Related papers: Junction conditions at spacetime singularities
The prediction of spacetime singularities, regions of infinite curvature where classical physics breaks down, is one of the most profound challenges in General Relativity (GR). In particular, black hole solutions such as the Schwarzschild…
The strong unique continuation property for Einstein metrics can be concluded from the well-known fact that Einstein metrics are analytic in geodesic normal coordinates. Here we give a proof of the same result that given two Einstein…
We present a systematic approach to embed $n$-dimensional vacuum general relativity in an $(n + 1)$-dimensional pseudo-Riemannian spacetime whose source is either a (non)zero cosmological constant or a scalar field minimally-coupled to…
There are several solutions of Einstein field equations that describe an inhomogeneity in an expanding universe. Among these solutions, the McVittie metric and its generalizations have been investigated through decades, though a full…
Einstein's theory of general relativity models the physical universe using spacetimes which satisfy Einstein's gravitational field equations. To date, Einstein's theory has been enormously successful in modeling observed gravitational…
This paper presents a comprehensive analysis of junction conditions for gluing different $f(R)$ gravitational theories across a non-null hypersurface. Using the variational approach, we systematically derive the junction conditions for both…
We examine various well known exact solutions available in the literature to investigate the recent criterion obtained in ref. [20] which should be fulfilled by any static and spherically symmetric solution in the state of hydrostatic…
A strongly well-posed initial boundary value problem based upon constraint-preserving boundary conditions of the Sommerfeld type has been established for the harmonic formulation of the vacuum Einstein's equations. These Sommerfeld…
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…
The intimate relations between Einstein's equation, conformal geometry, geometric asymptotics, and the idea of an isolated system in general relativity have been pointed out by Penrose many years ago. A detailed analysis of the interplay of…
In this article, we develop the formalism for singular hypersurfaces and junction conditions in generalized coupling theories using a variational approach. We then employ this formalism to examine the behavior of sharp matter density…
Singularity theorems demonstrate the inevitable breakdown of the concept of continuous, classical spacetime under highly general conditions. Quantum gravity is expected to intervene to avoid singularities and models so far hint towards…
Inflationary spacetimes have been argued to be past geodesically incomplete in many situations. However, whether the geodesic incompleteness implies the existence of an initial spacetime curvature singularity or whether the spacetime may be…
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…
We consider self-interacting scalar fields coupled to gravity. Two classes of exact solutions to Einstein's equations are obtained: the first class corresponds to the minimal coupling, the second one to the conformal coupling. One of the…
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…
We develop an extension of Bohmian mechanics by defining Bohm-like trajectories for quantum particles in a curved background space-time containing a spacelike singularity. As an example of such a metric we use the Schwarzschild metric,…
We work out the junction conditions for $f(R)$ gravity formulated in metric-affine (Palatini) spaces using a tensor distributional approach. These conditions are needed for building consistent models of gravitating bodies with an interior…
Excision techniques are used in order to deal with black holes in numerical simulations of Einstein equations and consist in removing a topological sphere containing the physical singularity from the numerical domain, applying instead…
Exact solutions of the Einstein-Maxwell equations that describe moving black holes in a cosmological setting are discussed with the aim of discovering the global structure and testing cosmic censorship. Continuation beyond the horizons…