss-free calculation on th

ALT We construct anisotropic self-bound stellar configurations through gravitational decoupling in the minimal geometric deformation framework and investigate their stability against linear radial perturbations. Retaining the Tolman IV temporal potential, we impose the generalized linear equation of state Pᵣ=η(ρ-ρₛ) on the complete matter distribution. Central regularity and Schwarzschild matching determine the radial geometry and relate the surface density to the compactness and stellar radius. Closed-form solutions are obtained for η=1,1/2,1/3,1/4, including the MIT bag radial relation when η=1/3 and ρₛ=4B. Since the equilibrium anisotropy does not determine its dynamical response, we introduce two material prescriptions that preserve either the anisotropy of each fluid layer or its ratio to ρ+Pᵣ. Including metric perturbations, we compute the fundamental mode and three overtones for twelve equilibrium configurations under both prescriptions. All 24 background response combinations have

ALT We construct complete vacuum initial data sets with prescribed asymptotically flat exterior geometry, including the gluing of two Schwarzschild exterior regions with small masses (which need not be positive). The construction allows for arbitrarily slow leading decay and nonzero second fundamental form. For leading terms with a fixed radial power, we first construct localized seed data sets whose constraint errors decay to any prescribed finite order, then apply the projection and stability theorems of our companion papers. The resulting vacuum data sets differ from seeds by harmonic terms controlled by Hamiltonian and momentum silhouettes, and by super-harmonic corrections. This difference of harmonic terms is measured by a relative notion of ADM energy-momentum, which is defined even for slowly-decaying data sets that do not admit an ADM energy-momentum. Upon adjusting seed data sets by either harmonic-decaying terms or compact transverse-traceless terms, we freely control this relat

ALT We study scalar-induced gravitational waves (SIGWs) in a spatially covariant gravity model with two tensorial degrees of freedom, minimally coupled to a k-essence scalar field. For the parameter choice considered during radiation domination, the quadratic tensor action coincides with that of general relativity (GR). We derive the scalar transfer functions at finite σ≡ C₂N̄ and in the large-|σ|limit. We then construct the source function of SIGWs. We further examine a cubic extrinsic-curvature interaction that modifies the source function of SIGWs without affecting the background or quadratic actions. We calculate the fractional energy density of SIGWs for monochromatic and log-normal primordial curvature power spectra. We find that, for the positive values of σ studied, finite-σ effects suppress the spectrum over a broad range of scales relative to the result in the σ→ ∞ limit. In this limit, the cubic interaction suppresses the spectrum at small wavenumbers and enhances it at larger w

ALT This paper investigates the energy-flux noise induced by imperfections of the Gaussian beam (GB) in the Li-Baker high-frequency gravitational wave (HFGW) detector. Modeling these imperfections with higher-order Laguerre-Gaussian (LG) beams, we analytically derive the resulting noise-to-signal ratio for both co- and cross-polarized LGₙₗ modes. It is found that higher-order co-polarized LG beams generate no tangential energy-flux noise at the optimal detection plane (φ=π/2 or 3π/2), whereas higher-order cross-polarized LG beams introduce non-negligible noise. Specifically, for an individual higher-order cross-polarized LGₙₗ mode under our representative parameters, maintaining the noise-to-signal ratio below unity typically requires the power fraction to satisfy σₙₗ<10⁻⁴⁶, with the LG₀₁ mode imposing the most stringent constraint of σ₀₁<6.0×10⁻⁴⁹. Monte Carlo simulations suggest that the total power fraction σₜₒₜₐₗ of multiple higher-order cross-polarized LGₙₗ modes needs to remain below

ALT We simulate the gravitational lensing of gravitational waves (GWs) by a Kerr black hole using a (1+1)-dimensional time-domain mode-sum approach. To enable efficient explicit time evolution, we implement a localized hyperboloidal foliation combined with a static field redefinition, ensuring bounded characteristic speeds across an extended, uniform tortoise-coordinate grid. Incident GW initial data are constructed by projecting a plane-wave Weyl tensor onto the Kinnersley tetrad. Through local spin-dyad rotations and Wigner D-matrix transformations, our framework accommodates both idealized wave packets and realistic binary coalescence signals at arbitrary incidence and polarization angles. To accurately resolve the lensed waveforms, we evolve over 68,000 coupled (j,m) modes. Our results reveal that a Kerr black hole acts as a diffraction-limited thick lens, focusing GWs into a forward beam. For idealized wave packets, the primary prompt pulse exhibits a spin-independent transverse Gauss

