Related papers: Notes on causal differencing in ADM/CADM formulati…
Causal reasoning provides a language to ask important interventional and counterfactual questions beyond purely statistical association. In medical imaging, for example, we may want to study the causal effect of genetic, environmental, or…
In previous work [L. Blanchet and A. Le Tiec, Phys. Rev. D 80, 023524 (2009)], motivated by the phenomenology of dark matter at galactic scales, a model of dipolar dark matter (DDM) was introduced. At linear order in cosmological…
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…
In certain extensions of General Relativity, wormholes generated by spherically symmetric electric fields can resolve black hole singularities without necessarily removing curvature divergences. This is shown by studying geodesic…
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…
It is shown here that in a flat, cold dark matter (CDM) dominated Universe with positive cosmological constant ($\Lambda$), modelled in terms of a Newtonian and collisionless fluid, particle trajectories are analytical in time…
We study black holes in two and three dimensions that have spacelike curvature singularities behind horizons. The 2D solutions are obtained by dimensionally reducing certain 3D black holes, known as quantum BTZ solutions. Furthermore, we…
Recently, different methods succeeded in calculating the spin dynamics at higher orders in the post-Newtonian (PN) approximation. This is an essential step toward the determination of more accurate templates for gravitational waves, to be…
The future finite-time singularities emerging in alternative gravity dark energy models are classified and studied in Jordan and Einstein frames. It is shown that such singularity may occur even in flat spacetime for the specific choice of…
When higher-derivative terms are added to a gravitational action, black hole solutions and their thermodynamic properties are generally corrected. Recent progress has shown that, by treating higher-derivative operators as perturbations, the…
A numerical solution scheme for the Einstein field equations based on generalized harmonic coordinates is described, focusing on details not provided before in the literature and that are of particular relevance to the binary black hole…
A paradigm deeply rooted in modern numerical relativity calculations prescribes the removal of those regions of the computational domain where a physical singularity may develop. We here challenge this paradigm by performing…
In this work, based on the $3+1$ decomposition in [24, 33], we present a fully exterior calculus breakdown of spacetime and Einstein's equations. Links to the orthonormal frame approach [38] are drawn to help understand the variables in…
We consider the numerical evolution of dynamic black hole initial data sets with a full 3D, nonlinear evolution code. These data sets consist of single black holes distorted by strong gravitational waves, and mimic the late stages of…
We study the discrete causal set geometry of a small causal diamond in a curved spacetime using the average abundance of k-element chains or total orders in the underlying causal set C. We begin by obtaining the first order curvature…
A new algorithm for solving the general relativistic MHD equations is described in this paper. We design our scheme to incorporate black hole excision with smooth boundaries, and to simplify solving the combined Einstein and MHD equations…
We justify the applicability of the background subtraction method to both Einstein's gravity and its higher derivative corrections in 5-dimensional asymptotically AdS spacetimes, where the corresponding higher derivative corrections to the…
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…
Solving Einstein's constraint equations for the construction of black hole initial data requires handling the black hole singularity. Typically, this is done either with the excision method, in which the black hole interior is excised from…
We present long-term-stable and convergent evolutions of head-on black hole collisions and extraction of gravitational waves generated during the merger and subsequent ring-down. The new ingredients in this work are the use of fixed…