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For axially symmetric solutions of Einstein equations there exists a gauge which has the remarkable property that the total mass can be written as a conserved, positive definite, integral on the spacelike slices. The mass integral provides…
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:…
In this lecture, I explain the gauge-invariant formulation for perturbations of background spacetimes with untwisted homologous Einstein fibres, which include lots of practically important spacetimes such as static black holes, static black…
According to general relativity, black holes are incomplete, which prevents developing a complete physical description of their dynamical formation and evolution once quantum effects are taken into account. Theories beyond general…
We construct dynamical many-black-hole spacetimes with well-controlled asymptotic behavior as solutions of the Einstein vacuum equation with positive cosmological constant. We accomplish this by gluing Schwarzschild-de Sitter or Kerr-de…
The search for solutions of Einstein's equations representing relativistic cosmological models with a discrete matter content has been remarkably fruitful in the last decade. In this review we discuss the progress made in the study of a…
We present a new initial data formulation to solve the full set of Einstein equations for spacetimes that contain a black hole under general conditions. The method can be used to construct complete initial data for spacetimes (the full…
We present an algorithm for treating mesh refinement interfaces in numerical relativity. We detail the behavior of the solution near such interfaces located in the strong field regions of dynamical black hole spacetimes, with particular…
In this paper, we consider finite difference approximations of the second order wave equation. We use finite difference operators satisfying the summation-by-parts property to discretize the equation in space. Boundary conditions and grid…
We review in a pedagogical fashion the 3+1-split which serves to put Einstein's equations into the form of a dynamical system with constraints. We then discuss the constraint equations under the simplifying assumption of time-symmetry.…
We study a simple analytic solution to Einstein's field equations describing a thin spherical shell consisting of collisionless particles in circular orbit. We then apply two independent criteria for the identification of circular orbits,…
A strongly well-posed initial boundary value problem based upon constraint-preserving boundary conditions of the Sommerfeld type has been established for the harmonic formulation of the vacuum Einstein's equations. These Sommerfeld…
We provide a detailed analysis of several aspects of the turduckening technique for evolving black holes. At the analytical level we study the constraint propagation for a general family of BSSN-type formulation of Einstein's field…
A systematic procedure is proposed for better understanding the evolution laws of black holes in terms of pure quantum states. We start with the two opposed regions I and II in the Penrose diagram, and study the evolution of matter in these…
This is the second paper in a series describing a numerical implementation of the conformal Einstein equation. This paper deals with the technical details of the numerical code used to perform numerical time evolutions from a "minimal" set…
We present the first stable dynamical numerical evolutions of the Einstein equations in terms of a conformally rescaled metric on hyperboloidal hypersurfaces extending to future null infinity. Axisymmetry is imposed in order to reduce the…
The numerical integration of particle trajectories in curved spacetimes is fundamental for obtaining realistic models of the particle dynamics around massive compact objects such as black holes and neutron stars. Generalized algorithms…
We report on the first results of self-consistent second order metric perturbations produced by a point particle moving in the Schwarzschild spacetime. The second order waveforms satisfy a wave equation with an effective source term build…
We study some general properties of two black hole solutions in Einstein's conformal gravity. Both solutions can be obtained from the Kerr metric with a suitable conformal rescaling, which leads, respectively, to a regular and a singular…
We perform a statistical analysis of the binary black hole problem in the post-Newtonian approximation by systematically sampling and evolving the parameter space of initial configurations for quasi-circular inspirals. Through a principal…