Related papers: Uniqueness and Non-uniqueness in the Einstein Cons…
Among various strong-curvature extensions to General Relativity, Einstein-Dilaton-Gauss-Bonnet gravity stands out as the only nontrivial theory containing quadratic curvature corrections while being free from the Ostrogradsky instability to…
Entangled Relativity is a non-linear reformulation of Einstein's General Theory of Relativity (General Relativity) that offers a more parsimonious formulation. This non-linear approach notably requires the simultaneous definition of matter…
The Einstein-Lovelock theory contains an infinite series of corrections to the Einstein term with an increasing power of the curvature. It is well-known that for large black holes the lowest (Gauss-Bonnet) term is the dominant one, while…
We present the topological solutions of Einstein-dilaton gravity in the presence of a non-Abelian Yang-Mills field. In 4 dimensions, we consider the $So(3)$ and $So(2,1)$ semisimple group as the Yang-Mills gauge group, and introduce the…
In the harmonic description of general relativity, the principle part of Einstein's equations reduces to 10 curved space wave equations for the componenets of the space-time metric. We present theorems regarding the stability of several…
In Einstein's general relativity, with its nonlinear field equations, the discoveries and analyzes of various specific explicit solutions made a great impact on understanding many of the unforeseen features of the theory. Some solutions…
In this paper we review various models of curvature singularity free black holes. In the first part of the review we describe semi-classical solutions of the Einstein equations which, however, contains a "quantum" input through the matter…
The Einstein-Cartan equations in first-order action of torsion are considered. From Belinfante-Rosenfeld equation special consistence conditions are derived for the torsion parameters relating them to the metric. Inside matter the torsion…
The standard argument for the uniqueness of the Einstein field equation is based on Lovelock's Theorem, the relevant statement of which is restricted to four dimensions. I prove a theorem similar to Lovelock's, with a physically modified…
We present a new non-BPS solution describing an asymptotically flat, stationary, bi-axisymmetric capped black hole in the bosonic sector of five-dimensional minimal supergravity. This solution describes a spherical black hole, while the…
An almost Einstein manifold satisfies equations which are a slight weakening of the Einstein equations; Einstein metrics, Poincare-Einstein metrics, and compactifications of certain Ricci-flat asymptotically locally Euclidean structures are…
In this work we have obtained the set of new exact solutions of the Einstein equations that generalize the known Lemaitre-Tolman-Bondi solution for the certain case of nonzero pressure under zero spatial curvature. These solutions are…
We establish various general results concerning static and spherically symmetric black hole solutions of general higher-derivative extensions of Einstein gravity. We prove that the only theories susceptible of admitting solutions with…
We consider thorny spheres, that is 2-dimensional compact surfaces which are everywhere locally isometric to a round sphere $S^2$ except for a finite number of isolated points where they have conical singularities. We use thorny spheres to…
The Harmonic Einstein equation is the vacuum Einstein equation supplemented by a gauge fixing term which we take to be that of DeTurck. For static black holes analytically continued to Riemannian manifolds without boundary at the horizon…
We show a uniqueness theorem for charged rotating black holes in the bosonic sector of five-dimensional minimal supergravity. More precisely, under the assumptions of the existence of two commuting axial isometries and spherical topology of…
We revisit the problem of solving the Einstein constraint equations in vacuum by a new method, which allows us to prescribe four scalar quantities, representing the full dynamical degrees of freedom of the constraint system. We show that…
We prove that for every natural number k there are simply connected topological four-manifolds which have at leat k distinct smooth structures supporting Einstein metrics, and also have infinitely many distinct smooth structures not…
We study the spacetime structures of the static solutions in the $n$-dimensional Einstein-Gauss-Bonnet-$\Lambda$ system systematically. We assume the Gauss-Bonnet coefficient $\alpha$ is non-negative. The solutions have the…
We study rotating black holes in five dimensions using the nAdS$_2$/nCFT$_1$ correspondence. A consistent truncation of pure Einstein gravity (with a cosmological constant) in five dimensions to two dimensions gives a generalization of the…