Related papers: Notes on causal differencing in ADM/CADM formulati…
The investigations presented in this study are directed at relativistic modifications of the uncertainty relation derived from the curvature of the background spacetime. These findings generalize previous work which is recovered in the…
We present single and binary black hole simulations that follow the moving puncture paradigm of simulating black-hole spacetimes without excision, and use moving boxes mesh refinement. Focussing on binary black hole configurations where the…
We investigate the causal structure of $(1+1)$-dimensional spacetimes. For two sets of field equations we show that at least locally any spacetime is a solution for an appropriate choice of the matter fields. For the theories under…
A class of nonstationary spacetimes is obtained by means of a conformal transformation of the Schwarzschild metric, where the conformal factor $a(t)$ is an arbitrary function of the time coordinate only. We investigate several situations…
Massive scalar charges are ubiquitous in extensions to General Relativity and the Standard Model in particle physics. We describe spectral methods which can accurately construct the spacetime of rotating black holes with dimensionless spin…
The physical interpretation and eventual fate of gravitational singularities in a theory surpassing classical general relativity are puzzling questions that have generated a great deal of interest among various quantum gravity approaches.…
We give a causal inference scheme using quantum observations alone for a case with both temporal and spatial correlations: a bipartite quantum system with measurements at two times. The protocol determines compatibility with 5 causal…
We present approximate analytical solutions to the Hamiltonian and momentum constraint equations, corresponding to systems composed of two black holes with arbitrary linear and angular momentum. The analytical nature of these initial data…
In contemporary scientific research, understanding the distinction between correlation and causation is crucial. While correlation is a widely used analytical standard, it does not inherently imply causation. This paper addresses the…
In this exploratory study, we demonstrate the capability of the numerical-relativity code BAM to simulate fully relativistic black-hole binary-single and binary-binary encounters. While previous work has demonstrated the general capability…
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.…
We describe a simple implementation of black hole excision in 3+1 numerical relativity. We apply this technique to a Schwarzschild black hole with octant symmetry in Eddington-Finkelstein coordinates and show how one can obtain accurate,…
Singularity theorems of general relativity utilize the notion of causal geodesic incompleteness as a criterion of the presence of a spacetime singularity. The incompleteness of a causal curve implies the end and/or beginning of the…
We calculate puncture initial data corresponding to both single and binary black hole solutions of the constraint equations by means of a pseudo-spectral method applied in a single spatial domain. Introducing appropriate coordinates, these…
Over the past two decades, the rapid surge in data-intensive computational techniques for statistical modeling may have had the effect of diminishing the use of applied mathematics in causal scientific inquiry. In this paper, co-authored by…
The ``moving puncture'' technique has led to dramatic advancements in the numerical simulations of binary black holes. Hannam et.al. have recently demonstrated that, for suitable gauge conditions commonly employed in moving puncture…
We describe an explicit in time, finite-difference code designed to simulate black holes by using the excision method. The code is based upon the harmonic formulation of the Einstein equations and incorporates several features regarding the…
I describe approaches to the study of black hole spacetimes via numerical relativity. After a brief review of the basic formalisms and techniques used in numerical black hole simulations, I discuss a series of calculations from axisymmetry…
I review the development of numerical evolution codes for general relativity based upon the characteristic initial value problem. Progress in characteristic evolution is traced from the early stage of 1D feasibility studies to 2D…
A partially first-order form of the characteristic formulation is introduced to control the accuracy in the computation of gravitational waveforms produced by highly distorted single black hole spacetimes. Our approach is to reduce the…