Papers

We investigate the local gravitational source and charges obtained by introducing translations as an internal Stückelberg redundancy in Weyl gauge theory. The internal-$T(4)$-invariant dressed coframe identifies the source of the translational potential with the existing coframe variational derivative, without introducing new dynamics. We derive an excitation/source equation and balance law whose structure is independent of the constitutive parameters of the parity-even quadratic torsion family. The gravitational self-current, defined relative to a specified gravitational/matter split and boundary representative, gives a density invariant under the internal gauge factors once its frame index is contracted with the coframe; this invariance neither establishes ordinary conservation nor identifies the density with the external translation Noether current. A surface charge follows by contraction with a covariantly constant internal direction, and we separately derive the three-sector Noether superpotential of generalized reducibility, with the asymptotic conditions for conservation of its flux. At the teleparallel equivalent of general relativity (TEGR) the excitation reduces to the teleparallel superpotential and the covariant coframe–connection pair gives the Schwarzschild ADM energy; flat cosmology and transverse-traceless waves give further checks. Away from TEGR, an exact solution of New General Relativity gives a charge whose fractional difference from the Kepler mass is half the deviation of the post-Newtonian spatial-curvature parameter from unity, at the adopted normalisation; independent Hamiltonian charge matching remains open. Finally, the integrable Hamiltonian charge is invariant under covariant Lagrangian boundary terms at fixed reference normalisation and presymplectic representative.

We consider whether the translation Noether current of a linearised metric spin-2 theory admits a strictly gauge-invariant local representative. For Fierz-Pauli and dynamically regular pure curvature-squared theories in four dimensions, we show that no such representative exists under the stated locality, polynomiality and covariance assumptions. A direct enumeration first excludes nonzero symmetric rank-two tensors at the dimension and derivative order of the quadratic action: in the curvature-squared case, the parity-even conservation kernel consists of the identically vanishing Lanczos–Lovelock combination, while both parity-odd coefficients vanish. Homogeneity of the actions in total derivative number then allows projection by field degree and derivative number, extending the exclusion to all finite-order local polynomial representatives with constant coefficients and no explicit coordinate dependence. The translation current nevertheless defines a nonzero conserved-current class. Independently, a constant translation is a Killing reducibility parameter of the linearised gauge symmetry and determines a nonzero linear surface-charge class, which is distinct from the quadratic energy current. A separate calculation shows why a direct compensator cancellation available in Maxwell theory fails for the metric spin-2 field, although this calculation is not needed for the current-class result. Maxwell theory, propagating free $p$-forms and Yang–Mills theory linearised about the trivial vacuum provide comparisons in which translations are not reducibility parameters and strictly gauge-invariant stress tensors exist. Gauss–Bonnet and pure flat-space $R^2$ gravity lie outside the regular scope of the result, through variational triviality and dynamical degeneracy, respectively.

Simulations of the evolution of matter on static metric backgrounds allow us to estimate backreaction effects like dynamical friction at first order in the matter density. Previous simulations of dynamical friction have used boosted isotropic and quasi-isotropic Kerr coordinates, which simplifies the extraction of the relevant diagnostics but results in a more complicated implementation of the evolution. In particular, the lack of horizon penetrating coordinates means that high resolutions are needed to ensure convergence, and the boosted, spinning black hole metric cannot easily be written in a closed form, making it more costly to evaluate. In this paper we describe how to reformulate the calculation of the diagnostics in the boosted Kerr-Schild frame for the non-spinning case. We verify that our implementation reproduces previous results quantifying dynamical friction in wave-like dark matter in the appropriate regimes. We discuss the subtleties of transforming diagnostic observables between frames in a 3+1 evolution and develop a general framework for this process.

