相关论文: Convergence of the Fefferman-Graham expansion and …

The existence of black holes in the Universe is nowadays established on the grounds of a blench of astrophysical observations, most notably those of gravitational waves from binary mergers and the imaging of supermassive objects at the…

A recently proposed model incorporating a series of higher-curvature corrections allows for analytic black-hole solutions at each order of the expansion, with a fully regular black hole emerging in the limit of infinite number of terms. An…

We report on some advances made in the problem of singularities in general relativity. First is introduced the singular semi-Riemannian geometry for metrics which can change their signature (in particular be degenerate). The standard…

We discuss a recently proposed limiting curvature theory of gravity and its application to the problem of singularities inside black holes. In this theory the growth of the curvature is suppressed by specially chosen inequality constraints…

An approach is presented to resolve key paradoxes in black hole physics through the application of complex Riemannian spacetime. We extend the Schwarzschild metric into the complex domain, employing contour integration techniques to remove…

Unless the reality of spacetime singularities is assumed, astrophysical black holes cannot be identical to their mathematical counterparts obtained as solutions of the Einstein field equations. Mechanisms for singularity regularization…

Macroscopic irreversible processes emerge from fundamental physical laws of reversible character. The source of the local irreversibility seems to be not in the laws themselves but in the initial and boundary conditions of the equations…

We revisit the non-singular black hole solution in (extended) mimetic gravity with a limiting curvature from a Hamiltonian point of view. We introduce a parameterization of the phase space which allows us to describe fully the Hamiltonian…

An important tool in the study of conformal geometry, and the AdS/CFT correspondence in physics, is the Fefferman-Graham expansion of conformally compact Einstein metrics. We show that conformally compact metrics satisfying a generalization…

The divergence of curvature invariants at a given point signals the impossibility of extending the spacetime to that point, with the derivative order of these diverging invariants determining the differentiability class of the considered…

In this paper, we study the asymptotic structure of the Fefferman-Graham ambient metric. We prove that every straight ambient metric admits a conformal completion with a well-defined null infinity, and that the asymptotic expansion of the…

Recent results show that important singularities in General Relativity can be naturally described in terms of finite and invariant canonical geometric objects. Consequently, one can write field equations which are equivalent to Einstein's…

Hawking's local rigidity theorem, proven in the smooth setting by Alexakis-Ionescu-Klainerman, says that the event horizon of any stationary non-extremal black hole is a non-degenerate Killing horizon. In this paper, we prove that the full…

We study conformally compact metrics satisfying the Lovelock equations, which generalize the Einstein equation. We show that these metrics admit polyhomogeneous expansions, thereby naturally realizing the Fefferman-Graham expansion, which…

In general, a finite metric function at the center of a black hole describes a non-singular spacetime but an infinite metric at the center gives a singular spacetime, where the former is associated with convergent Ricci and Kretschmann…

Through an illuminating thought experiment we demonstrate that the nonsingular "continued collapse" picture of a black hole is the only consistent and physical one. We provide a class exact solutions on the boundary of the space of physical…

We present a quantum description of black holes given by coherent states of gravitons sourced by a matter core. The expected behaviour in the weak-field region outside the horizon is recovered, with arbitrarily good approximation, but the…

The Event Horizon Telescope (EHT) has revealed the horizon-scale radiation of Sagittarius A* (Sgr A*), our galaxy's central supermassive black hole, offering a new platform to test gravitational theories. The next step involves studying…

Since the conformal transformations of metric do not change its causal structure, we use these transformations to embed the Lemaitre metrics into the FRW background. In our approach, conformal transformation is in agreement with the…

The set of all metrics that can be placed on a given manifold defines an infinite-dimensional `superspace' that can itself be imbued with the structure of a Riemannian manifold. Geodesic distances between points on Met$(M)$ measure how…