ALT We develop a double-confluent Heun (HeunD) method that extends our construction of complete quasinormal-mode (QNM) spectra to extremal Kerr black holes. Matching the horizon-ingoing and infinity-outgoing radial solutions together with angular regularity yields the frequencies directly at extremality, without extrapolation from nonextremal spins. For gravitational perturbations, we obtain an expanded spectrum on both conventional and unconventional Riemann sheets, including additional QNMs revealed by analytic continuation across frequency branch cuts. Continuation in spin connects the extremal modes to our complete Schwarzschild spectrum, including its unconventional branches. We show for the first time that unconventional Class I sequences with m<0, continued from unconventional Schwarzschild modes, approach negative superradiant bounds with vanishing damping in the extremal limit. We also identify finite-damping modes interspersed among sequences approaching zero damping, showing tha

ALT Black hole ringdowns are modelled as a superposition of quasinormal modes (QNMs), although the branch cut of the Green's function produces a nonoscillatory tail that may contaminate early-time ringdown analyses. Within linear perturbation theory, we quantify this branch-cut contribution for the scattering of localised Gaussian wave packets by a Kerr black hole with mass M. Defining the onset of ringdown as the earliest time at which the QNM and branch-cut contributions reconstruct the waveform, we evaluate the branch-cut amplitude relative to the QNM amplitude. For wave packets with a characteristic frequency ω₀∼ 1/M, the branch-cut amplitude is typically of order 10% of the QNM amplitude at ringdown onset with only a mild dependence on spin. We further find that the tail waveform before convolving with a source is almost independent of spin. The spin dependence of the relative amplitude therefore resides primarily in the excitation of the QNMs. Our results suggest that the branch-cut

ALT Gravitational-wave observations of compact binaries offer a direct way to test whether gravity admits polarizations beyond the two tensor modes of general relativity. We perform a forecast to assess how well future multi-messenger events will constrain the presence of scalar polarizations in gravitational waves. Performing binary neutron star injections, we forecast next-generation constraints on three modified gravity parameters in the PPE formalism: α (tensor amplitude), α_B (scalar amplitude) and β (tensor and scalar phase). Cosmic Explorer (CE) and Einstein Telescope (ET) each tighten every parameter by 1–2 orders of magnitude over an O5 LIGO-Virgo network, with ET's triangular geometry giving a persistent ≈2× improvement over 2×CE on the scalar-mode amplitude α_B in both a GW170817-like and a second, representative BNS. We show that, if the sky position and luminosity distance are known from EM observations, adding an EM-based prior on the orbital inclination ι narrows the α_B con

ALT Black-hole interiors with an inner (Cauchy) horizon are unstable through the Poisson-Israel-Ori mass-inflation mechanism, governed by the Dray-'t Hooft-Redmount relation and widely regarded as a dynamical realization of strong cosmic censorship. We show that static, spherically symmetric anisotropic interiors supported by a marginally divergent but integrable density ρ∼ A/r², with A>1/(8π) and mild screening at finite radius, are incompatible with this mechanism. The compactness q=m/r decreases monotonically from a super-critical central value to 1/2 at the unique event horizon, producing a strictly positive compactness gap throughout the trapped region and excluding any second zero of the lapse. This gap enters the dynamics quantitatively. (i) Under the null energy condition and a dynamical screening condition, 2m/r is non-decreasing along both future null directions of a trapped domain, so the gap propagates under nonlinear spherically symmetric evolution. (ii) For ingoing radiation

ALT We establish the general-relativistic limit of f(R) gravity coupled to a massless scalar field for small, asymptotically Euclidean, well-prepared Cauchy data near Minkowski spacetime. We prove global existence and future causal geodesic completeness, with uniform estimates for the metric, matter, and rescaled effective field as an admissible family of modified Lagrangians f(R) approaches the Einstein-Hilbert Lagrangian R. The physical and conformal metrics and the matter field converge to the limiting Einstein-massless-scalar development, uniformly on the entire future spacetime, together with finitely many space and time derivatives. The effective field, defined by a nonlinear reparametrization of the physical scalar curvature, converges to the scalar curvature of the limiting Einstein development. The main analytical difficulty is that the effective-field mass tends to infinity, while its evolution equation becomes an algebraic trace relation. Small field amplitudes may coexist with

ALT Over the past decade, the Advanced LIGO, Advanced Virgo, and KAGRA detectors have detected nearly 400 compact binary mergers, most of which are stellar-mass binary black-hole (BBH) mergers. Nevertheless, most mergers in the Universe are too weak to be individually detected at current sensitivity levels. Since a BBH merger in band is much shorter than the average time between successive mergers, the population of these subthreshold events gives rise to an intermittent background of gravitational waves (GWs). This GW background is guaranteed to exist, but it has not yet been detected with current stochastic or deterministic searches. Here we propose a fast and accurate likelihood-based search for this background, which unifies the standard model-agnostic cross-correlation search and a fully deterministic, template-based search in a single likelihood. Our search is based on a truncated likelihood ratio, which is fully marginalized over the extrinsic parameters of the individual mergers, a