We complement and extend our recent study of the non-linear evolution of the Gregory-Laflamme instability of black strings in Einstein-Gauss-Bonnet gravity in five spacetime dimensions. First, we study time-dependent perturbations of uniform black strings in Einstein-Gauss-Bonnet theory and determine the growth rates as a function of the coupling. We find that for positive Gauss-Bonnet couplings, the black strings are more unstable than in general relativity in the sense that the growth rates are larger and shorter wavelengths are unstable. In the second part of the paper we show that the hyperbolicity of the equation of motion of Einstein-Gauss-Bonnet theory is determined by an effective metric when the dynamics is restricted to spherical symmetry in the asymptotically flat directions. When the effective field theory becomes strongly coupled, as it happens near the endpoint of the Gregory-Laflamme instability of the black string, this effective metric becomes degenerate and the Cauchy evolution breaks down. Applying this criterion to uniform black strings, we find that for any positive Gauss-Bonnet coupling there is an open set of regular solutions (including the one of minimal thickness) on which the effective metric degenerates in a neighbourhood of the horizon. Therefore, we argue that these solutions cannot be attained from weakly coupled initial data by Cauchy evolution and the solutions of the linearized equations around them cannot be interpreted as approximations to nearby non-linear evolutions. We provide further evidence for this picture with non-linear simulations of the Gregory-Laflamme instability. The non-linear simulations terminate through a loss of hyperbolicity of the Tricomi or Keldysh type, depending on the sign of the Gauss-Bonnet coupling.

The $SU(2)$ Skyrme model admits exact solutions when coupled to General Relativity in four spacetime dimensions. Here, we demonstrate that relevant gravitational configurations, such as black holes, wormholes, and cosmologies, are robust under the extension to $SU(N)$ with an arbitrary number of flavors. We show that key physical features, such as the thermodynamic properties, the baryon number of the configurations, and the geometry, are crucially determined by the number of flavors as well as the coupling constants of the theory. In particular: first, we prove that an increase in the matter content favors the local thermal stability of spherically symmetric black holes. Second, for cosmological solutions, we demonstrate analytically that as the hadronic matter content increases, the scale factor grows more slowly due to enhanced gravitational attraction, while the expansion rate (measured by the Hubble parameter) increases as a consequence of the higher energy density. Third, we find that the throat of traversable wormhole solutions can be enlarged by increasing the number of flavors, since the energy density required to keep the throat open does not grow indefinitely but rather saturates at a finite value.

This paper argues for the historical utility of general relativity textbooks written during, or shortly before, the Renaissance of general relativity. More so than research papers, textbooks offer a narrative account of the field–one that may differ substantially from the accounts of other authors addressing the same subject. Textbooks on general relativity therefore constitute a distinctive form of testimony to the intellectual forces that shaped general relativity, particularly during its reinvention period from 1955 to the mid-1970s. A second pillar of this argument is the observation that nearly all principal investigators at the research centers previously identified by Lalli et al.–centers that functioned as intellectual epicenters of the Renaissance of general relativity–eventually produced a textbook associated with their own school of thought. To situate this observation within the broader development of the field, the paper presents a concise history of general relativity textbooks from the theory's inception in 1915-16 to the 1980s. This history illustrates one way in which textbooks can serve as sources for reconstructing the intellectual dynamics of the Renaissance of general relativity.

We investigate holographic Krylov complexity in bottom-up holographic QCD models describing the confined phase, using the recently proposed correspondence between the growth rate of Krylov complexity and the proper radial momentum of probes, such as particles and strings, falling in the bulk spacetime. As representative confining backgrounds, we consider two horizonless geometries, namely the dilaton-deformed AdS-soliton and the deformed thermal-AdS spacetime, both arising as solutions of an Einstein-dilaton gravity system. We find that the Krylov complexity associated with a massive particle exhibits qualitatively distinct behavior in these two backgrounds when analyzed in the Einstein frame. In the deformed AdS-soliton geometry, the complexity undergoes periodic oscillations, with both the oscillation period and amplitude depending on the parameters of the model. In contrast, in the deformed thermal-AdS geometry, the complexity grows exponentially at late times and does not display oscillatory behavior. We then investigate string dynamics in the string frame and find that the Krylov complexity exhibits oscillatory behavior in both confining backgrounds. This behavior is traced to the emergence of an additional turning point in the deep infrared of the string-frame geometry. Motivated by this observation, we further analyze massive-particle dynamics in the string frame, where we find qualitatively similar behavior in the two confining backgrounds. Our results demonstrate that the Krylov complexity of confined holographic systems depends sensitively on the choice of probe and frame, while also revealing a closer correspondence between the two confining geometries in the string-frame description.

