Related papers: Remark on non-existence of self-similar solutions …
We present a new numerical code designed to solve the Einstein field equations for axisymmetric spacetimes. The long term goal of this project is to construct a code that will be capable of studying many problems of interest in axisymmetry,…
We first present a review, intended for classical relativists, of the ultraviolet difficulties faced by local quantum gravity theories in both the usual Einstein versions and in their supergravity extensions, at least perturbatively. These…
It is shown that all contracting, spatially homogeneous, orthogonal Bianchi cosmologies that are sourced by an ultra-stiff fluid with an arbitrary and, in general, varying equation of state asymptote to the spatially flat and isotropic…
We extend previous analyses of soliton solutions in (4+1) gravity to new ranges of their defining parameters. The geometry, as studied using invariants, has the topology of wormholes found in (3+1) gravity. In the induced-matter picture,…
An immense class of physical counterexamples to the four dimensional strong cosmic censor conjecture---in its usual broad formulation---is exhibited. More precisely, out of any closed and simply connected 4-manifold an open Ricci-flat…
We show using covariant techniques that the Einstein static universe containing a perfect fluid is always neutrally stable against small inhomogeneous vector and tensor perturbations and neutrally stable against adiabatic scalar density…
A topological version of four-dimensional (Euclidean) Einstein gravity which we propose regards anti-self-dual 2-forms and an anti-self-dual part of the frame connections as fundamental fields. The theory describes the moduli spaces of…
The double copy is by now a firmly-established correspondence between amplitudes and classical solutions in biadjoint scalar, gauge and gravity theories. To date, no strongly coupled examples of the double copy in four dimensions have been…
The perturbation of an exact solution exhibits a movable transcendental essential singularity, thus proving the nonintegrability. Then, all possible exact particular solutions which may be written in closed form are isolated with the…
The perturbation of an exact solution exhibits a movable transcendental essential singularity, thus proving the nonintegrability. Then, all possible exact particular solutions which may be written in closed form are isolated with the…
One says that a Riemannian four-manifold is \emph{weakly Einstein} if the three-index contraction of its curvature tensor against itself equals a function times the metric. Since this includes all four-manifolds that are Einstein, or…
We solve the Einstein equations for the 2+1 dimensions with and without scalar fields. We calculate the entropy, Hawking temperature and the emission probabilities for these cases. We also compute the Newman-Penrose coefficients for…
We study Bianchi cosmologies in the ghost-free bigravity theory assuming both metrics to be homogeneous and anisotropic, of the Bianchi class A, which includes types I,II,VI$_0$,VII$_0$,VIII, and IX. We assume the universe to contain a…
Assuming SO(3)-spherical symmetry, the 4-dimensional Einstein equation reduces to an equation conformally related to the field equation for 2-dimensional gravity following from the Lagrangian L = R^(1/3). Solutions for 2-dimensional gravity…
We investigate the dynamics of spatially homogeneous solutions of the Einstein-Vlasov equations with Bianchi type I symmetry by using dynamical systems methods. All models are forever expanding and isotropize toward the future; toward the…
In three spacetime dimensions, general relativity drastically simplifies, becoming a ``topological'' theory with no propagating local degrees of freedom. Nevertheless, many of the difficult conceptual problems of quantizing gravity are…
We numerically investigate the dynamics near black hole formation of solutions to the Einstein--Vlasov system in axisymmetry. Our results are obtained using a particle-in-cell and finite difference code based on the $(2+1)+1$ formulation of…
In this paper, we present two new families of spatially homogeneous black hole solution for $z=4$ Ho\v{r}ava-Lifshitz Gravity equations in $(4+1)$ dimensions with general coupling constant $\lambda$ and the especial case $\lambda=1$,…
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…
Let $(M,g)$ be a compact Riemannian manifold on which a trace-free and divergence-free $\sigma \in W^{1,p}$ and a positive function $\tau \in W^{1,p}$, $p > n$, are fixed. In this paper, we study the vacuum Einstein constraint equations…