Related papers: On matching LTB and Vaidya spacetimes through a nu…
We examine the fully relativistic evolution of cosmic voids constituted by baryons and cold dark matter (CDM), represented by two non-comoving dust sources in a $\Lambda$CDM background. For this purpose, we consider numerical solutions of…
In the present work, we study the general surrounded Vaidya solution by the various cosmological fields and its nature describing the possibility of the formation of naked singularities or black holes. Motivated by the fact that real…
We obtain a general spherically symmetric solution of a null dust fluid in $n (\geq 4)$-dimensions in Gauss-Bonnet gravity. This solution is a generalization of the $n$-dimensional Vaidya-(anti)de Sitter solution in general relativity. For…
In a previous work [I. Rodnianski and Y. Shlapentokh-Rothman, Naked Singularities for the Einstein Vacuum Equations: The Exterior Solution, arXiv:1912.08478] we constructed solutions to the Einstein vacuum equations in 3+1 dimensions which…
We investigate the relation between the standard Newtonian equations for a pressureless fluid (dust) and the Einstein equations in a double expansion in small scales and small metric perturbations. We find that parts of the Einstein…
We consider stationary rotating cylindrically symmetric dust spacetimes. We first show that the Maitra spacetime is the unique non-rigidly (non null shear scalar) rotating solution with a regular axis and that is the most general one of the…
In this paper the structure of the generalized Vaidya spacetime when the type-II of the matter field satisfies the equation of the state $P=\rho$ is investigated. Satisfying all energy conditions we show that this spacetime contains the…
In this paper, we evaluate kinematic self-similar perfect fluid and dust solutions for the most general cylindrically symmetric spacetime. We explore kinematic self-similar solutions of the first, second, zeroth and infinite kinds for…
We present a menagerie of solutions to the vacuum Einstein equations in six, eight and ten dimensions. These solutions describe spacetimes which are either locally asymptotically adS or locally asymptotically flat, and which have…
We reformulate the standard local equations of general relativity for asymptotically flat spacetimes in terms of two non-local quantities, the holonomy $H$ around certain closed null loops on characteristic surfaces and the light cone cut…
We study the solutions of the Einstein equations in the presence of a thick infinite slab with constant energy density. When there is an isotropy in the plane of the slab, we find an explicit exact solution that matches with the Rindler and…
We prove existence of vacuum space-times with freely prescribable cone-smooth initial data on past null infinity.
Recent theoretical results show the existence of arbitrary speeds (0 <= v < \infty) solutions of all relativistic wave equations. Some recent experiments confirm the results for sound waves. The question arises naturally: What is the…
In contrast to Einstein's theory, the first order formulation of gravity turns out to be a natural habitat for double-sheeted spacetime solutions which satisfy the vacuum field equations everywhere. These bridge-like geometries exhibit…
We construct a four-dimensional spacetime using a three-dimensional contact manifold equipped with a degenerate metric. The degenerate metric is set to be compatible with the contact structure. The compatibility condition is defined in this…
We study spherically symmetric static spacetimes generally filled with an anisotropic fluid in the nonrelativistic general covariant theory of gravity. In particular, we find that the vacuum solutions are not unique, and can be expressed in…
Using black brane solutions in 5d Lifshitz-like backgrounds with arbitrary dynamical exponent $\nu$, we construct the Vaidya geometry, asymptoting to the Lifshitz-like spacetime, which represents a thin shell infalling at the speed of…
In a recent paper Liu considered the complete Schwarzschild interior and exterior solution in harmonic coordinates. There he argued about the necessity to keep an integration constant, in contrast with previous treatments. The purpose of…
We study Einstein's equations with matter in hydrostatic equilibrium in the nonstandard gauge which was recently investigated in the vacuum case. We obtain spherically symmetric solutions for any given rotation curve. These solutions can be…
Conditions, related to the so-called bending problem are considered for hypersurfaces of a pseudo-Euclidean space. Corresponding theorems are proved.