Understanding the gravitational interaction is one of the great scientific endeavors of the 21st century. The Nobel Prize-winning discovery of gravitational waves in 2015, and subsequent detections by the LIGO-Virgo-KAGRA Collaboration, have marked a revolutionary step forward in physics and astrophysics by opening an entirely new window for exploring the Universe. Future upgrades to these detectors, along with upcoming facilities such as LISA, the Einstein Telescope, and radio and optical instruments, promise other breakthrough discoveries that the next generation of scientists will need to interpret. The School on Gravity (22–26 June 2026, Copenhagen) aimed to introduce junior scientists–graduate students and advanced undergraduates with a background in general relativity–to a wide range of foundational topics in the exciting new field of gravitational-wave physics. Topics spanned from the theory of motion, to new challenges introduced by quantum physics, to the astrophysics of black holes and source modeling for gravitational-wave detectors. The School on Gravity took place at the legendary Auditorium A of the Niels Bohr Institute, inviting students and lecturers to challenge current paradigms in gravitational physics in the spirit of the quantum revolution that unfolded in this very room. These lecture notes aim at opening up those new ideas presented in Auditorium A to the rest of the scientific community.

On the Riemannian Schwarzschild–Tangherlini metric of dimension $n\geq 4$, we show that the destabilizing TT tensor of Ozuch lies in the image of the “TT-tensor machine”. By continuity, it can then be approximated, in suitable weighted Sobolev spaces, by smooth compactly supported TT tensors, on which the stability quadratic form is still negative. This proves instability in the usual sense for noncompact manifolds. To our knowledge, no exact smooth compactly supported destabilizing TT tensor was known before, even in 4D.

We describe a family of two-dimensional metric deformations that preserve integrability. The seeds are (classically) conformal integrable field theories and the deformations are directly related to different classes of auxiliary field sigma models. We introduce a master action connecting deformations by Lie-algebra-valued auxiliary fields, the so-called $\nu$-frame, to deformations by two Lorentz-charged scalars. These auxiliary scalar fields can be identified as Beltrami differentials of an auxiliary two-dimensional metric, providing a direct connection with the metric approach to $T\bar{T}$-like deformations. For Weyl-invariant seed matter theories, the auxiliary metric sector is described by a reduced gravitational potential. We show that the resulting framework preserves classical Lax integrability whenever the seed matter theory admits a Lax representation of its equations of motion on a generic curved two-dimensional spacetime. Finally, within the Lorentz-invariant family and the zweibein deformations of conformal matter theories considered here, we identify $T\bar{T}$ as the only deformation that can be interpreted as a field-dependent coordinate transformation.

We present GRHD simulations of Bondi-Hoyle-Lyttleton accretion onto a rotating black hole in Weyl conformal gravity, described by the Kerr-Weyl metric. The equatorial flow is evolved for spins a=0.9M and a=0.5M and several Weyl coefficients, which enter through an effective curvature parameter k, and is compared with Kerr runs sharing the same setup. For the k considered, the horizon, ISCO and test-particle frequencies differ from Kerr by at most ~2%. However, the curvature term grows as kr^2 and acts at the accretion radius R_acc. The flow is controlled by one quantity, eta=|k|R_acc^3/M, the ratio of curvature-induced to Newtonian acceleration at R_acc. For eta<~0.03 a stable shock cone forms, indistinguishable from Kerr. For eta~0.2-0.3 the anti-de Sitter-like term traps shocked gas behind the black hole and drives persistent flip-flop oscillations. For eta>~1.6 the cone is destroyed and an oscillating torus forms. Spin modifies only the inner few gravitational radii and does not change the regime. In strongly deviating models the mean accretion rate is 1.7-3 times the Kerr value and varies by 20-60% rms, versus 0.1-1% in Kerr-like flows. The power spectra show global QPOs with fundamentals at 2.9-4.8 Hz for a 10 Msun black hole, with harmonic ladders whose 3:2 and 2:1 ratios come from one non-sinusoidal oscillation, not resonances. These lie in the low-frequency QPO band and are unrelated to test-particle frequencies (~70-200 Hz). They scale as f_0=xi f_K(R_acc), with xi~0.7-1.1 for stable cones and xi~0.23-0.38 for flip-flop and torus regimes. Strong oscillations would be detectable within seconds for a bright Galactic source. The required |k| exceeds galactic-rotation-curve values by 18-36 orders of magnitude, so a detected shock-driven QPO would measure a local deviation from Kerr, and its absence would constrain |k|.

