Related papers: On General Solutions of Einstein Equations
We construct two classes of exact solutions to six and higher dimensional Einstein-Maxwell theory in which the metric functions can be written as convolution-like integrals of two special functions. The solutions are regular everywhere and…
Towards the investigation of the full dynamics in higher-dimensional and/or stringy gravitational model, we present the basic equations of the Einstein-Gauss-Bonnet gravity theory. We show $(N+1)$-dimensional version of the ADM…
A general covariant extension of Einstein's field equations is considered with a view to Numerical Relativity applications. The basic variables are taken to be the metric tensor and an additional four-vector. The extended field equations,…
We present a new class of solutions in odd dimensions to Einstein's equations containing either a positive or negative cosmological constant. These solutions resemble the even-dimensional Eguchi-Hanson--(anti)-de Sitter ((A)dS) metrics,…
We present solution generating methods which allow to construct exact static solutions to the equations of four-dimensional Einstein-Maxwell-Dilaton gravity starting with arbitrary static solutions to the pure vacuum Einstein equations,…
A general formula for the metric as an explicit function of the generic energy-momentum tensor is given which satisfies static plane symmetric Einstein's equations with cosmological constant.In order to illustrate it, the solutions for the…
In this paper we study regular cosmic string solutions of the non-Abelian Higgs model coupled with the Einstein gravity. In order to do that, we constructed a set of coupled differential ordinary equation. Because there is no closed…
The field equations of general relativity can be derived from the Einstein action, which is quadratic in connection coefficients, rather than the standard action involving the Gibbons-Hawking-York term and counterterm. We show that it is…
The generalized harmonic representation of Einstein's equation is manifestly hyperbolic for a large class of gauge conditions. Unfortunately most of the useful gauges developed over the past several decades by the numerical relativity…
We obtain the static spherically symmetric solutions of a class of gravitational models whose additions to the General Relativity (GR) action forbid Ricci-flat, in particular, Schwarzschild geometries. These theories are selected to…
The curvature-squared model of gravity, in the affine form proposed by Weyl and Yang, is deduced from a topological action in 4D. More specifically, we start from the Pontrjagin (or Euler) invariant. Using the BRST antifield formalism with…
A recent proposal equates the circuit complexity of a quantum gravity state with the gravitational action of a certain patch of spacetime. Since Einstein's equations follow from varying the action, it should be possible to derive them by…
On vacuum spacetimes of general dimension, we study the linearized Einstein vacuum equations with a spatially compactly supported and (necessarily) divergence-free source. We prove that the vanishing of appropriate charges of the source,…
Near the singularity, gravity should be modified to an effective theory, in the same sense as with the Euler-Heisenberg electrodynamics. This effective gravity surmounts to higher derivative theory, and as is well known, a much more reacher…
In this work a study of the gravity is made using Einstein's equation in the post-Newtonian approach. This is a method to linearise the General Relativity indicated to treat non-relativistic objects. It enables us to construct, from…
The non-relativistic versions of the generalized Poincar\'{e} algebras and generalized $AdS$-Lorentz algebras are obtained. This non-relativistic algebras are called, generalized Galilean algebras type I and type II and denoted by…
Solutions to vacuum Einstein field equations with cosmological constant, such as the de Sitter space and the anti-de Sitter space, are basic in different cosmological and theoretical developments. It is also well known that complex…
We study the most general solution for affine connections that are compatible with the variational principle in the Palatini formalism for the Einstein-Hilbert action (with possible minimally coupled matter terms). We find that there is a…
General Relativity in 4 dimensions can be equivalently described as a dynamical theory of SO(3)-connections rather than metrics. We introduce the notion of asymptotically hyperbolic connections, and work out an analog of the…
We construct the most general, to cubic order in curvature, theory of gravity whose (most general) static spherically symmetric vacuum solutions are fully described by a single field equation. The theory possess the following remarkable…