Related papers: Conformal Thin-Sandwich Solver for Generic Initial…
Astrophysical black holes arise as exact solutions of the Einstein field equations. Therefore, any alternative, such as a gravastar, must satisfy the same level of mathematical rigor and internal consistency. A physically viable gravastar…
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.…
In numerical evolutions of binary black holes (BBH) it is desirable to easily control the orbital eccentricity of the BBH, and the number of orbits completed by the binary through merger. This paper presents fitting formulae that allow to…
A new development of the ``monodromy transform'' method for analysis of hyperbolic as well as elliptic integrable reductions of Einstein equations is presented. Compatibility conditions for some alternative representations of the…
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…
In this paper, we study Einstein gravity either minimally or non-minimally coupled to a vector field which breaks the gauge symmetry explicitly in general dimensions. We first consider a minimal theory which is simply the Einstein-Proca…
The Einstein-Bianchi system uses symmetric and traceless tensors to reformulate Einstein's original field equations. However, preserving these algebraic constraints simultaneously remains a challenge for numerical methods. This paper…
This work presents a novel methodology for deriving stationary and axially symmetric solutions to Einstein field equations using the 1+3 tetrad formalism. This approach reformulates the Einstein equations into first order scalar equations,…
We study conformally-invariant theories of gravity in six dimensions. In four dimensions, there is a unique such theory that is polynomial in the curvature and its derivatives, namely Weyl-squared, and furthermore all solutions of Einstein…
In this paper we study a numerical implementation for the initial boundary value formulation for the generalized conformal field equations. We propose a formulation which is well suited for the study of the long-time behaviour of perturbed…
The Cauchy problem of the vacuum Einstein's equations aims to find a semi-metric $g_{\alpha\beta}$ of a spacetime with vanishing Ricci curvature $R_{\alpha,\beta}$ and prescribed initial data. Under the harmonic gauge condition, the…
An exact solution of the vacuum Einstein field equations over a nonsimply-connected manifold is presented. This solution is spherically symmetric and has no curvature singularity. It can be considered to be a regularization of the…
In this work, we introduce an analytical approximate black hole solution in Einstein-Cubic gravity. To obtain complete solutions, we construct the near horizon and asymptotic solutions as the first step. Then, the approximate analytic…
Inspired by a similar analysis for the vacuum conformal Einstein field equations by Paetz [Ann. H. Poincar\'e 16, 2059 (2015)], in this article we show how to construct a system of quasilinear wave equations for the geometric fields…
We construct and parametrize solutions to the constraint equations of general relativity in a neighborhood of Minkowski spacetime with arbitrary prescribed decay properties at infinity. We thus provide a large class of initial data for the…
We consider the conformal decomposition of Einstein's constraint equations introduced by Lichnerowicz and York, on a compact manifold with boundary. We use order relations on appropriate Banach spaces to derive weak solution generalizations…
We prove a strong localized gluing result for the general relativistic constraint equations (with or without cosmological constant) in $n\geq 3$ spatial dimensions. We glue an $\epsilon$-rescaling of an asymptotically flat data set…
We numerically construct an one-parameter family of initial data of an expanding inhomogeneous universe model which is composed of regularly aligned black holes with an identical mass. They are initial data for vacuum solutions of the…
This thesis is concerned with the development and application of conformal techniques to numerical calculations of asymptotically flat spacetimes. The conformal compactification technique enables us to calculate spatially unbounded domains,…
This article begins with a brief introduction to numerical relativity aimed at readers who have a background in applied mathematics but not necessarily in general relativity. I then introduce and summarise my work on the problem of treating…