We show how the covariant phase space Hamiltonian can be constructed in theories in which some of the fields have gauge freedoms. The addition to the action of boundary terms that guarantee the well-posedness of a variational principle and its exact gauge invariance for the prescribed boundary conditions turn out to be essential in this construction. The same ingredients are essential in the use of the action in the framework of Gibbons and Hawking's Euclidean approach to Quantum Gravity and we show how the on-shell action constructed with a Lagrangian with those properties can be expressed in terms of the covariant phase space Hamiltonian. We compute the Hamiltonian of several theories, one of which has Chern–Simons terms, using our prescription and show that, in black-hole backgrounds, the Hamiltonian gives directly the quantum statistical relation including terms related to non-gravitational charges and chemical potentials, as expected.

We discuss General Relativity and some of its modifications as effective field theories of the breaking of the affine general linear group using the coset approach and the Maurer-Cartan form. While the ultimate goal is to break the symmetry down to the Lorentz subgroup, we argue that there are three interesting breaking cascades in which the affine general linear group is first broken to a larger subgroup that contains the Lorentz group. In all cases, the breaking of translations always generates Goldstone modes that can be interpreted as metric degrees of freedom. We argue that the effective field theories that emerge as a result of the different breaking patterns are all dynamically equivalent at the lowest order of the derivative expansion, e.g., using Einstein-Hilbert-like actions, but can differ beyond the leading order.

Holographic complexity is expected to capture the linear growth of black hole interiors, with quantum corrections ultimately leading to a late-time saturation. We develop a spectral formulation of holographic complexity measures associated with codimension-zero bulk regions in the framework of the complexity=anything proposal. The corresponding generating function of complexity is governed by three-point correlation functions of the density of states, establishing a direct connection between bulk geometric observables and nonperturbative Euclidean spacetime wormholes. We find that the codimension-zero holographic complexity reduces to the sum of two codimension-one contributions and exhibits a universal time evolution, characterized by an exponentially long regime of linear growth followed by saturation at the Heisenberg time. The late-time plateau is a direct result of the spectral level repulsion, a generic feature of quantum chaotic systems, thereby providing a universal mechanism for the saturation of holographic complexity. We also develop a complementary operator interpretation, in which Euclidean wormhole corrections render the semiclassical basis of fixed-complexity states overcomplete. Constructing a complete orthonormal basis then yields well-defined holographic complexity operators that reproduce the same universal time evolution. Our results establish a unified connection among black hole interiors, chaotic spectral statistics, and Euclidean wormholes in quantum gravity.

Lagrangian Neural Networks (LNNs) learn dynamics from trajectory data by parameterizing a scalar Lagrangian and deriving accelerations through the Euler–Lagrange equation, providing a variational inductive bias that improves physical consistency over purely data-driven models. LNNs have recently been extended to general relativistic settings, leaving Schwarzschild geodesics as an open challenge. Training on complex relativistic systems is hindered by the diversity of the dynamics, as well as numerical instabilities and the difficulty of adequately sampling physically relevant, diverse orbital regimes. We introduce two coordinated improvements: a decoupled position–velocity normalization scheme that independently rescales each coordinate and its time derivatives, reweighting acceleration targets to balance contributions across all channels; and an energy-constrained log-uniformly sampled dataset generation strategy informed by the innermost stable circular orbit (ISCO) structure. With these improvements, our model accurately reproduces perihelion precession and relativistic time dilation, conserves energy and angular momentum to within a few percent even after completing multiple orbits around the central mass and predicts orbital trajectories across eight orbital scenarios in close, medium, and far-field regimes. These results establish that LNNs, augmented with physically motivated normalization and sampling, can reliably learn geodesic dynamics in curved spacetime. Our work also represents the first successful training of LNNs on Schwarzschild geodesics and offers a promising direction for data-driven modeling of complex relativistic systems.

