Related papers: 3+1 General Relativity in Hyperbolic Form

We review recent progress in taking the large dimension limit of Einstein's equations. Most of our analysis is classical in nature and concerns situations where there is a black hole horizon although we briefly discuss various extensions…

We present, in closed analytic form, a general stationary, slowly rotating black hole, which is solution to a large class of alternative theories of gravity in four dimensions. In these theories, the Einstein-Hilbert action is supplemented…

We investigate the existence of black bounce solutions in $2+1$ dimensions within the framework of $f(R)$ gravity. We analyze whether black bounce geometries originally obtained in general relativity can be consistently generalized to…

Black holes are an ubiquitous end state of stellar evolution and successfully explain some of the most extreme physics encountered in astronomical observations. The Kerr geometry is the known exact solution to Einstein's equations for a…

This paper presents both a numerical method for general relativity and an application of that method. The method involves the use of harmonic coordinates in a 3+1 code to evolve the Einstein equations with scalar field matter. In such…

We investigate how the accuracy and stability of numerical relativity simulations of 1D colliding plane waves depends on choices of equation formulations, gauge conditions, boundary conditions, and numerical methods, all in the context of a…

Waves propagating in the relativistic electron-positron or ions plasma are investigated in a frame of two-fluid equations using the 3+1 formalism of general relativity developed by Thorne, Price and Macdonald (TPM). The plasma is assumed to…

In this article, we provide notes that complement the lectures on the relativistic Euler equations and shocks that were given by the second author at the program Mathematical Perspectives of Gravitation Beyond the Vacuum Regime, which was…

A novel perspective on defining black holes designed to be more broadly applicable outside of asymptotically flat spacetimes, in the context of classical general relativity, is presented, discussed, and characterized. The construction…

At the horizon of a black hole, the action of (3+1)-dimensional loop quantum gravity acquires a boundary term that is formally identical to an action for three-dimensional gravity. I show how to use this correspondence to obtain the entropy…

Over the last three years, a number of fundamental physical issues were addressed in loop quantum gravity. These include: A statistical mechanical derivation of the horizon entropy, encompassing astrophysically interesting black holes as…

We investigate the interior hyperbolic region of axisymmetric and stationary black holes surrounded by a matter distribution. First, we treat the corresponding initial value problem of the hyperbolic Einstein equations numerically in terms…

Cosmological simulations involving the fully covariant gravitational dynamics may prove relevant in understanding relativistic/non-linear features and, therefore, in taking better advantage of the upcoming large scale structure survey data.…

In this second paper, I construct a limit space of a Cauchy sequence of globally hyperbolic spacetimes. In the second section, I work gradually towards a construction of the limit space. I prove the limit space is unique up to isometry. I…

In this small paper, we study a boundary value problem for an equation of parabolic-hyperbolic type. The goal is to show how we can prove existence and uniqueness theorem for a regular solution.

The causal structure of Einstein's evolution equations is considered. We show that in general they can be written as a first order system of balance laws for any choice of slicing or shift. We also show how certain terms in the evolution…

In this thesis we investigate black holes in the Randall-Sundrum braneworld scenario. We begin with an overview of extra-dimensional physics, from the original proposal of Kaluza and Klein up to the modern braneworld picture of extra…

The simple quantum gravity model, based on a new conjecture within the canonically quantized 3+1 general relativity, is presented. The conjecture states that matter fields are functionals of an embedding volume form only, and reduces the…

The recent detections of gravitational waves from binary systems of black holes are in remarkable agreement with the predictions of General Relativity. In this pedagogical mini-review, I will go through the physics of the different phases…

The presence of a horizon breaks the gauge invariance of (2+1)-dimensional general relativity, leading to the appearance of new physical states at the horizon. I show that the entropy of the (2+1)-dimensional black hole can be obtained as…