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The Einstein equations in wave map gauge are a geometric second order system for a Lorentzian metric. To study existence of solutions of this hyperbolic quasi diagonal system with initial data on a characteristic cone which are not zero in…
We review the solution space for the field equations of Einstein's General Relativity for various static, spherically symmetric spacetimes. We consider the vacuum case, represented by the Schwarzschild black hole; the de…
We have recently constructed a numerical code that evolves a spherically symmetric spacetime using a hyperbolic formulation of Einstein's equations. For the case of a Schwarzschild black hole, this code works well at early times, but…
A reformulation of the Schwarzschild solution of the linearised Einstein field equations in post-Riemannian Finsler spacetime is derived. The solution is constructed in three stages: the exterior solution, the event-horizon solution and the…
We construct a novel exact solution of the Einstein-scalar-Maxwell equations describing a dynamical black hole immersed in an external, time-dependent electromagnetic field. Motivated by the need for more realistic analytical black hole…
The Schwarzschild singularity's resolution has key values in cracking the key mysteries related with black holes, the origin of their horizon entropy and the information missing puzzle involved in their evaporations. We provide in this work…
In this paper two things are done. First, it is pointed out the existence of exact asymptotically flat, spherically symmetric black holes when a self interacting, minimally coupled scalar field is the source of the energy momentum of the…
The second Bianchi identity can be recast as an evolution equation for the Riemann curvatures. Here we will report on such a system for a vacuum static spherically symmetric spacetime. This is the first of two papers. In the following paper…
We present a general framework for analyzing spatially inhomogeneous cosmological dynamics. It employs Hubble-normalized scale-invariant variables which are defined within the orthonormal frame formalism, and leads to the formulation of…
We discuss the initial-boundary value problem for the Baumgarte-Shapiro-Shibata-Nakamura evolution system of Einstein's field equations which has been used extensively in numerical simulations of binary black holes and neutron stars. We…
The Einstein equations have proven surprisingly difficult to solve numerically. A standard diagnostic of the problems which plague the field is the failure of computational schemes to satisfy the constraints, which are known to be…
The Einstein's linear equation of a small perturbation in a space-time with a homogeneous section of low dimension, is studied. For every harmonic mode of the horizon, there are two solutions which behave differently at large distance $r$.…
For the fields depending on two of the four space-time coordinates only, the spaces of local solutions of various integrable reductions of Einstein's field equations are shown to be the subspaces of the spaces of local solutions of the…
The focus of this work is on the construction of initial data including a neutron star on a hyperboloidal slice. As simplest scenario for this first step, spherical symmetry is considered together with a polytropic-like equation of state…
We present an algorithm for solving the general relativistic initial value equations for a corotating polytropic star in quasicircular orbit with a nonspinning black hole. The algorithm is used to obtain initial data for cases where the…
According to the Einstein hole argument, vacuum metric solutions are equivalent only if they correspond to the same energy--momentum tensor in the source region. In this paper it is shown that singular coordinates that are used to show…
We construct two solutions of the minimally coupled Einstein-scalar field equations, representing regular deformations of Schwarzschild black holes by a self-interacting, static, scalar field. One solution features an exponentially decaying…
We present an alternative approach to setting initial data in general relativity. We do not use a conformal decomposition, but instead express the 3-metric in terms of a given unit vector field and one unknown scalar field. In the case of…
The purpose of this paper is to demonstrate a new method of generating exact solutions to the Einstein's equations obtained by the Hamiltonian reduction. The key element to the successful Hamiltonian reduction is finding the privileged…
The principle part of Einstein equations in the harmonic gauge consists of a constrained system of 10 curved space wave equations for the components of the space-time metric. A well-posed initial boundary value problem based upon a new…