We present what are, to our knowledge, the first 3D numerical-relativity evolutions of wormhole binaries: pairs of massive Ellis-Bronnikov drainholes held open by a ghost scalar field. Each throat is an unstable fixed point whose e-fold time matches the González-Guzmán-Sarbach linear rate to within 1.9%. Two throats obey a charge-sign rule: like scalar charges repel and opposite charges attract, with a measured attraction-to-repulsion ratio of $1.462\pm0.022$ against the predicted 3/2, so only opposite-signed pairs merge. A head-on collision forms a common MOTS around both still-open throats, born with about their combined area. The horizon then loses 28% of its area as it swallows the phantom field, and by $t=100$ lies within 1.4% of the Schwarzschild radius of the pair's mass, still shrinking. Fly-by pairs form no horizon and both mouths inflate, the one nearest capture radiating the most gravitational-wave energy measured. A lone collapsing throat sheds its seeded quadrupole as a burst ringing at the Schwarzschild frequency of the black hole it becomes, and every encounter radiates its own burst of gravitational waves and a scalar dipole of comparable energy and negative sign. A throat survives at most a few orbital periods for any plausible perturbation, and the negative-energy dipole would pump rather than drain the orbit, so these binaries have no inspiral.

The Boltzmann flux reflectivity used in quantum-horizon models does not by itself define a causal black-hole boundary response. We study two related questions for stationary Schwarzschild scattering. First, a classical Hardy-space condition excludes an exact Boltzmann modulus on the entire positive frequency axis for any nonzero bounded causal reflection amplitude at a fixed matching plane. We construct causal completions that preserve the modulus on any prescribed finite band. Second, we prove a low-frequency outer-phase expansion for a class of completions with fixed profiles and a common Boltzmann slope, including an exact-band completion and a smooth crossover completion. The logarithmic coefficient is common to this class, while the linear constant is an explicit functional of the completion. When the fixed proper-frame cutoff is redshifted to the matching surface and the local temperature is the Tolman redshift of the Hawking temperature, the outer phase cancels the leading logarithmic dependence of the propagation phase on the matching distance. The geometric remainder is quadratic in the proper distance, while a separate dispersive remainder depends on the completion. This is a low-energy comparison of specified response families, not an exact matching invariance or a phase fixed by causality alone. In an axial Schwarzschild example at a fixed matching plane, accounting for the predicted linear-delay difference reduces the maximum relative cavity-factor difference between two cutoffs from about $21\%$ to $0.11\%$ on the sampled frequency band. A passive quantum completion supplies the associated absorption-noise relation and checks the consistency of the asymptotic output.

Geometric Inflation adds an infinite tower of curvature invariants to the Einstein-Hilbert action while preserving certain key features such as leading to second order modified Friedmann equations for FRW backgrounds. Sourcing them with a perfect barotropic fluid can easily produce a slow-roll inflationary regime, no inflaton field is required. In this work, we perform the Wheeler-DeWitt quantization of minisuperspace Geometric Inflation models. First, we construct an effective 1D FRW action and perform the Hamiltonian formulation using both Ostrogradsky's approach and Dirac's algorithm for constrained systems. The Lagrangian and Hamiltonian treatment of the perfect fluid is based on Schutz's formalism. Second, we postulate the Wheeler-DeWitt equation and investigate its solutions both analytically and numerically. For radiation we are led to a system of fractional differential equations for which we use Caputo fractional derivative operator. We construct wave packets in momentum space, with the fluid's variable acting as external time parameter.

