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. less

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. less

The so-called Geometric Trinity of Gravity is based on three distinct geometric features of spacetime, i.e.\ curvature, torsion and non-metricity, which give rise to equivalent dynamics for General Relativity (GR), Teleparallel Equivalent of General Relativity (TEGR) and Symmetric Teleparallel Equivalent of General Relativity (STEGR). Pre-geometric gravity, on the other hand, offers a unifying framework from which all metric-affine theories can emerge. Starting from a gauge formulation \textit{à la} Yang--Mills with a Higgs-like field, a mechanism of spontaneous symmetry breaking can give rise to an effective metric as well as to the classical dynamics of the gravitational field. In particular, the emergence of gravity in the spontaneously broken phase is shown to be consistent with all the different formulations of the Geometric Trinity of Gravity, in terms both of actions and of gauge choices for the affine connection. This general result is achieved by deriving and analysing suitable expressions in the unbroken phase for pre-geometric actions and for pre-geometric gauge-fixing conditions respectively. less

We study the action principle for space-times whose boundary is singular. We suggest that it is natural to treat the singularity as a {\it free} boundary, where the variation is unconstrained. Demanding that the action is stationary under such free variations then implies certain (on-shell) boundary conditions at the singularity. We derive these boundary conditions for the case of Einstein gravity coupled to matter and show that, when applied to an initial spacelike singularity, they exclude Kasner-like or BKL space-times, but admit conformally regular space-times (including FLRW models) sourced by fluids satisfying $0 \leq P < ρ$. For standard hot big bang FLRW cosmologies, the admissible linear (scalar, vector, tensor) perturbations satisfy reflecting boundary conditions at the bang, in agreement with large-scale cosmological observations. less

We classify 4-dimensional gravitational theories with integrability properties analogous to quasi-topological gravity, but for metrics with the symmetries of spherical, hyperbolic, and planar Schwarzschild and Taub-NUT solutions, their double-Wick-rotated counterparts - the B-metrics, the near-horizon extreme Kerr, and the swirling universe - and the Eguchi-Hanson instanton. These are the symmetries that allow consistent reductions (principle of symmetric criticality) with 4 Killing vectors and 3-dimensional orbits. Considering theories depending only on the Riemann tensor, we show that, for these metrics, only those with third-order equations (second-order after trivial integration) can be analytic in the Riemann tensor. We show that there is a unique theory with first-order field equations (algebraic after trivial integration, with the same integrability as general relativity) at each order in curvature and construct regular static black holes from infinite towers of these high-energy corrections to general relativity. For these theories, we obtain closed-form solutions for all the symmetries listed above, which we analyze to ensure they have a clear physical interpretation. less

Near-extremal Kerr black holes support zero-damped modes (ZDMs), whose small time-domain damping rates make them long-lived probes of the near-horizon region. We show that bound extreme-mass-ratio inspirals (EMRIs) can resonantly drive this response in vacuum general relativity. Using frequency-domain Teukolsky amplitudes for eccentric-inclined Kerr geodesics, we identify a source-supported orbital harmonic whose real frequency falls within one pole half-width of the fundamental gravitational ZDM. In the complex response, the pole contribution is enhanced by this small half-width, while complex-response tomography recovers the independently computed Kerr pole from real-frequency orbital data. After subtracting the smooth non-pole component, the residual exhibits the phase winding of a coherent simple pole, with a pole contribution comparable to the smooth non-pole part of the EMRI-sourced Teukolsky amplitude. The driven branch also lies in the superradiant regime and carries negative horizon flux. These results establish a pole-resolved, resonantly driven ZDM response by EMRIs and make the recovered pole half-width a route to measuring the horizon surface gravity. less

Recently, a new family of asymptotically flat black-hole solutions endowed with primary scalar hair has been discovered in beyond-Horndeski gravity. We study in detail the quasinormal modes spectra, graybody factors, and Hawking radiation of this class of black holes. We demonstrate that presence of primary scalar hair leaves characteristic imprints on the ringdown properties, shifts the quasinormal frequencies, inducing overtone rearrangements, and rise of echoes. While the fundamental modes associated with the light-ring are affected moderately, higher overtones are highly sensitive to the small near-horizon deformation produced by scalar field. In certain parameter regimes, the graybody factors exhibit resonant-tunnelling behavior, which leads to an oscillatory frequency dependence of the Hawking emission rate. Thus, both black-hole spectroscopy and Hawking radiation may provide complementary and distinctive probes of the beyond-Horndeski gravity. Additionally, we demonstrate that the corresponding naked singularites are quantum mechanically singular and do not admit a well-defined dynamics. less

Extreme mass-ratio inspirals (EMRIs) constitute one of the most promising probes of strong field gravity for future space borne gravitational-wave observatories. As a representative higher-curvature extension of General Relativity (GR), four-dimensional Einstein-Gauss-Bonnet (4D EGB) gravity is distinguished by its strictly linear geometric coupling. By this mathematical property, the pathological Fisher-matrix singularities that typically plague conventional modified black hole models are effectively evaded, thereby providing an ideal framework to test topological deviations from classical spacetimes. Through the classification of equatorial periodic orbits via an integer taxonomy $(z,w,v)$, it is demonstrated that even modest Gauss-Bonnet couplings ($α\sim 0.1M^2$) imprint measurable geometric signatures onto the zoom-whirl architecture. Although the global conservative energy budget is shifted by a mere $\sim 0.2\%$, the short-range repulsive EGB core severely alters the strong field whirl dynamics, whereby a resolvable macroscopic dephasing of several radians per orbit is accumulated. Through semi-relativistic waveform modeling, it is revealed that this temporal compression manifests as a rigid, high-frequency stretching of the gravitational-wave harmonic comb -- a clean, amplitude-independent spectral signature ideally suited for detection by LISA, Taiji, and TianQin. A rigorous Fisher information analysis confirms that for a typical four-year observation at a signal-to-noise ratio of $ρ=20$, the marginalized error on the EGB coupling can be tightly bounded to $σ_α\sim \mathcal{O}(10^{-6}) M^2$, with virtually negligible parameter degeneracy with the orbital eccentricity. less