Related papers: Recent analytical and numerical techniques applied…
We present an overview of recent developments in numerical relativity studies of higher dimensional spacetimes with a focus on time evolutions of black-hole systems. After a brief review of the numerical techniques employed for these…
We extend a recently developed numerical code to obtain stationary, axisymmetric solutions that describe rotating black hole spacetimes in a wide class of modified theories of gravity. The code utilizes a relaxed Newton-Raphson method to…
In this work numerical methods for solving Einstein's equations are developed and applied to the study of inhomogeneous cosmological models. A two-dimensional computer code is described which implements two advanced numerical methods:…
We discuss simple vacuum solutions to the Einstein Equations in five dimensional space-times compactified in two different ways. In such spaces, one black hole phase and more then one black string phase may exist. Several old metrics are…
The spectrum of known black-hole solutions to the stationary Einstein equations has been steadily increasing, sometimes in unexpected ways. In particular, it has turned out that not all black-hole-equilibrium configurations are…
Numerical relativity is finally approaching a state where the evolution of rather general (3+1)-dimensional data sets can be computed in order to solve the Einstein equations. After a general introduction, three topics of current interest…
Multi-black hole solutions play a relevant role both from the theoretical and the phenomenological point of view. In this Thesis, we construct some regular multi-black hole spacetimes in pure Einstein's General Relativity with the aid of…
Solving Einstein's equations precisely for strong-field gravitational systems is essential to determining the full physics content of gravitational wave detections. Without these solutions it is not possible to infer precise values for…
The numerical evolution of Einstein's field equations in a generic background has the potential to answer a variety of important questions in physics: from applications to the gauge-gravity duality, to modelling black hole production in TeV…
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…
This paper presents solutions to Einstein's equation -- and the numerical methods used to construct them -- that describe simple cosmological models on manifolds with compact non-orientable spatial slices. These solutions have been…
An approximate solution to Einstein's equations representing two widely-separated non-rotating black holes in a circular orbit is constructed by matching a post-Newtonian metric to two perturbed Schwarzschild metrics. The spacetime metric…
The evolution of the methods used to find solutions of Einstein's field equations during the last 100 years is described. Early papers used assumptions on the coordinate forms of the metrics. Since the 1950s more invariant methods have been…
Spherically symmetric (1D) black-hole spacetimes are considered as a test for numerical relativity. A finite difference code, based in the hyperbolic structure of Einstein's equations with the harmonic slicing condition is presented.…
The application of numerical relativity to cosmological spacetimes is providing new insights into the behavior of Einstein's equations, beyond common approximations. In order for simulations to be performed as accurately and efficiently as…
Recent results on solutions of the Einstein equations with matter are surveyed and a number of open questions are stated. The first group of results presented concern asymptotically flat spacetimes, both stationary and dynamical. Then there…
Several types of static solutions to Einstein's equations coupled with antisymmetric tensor fields are found in $(2+N+1)$-dimensional spacetime. The solutions describe a product of a three-dimensional radially symmetric spacetime and an…
The advent of long-term stability in numerical relativity has yielded a windfall of answers to long-standing questions regarding the dynamics of space-time, matter, and electromagnetic fields in the strong-field regime of black-hole binary…
This paper has been withdrawn by the author due to the triviality of the considered coordinate transformations. A consistent treatment, based on the extended physical radial coordinates, is presented in the publications of the author 2000 -…
We perform simulations in a gravitational collapsing model using the Einstein equations. In this paper, we review the equations for constructing the initial values and the evolution form of the Einstein equations called the BSSN…