We calculate the spectrum of gravitational waves generated by a cosmological magnetic field with a narrow-band power spectrum. For a spectrum narrowly peaked at a comoving wavenumber $k_c$, we find that the gravitational wave signal peaks at $2k_c$ and has a sharp cutoff at this scale. We apply this result to an ultralight dark matter model of magnetogenesis operating around recombination, in which an axion-photon coupling generates a helical magnetic field by parametric resonance. We determine the conditions for the resulting gravitational waves to enter the frequency range of pulsar timing experiments. Although the required frequency can be reached for sufficiently large coupling, the corresponding amplitude is below the experimental sensitivity for physically allowed energy densities of the magnetic field. We generalize this conclusion to models of magnetogenesis operating at other epochs, estimating as $T \simeq 160 \mathrm{MeV}$ the temperature of a magnetogenesis process assumed to be the source of the stochastic gravitational wave background suggested by pulsar timing arrays. We place the lower bound $T \gtrsim 1$-$10 \mathrm{MeV}$ on such viable models.

We study the reheating epoch and total bounce-to-present expansion in modified loop quantum cosmology using current observational determinations of the scalar amplitude and spectral index. We consider the power-law plateau potential, whose normalization is determined independently from the observed values of the scalar amplitude and spectral index. We find that, for the kinetic-energy-dominated initial conditions, the quantum-bounce regime is remarkably insensitive to this normalization, while the subsequent inflationary and reheating evolution shows a more appreciable dependence. We then investigate the sensitivity of the results to the inflationary potential by considering the Starobinsky and polynomial chaotic potentials. The reheating e-fold number and reheating temperature are found to depend strongly on both the form of the potential and, in the polynomial case, the branch selected. In contrast, the total bounce-to-present expansion satisfies the conservative bound N > 129 over the ranges considered here and remains close to the characteristic scale found in LQC. Moreover, the difference between mLQC-I and LQC is remarkably stable for all three potentials. These results suggest that reheating is strongly model dependent, whereas the small systematic shift in the total expansion is primarily associated with the different background quantum geometries of LQC and mLQC-I.

Universal horizons trap even arbitrarily fast signals, providing a test of black-hole thermodynamics in theories with a preferred time direction. In Einstein–aether theory, this direction is defined by a dynamical field, the aether, that can remain non-aligned relative to stationary time at infinity. In particular, for asymptotically anti-de Sitter black holes, it was so far impossible to recover a first law of black-hole mechanics when such asymptotic tilt of the aether is present. Here, we resolve this issue for an exact family of static, spherically symmetric solutions. Using the covariant phase-space formalism, we identify the asymptotic tilt and the decaying part of the aether field as a boundary source and its conjugate response. Allowing both to vary independently obstructs the definition of an energy that generates time translations. Fixing either quantity, or imposing a relation between them, restores such an energy, while externally varying the boundary data introduces work into the first law. The energies obtained by fixing the source or its response are related by a Legendre transformation. At the universal horizon, heat includes both the metric area contribution and an irreducible aether energy flux. The resulting balance separates work at infinity from horizon heat and explains why the physical temperature cannot generally be inferred from the coefficient of an area variation in the black-hole mass.

The OSV conjecture relates the helicity supertrace of black holes in $4d$ $\mathcal{N}=2$ supergravity obtained through a Calabi–Yau compactification of Type IIA string theory to the modulus squared of the topological string partition function evaluated at the attractor point in moduli space for a given set of magnetic black hole charges and electric chemical potentials. We find Euclidean black hole saddles that compute this index to all orders in the 4d supergravity derivative expansion and calculate their action using equivariant localization. The gravitational on-shell action localizes entirely to the north and south poles of each black hole, with the two contributions determined by the holomorphic and anti-holomorphic topological string free energies, respectively, evaluated at the attractor values of the moduli. For single-center black hole saddles, this provides a proof of the OSV conjecture to all orders in the topological string coupling. The same localization formula also applies to all saddles that contribute to the helicity supertrace, such as multi-center black holes, which leads to a non-perturbative refinement of the conjecture.

