Related papers: Mathematical General Relativity
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…
Contents: 1) Introduction and a few excursions [A word on the role of explicit solutions in other parts of physics and astrophysics. Einstein's field equations. "Just so" notes on the simplest solutions: The Minkowski, de Sitter and anti-de…
For asymptotically flat spacetimes the Penrose inequality gives an initial data test for the weak cosmic censorship hypothesis. We give a formulation of this inequality for asymptotically anti-deSitter (AAdS) spacetimes, and show that the…
We investigate extremal electrically charged black holes in Einstein-Maxwell-dilaton theory with a cosmological constant inspired by string theory. These solutions are not static, and a timelike singularity eventually appears which is not…
The existence of spacetime singularities is one of the biggest problems of nowadays physics. According to Penrose, each physical singularity should be covered by a "cosmic censor" which prevents any external observer from perceiving their…
The averaging problem in cosmology and the approach of macroscopic gravity to resolve the problem is discussed. The averaged Einstein equations of macroscopic gravity are modified on cosmological scales by the macroscopic gravitational…
While many observations support the validity of Einstein's general relativity as the theory of gravity, there are yet many that suggest the presence of new physics. In order to explain the high-redshift supernovae Ia observations together…
In this article, we test the validity of the weak cosmic censorship conjecture (wCCC) in the background of a quantum Kerr-de Sitter (qKdS) black hole, incorporating exact backreaction from quantum matter fields. Using a test particle…
We formulate spacetime inequalities applicable to quantum-corrected black holes to all orders of backreaction in semiclassical gravity. Namely, we propose refined versions of the quantum Penrose and reverse isoperimetric inequalities, valid…
We find a simple modification of the longitudinal mode in General Relativity which incorporates the idea of limiting curvature. In this case the singularities in contracting Friedmann and Kasner universes are avoided, and instead, the…
Possibilities emerging out of the dynamical evolutions of collapsing systems are addressed in this thesis through analytical investigations of the highly non-linear Einstein Field Equations. Studies of exact solutions and their properties,…
Considerable attention has recently focused on gravity theories obtained by extending general relativity with additional scalar, vector, or tensor degrees of freedom. In this paper, we show that the black-hole solutions of these theories…
Possibility of gravitational repulsion in General Relativity is discussed and astronomical data in favor of cosmological acceleration are described. The problem of vacuum energy is emphasized and possible ways of its solution are indicated.…
We examine the $C^{0}$-formulation of the strong cosmic censorship conjecture (SCC) from a quantum complexity-theoretic perspective and argue that for generic black hole parameters as initial conditions for the Einstein equations,…
In this paper it is argued that even invoking the dominant energy condition, the Einstein's field equations admit nonglobally hyperbolic, asymptotically de Sitter spacetimes with locally naked singularities and with Cauchy horizons failing…
The essential singularity in Einstein's gravity can be avoidable if the preconditions of Penrose's theorem can be bypassed, i.e., if the strong energy condition is broken in the vicinity of a black hole center. The singularity mentioned…
General relativity has two fundamental problems that render it unsuitable for tackling the gravitational field's quantization. The first problem is the lack of a genuine gravitational variable representing gravitation only, inertial forces…
A fundamental problem of Einstein's theory of classical general relativity is the existence of singularities such as the big bang. All known laws of physics end at these boundaries of classical space-time. Thanks to recent developments in…
The issues related to bringing together the principles of general relativity and quantum theory are discussed. After briefly summarising the points of conflict between the two formalisms I focus on four specific themes in which some contact…
As we now know, there are indeed at least two major difficulties with General Relativity (GR). The first one is related with its incompatibility with quantum mechanics, in the absence of a widely accepted consistent theory that combines the…