We report the first Monte Carlo simulation of quantum field theory on Euclidean de Sitter space, $S^4$. Rather than discretizing space, we use a spectral lattice based on spherical harmonics, keeping all symmetries exact at finite cutoff. For a massless $\lambda\phi^4$ theory, the zero-mode distribution reproduces the Starobinsky-Yokoyama equilibrium at weak coupling, and deviations closely follow the one-loop renormalization of $\lambda$. At strong bare coupling, the renormalized quartic coupling saturates near the ceiling of the one-loop renormalization-group flow. This saturation is the de Sitter counterpart of the triviality mechanism that bounds the Higgs mass in flat space. Our results confirm nonperturbatively that the infrared divergences of light scalars in de Sitter are correctly resummed by the stochastic formalism. More broadly, this work opens up de Sitter space to lattice Monte Carlo methods.

We investigate the dynamics of charged test particles around a Letelier black hole, i.e. a black hole surrounded by a cloud of strings (CoS), in Kalb-Ramond (KR) gravity, immersed in an external, asymptotically uniform magnetic field aligned with the symmetry axis. The geometry depends on the CoS parameter and on the Lorentz-violating KR parameter only through a single combination of the two, so that the two effects can compensate each other and the Schwarzschild metric is recovered when both parameters are equal. Because the spacetime is not Ricci flat, the Wald potential is not a solution of the Maxwell equations; we show that the regular source-free magnetic test field is given in closed form by a Gauss hypergeometric function of the radial coordinate, which reduces to the Wald solution in the Schwarzschild limit. Using this exact field we derive the equations of motion, the effective potential, the circular orbits, the innermost stable circular orbit (ISCO), representative escaping, captured and curled trajectories, and the orbital, radial and vertical epicyclic frequencies in closed form; all frequency expressions are cross-checked against direct numerical integration of the full equations of motion. Within the relativistic precession model, we perform a Markov chain Monte Carlo (MCMC) analysis of the twin-peak high-frequency quasi-periodic oscillations (QPOs) of GRO J1655-40, XTE J1550-564 and GRS 1915+105 for four nested models, complemented by nested sampling to compute Bayesian evidences and to weight the two (Larmor and anti-Larmor) magnetic modes of the posterior. The Schwarzschild model is excluded for GRO J1655-40 and XTE J1550-564, with a difference in the Akaike information criterion of about 110.

Testing the horizon properties of astrophysical black holes is a central goal of gravitational-wave astronomy. The recently identified Direct Wave (DW), a prompt non-quasinormal component of GW250114, provides a new probe of near-horizon physics. While it remains unclear whether the DW itself carries horizon information, we show that it enables a novel null test of horizon reflectivity. If the remnant is an exotic compact object (ECO) with a partially reflecting surface, inward plunge radiation is reflected and leaks back through the gravitational potential barrier, producing a delayed DW echo whose amplitude is set by the surface reflectivity ($|\mathcal{R}_s|$). We construct the corresponding echo template, normalized by the observed DW, and search for it in quasinormal-mode-filtered data. We find no evidence for an echo ($\ln\mathcal{B}=-2.9$) and obtain the 90% credible bound $|\mathcal{R}_s|<0.06$, corresponding to a reflected energy fraction below $0.4\%$, for surfaces from $0.1\, M_f$ to a Planck length from the would-be horizon. Our method thus turns the prompt ringdown signal into a direct test of horizon reflectivity.

Gravitational waves from vacuum first-order phase transitions probe the nonlinear dynamics of relativistic bubble collisions. Predicting their spectrum requires resolving Lorentz-contracted scalar bubble walls throughout a volume containing many bubbles, making the large-boost regime prohibitively expensive for direct lattice simulations. We develop a simulation-based pairwise surrogate that separates the microscopic collision dynamics from the geometry of the multi-bubble transition. This utilizes symmetry-reduced $(1+1)$-dimensional scalar-field simulations to build a library of two-bubble gravitational-wave spectra, including the nonlinear post-collision evolution. These spectra are combined with geometric weights that account for screening by other bubbles. We test the two-bubble spectra and the reconstructed spectra of three- and many-bubble systems against full $(3+1)$-dimensional lattice simulations. Not only can the surrogate be orders of magnitude cheaper computationally, but it also provides access to highly relativistic collisions beyond the practical reach of direct many-bubble simulations. This provides a route to studying how the spectral amplitude and shape depend on the collision boost and scalar potential.

We construct higher-dimensional swirling spacetimes in vacuum General Relativity using the hidden symmetries of the dimensionally reduced theory. Working directly with the coset-space formulation, we perform in five dimensions a reduction along the two independent axial Killing vectors, obtaining an $SL(3,\mathbb{R})/SO(3)$ sigma model and a genuinely five-dimensional background with two independent swirling parameters. The same transformation yields doubly swirling Schwarzschild–Tangherlini and Myers–Perry geometries. A distinctive feature of the new background is its multidirectional asymptotic structure. Correlated radial-angular limits reveal directional curvature singularities that are invisible in the usual large-radius limit at fixed angle. We further exhibit causal geodesics that reach such singular asymptotic ends in finite affine parameter. Finally, we describe the maximally axial extension of this construction to higher dimensions: five dimensions are maximal for an entirely axial reduction to three dimensions, while six dimensions admit an additional nontrivial translational deformation, with further dimensions contributing only flat spectator directions.

In this paper, we study the nature of wave packets and their decay behavior in the $\kappa$-Minkowski space. We employ techniques from singularity theory throughout our analysis. Specifically, we use methods from the theory of Lagrangian singularities and caustics to study the topology of the energy-level manifold. The Newton polyhedron method from the theory of oscillatory integrals is applied to analyze the decay behavior of wave packets. We find that for a generic Hamiltonian in the $\kappa$-Minkowski space, the associated wave packets exhibit different decay rates depending on the control parameter of the system. When the control parameter takes values on the cusp, the system exhibits decay of order $t^{-1/4}$; otherwise, it exhibits decay of order $t^{-1/2}$. This distinctive behavior of wave packets in the $\kappa$-Minkowski makes it fundamentally different from commutative spacetime.

We demonstrate how horizon symmetries of AdS black holes are realised in the hydrodynamic actions for the dynamics of the dual stress tensor. A recent approach for obtaining such actions involves a choice of horizon boundary conditions, and we show that diffeomorphisms that preserve these give rise to symmetries of the corresponding hydrodynamic action. We obtain explicit hydrodynamic actions for small amplitude perturbations of black holes in JT and AdS$_3$ gravity using this approach and demonstrate explicitly the existence of these symmetries. For a natural choice of boundary conditions, the resulting actions manifestly realise gauge symmetries previously proposed for effective theories of maximal chaos.

Non-Abelian gauge theories above four dimensions may admit an interacting ultraviolet fixed point through the competition between canonical scaling and gauge-field antiscreening. Using the four-loop $\overline{\mathrm{MS}}$ beta function continued to $D=4+2\epsilon$, we determine the largest dimension $D_{\mathrm{pt}}=4+2\epsilon_{\mathrm{pt}}$ below which successive loop corrections to the fixed point remain hierarchically ordered under a specified ratio criterion, and map $D_{\mathrm{pt}}$ over color and flavor numbers for fermions in the fundamental representation of $SU(N)$. At $D=5$, we construct rational anomalous dimensions with a fixed, pole-regularized denominator inspired by the functional renormalization group (fRG). Matching to the $\overline{\mathrm{MS}}$ series through one, two, and three loops produces progressively smaller shifts in the critical flavor number and coupling at the ultraviolet–infrared merger (the point where the infrared and ultraviolet fixed points coincide), yielding $N_f^{\mathrm{cr}}\simeq 2.09 \, N$ at large $N$ in the three-loop construction. This low-order stabilization, together with qualitative evidence from fRG flows including higher gauge operators, suggests a potential merger scenario that bounds the candidate asymptotically safe region in flavor number. The resulting color–flavor map provides guidance for five-dimensional model building by displaying both the baseline perturbative-control boundary and the candidate three-loop merger boundary. Four-loop matching, however, retains an interacting ultraviolet fixed point beyond the three-loop merger boundary, with no merger found for integer $2\le N\le15$ and $0\le N_f/N\le11/2$. The sensitivity of the fixed-point structure to higher-order terms leaves both scenarios open, highlighting fixed-point annihilation as a potential constraint on five-dimensional asymptotic safety.