Related papers: The finite volume method on a Schwarzschild backgr…
The issue of defining the volume of black holes has significant implications for quantum gravity. Drawing on concepts from quantum theory and general relativity, several motivations for introducing discreteness in geometry can be proposed.…
We build a finite volume scheme for the scalar conservation law $\partial_t u + \partial_x (H(x, u)) = 0$ with bounded initial condition for a wide class of flux function $H$, convex with respect to the second variable. The main idea for…
We consider the numerical approximation of a system of partial differential equations involving a nonlinear Schr\"odinger equation coupled with a hyperbolic conservation law. This system arises in models for the interaction of short and…
We advocate for a holographic definition of thermodynamic pressure and volume for black holes based on quasi-local gravitational thermodynamics. When a black hole is enclosed by a finite timelike boundary, York's quasi-local first law…
This article proposes a highly accurate and conservative method for hyperbolic systems using the finite volume approach. This innovative scheme constructs the intermediate states at the interfaces of the control volumes using the method of…
This paper investigates some properties of entropy solutions of hyperbolic conservation laws on a Riemannian manifold. First, we generalize the Total Variation Diminishing (TVD) property to manifolds, by deriving conditions on the flux of…
We demonstrate numerically the existence of solutions of five-dimensional vacuum gravity describing the formation, in finite time, of an extremal rotating black hole from a pre-existing Schwarzschild black hole. This is the first example of…
We investigate a static, spherically symmetric black hole solution arising from Einstein gravity coupled to a confining nonlinear electrodynamics model that reproduces Maxwell theory in the strong-field regime while introducing…
Through the consideration of spherically symmetric gravitating systems consisting of perfect fluids with linear equation of state constrained to be in a finite volume, an account is given of the properties of entropy at conditions in which…
We argue, using methods taken from the theory of noiseless subsystems in quantum information theory, that the quantum states associated with a Schwarzchild black hole live in the restricted subspace of the Hilbert space of horizon boundary…
We address numerical challenges in solving hyperbolic free boundary problems described by spherically symmetric conservation laws that arise in the modeling of tumor growth due to immune cell infiltrations. In this work, we normalize the…
Following Ben-Artzi and LeFloch, we consider nonlinear hyperbolic conservation laws posed on a Riemannian manifold, and we establish an L1-error estimate for a class of finite volume schemes allowing for the approximation of entropy…
We present a new many-parameter family of hyperbolic representations of Einstein's equations, which we obtain by a straightforward generalization of previously known systems. We solve the resulting evolution equations numerically for a…
We explore the quantum nature of black holes by introducing an effective framework that takes into account deviations from the classical results. The approach is based on introducing quantum corrections to the classical Schwarzschild…
Entropy solutions have been widely accepted as the suitable solution framework for systems of conservation laws in several space dimensions. However, recent results in \cite{CDL1,CDL2} have demonstrated that entropy solutions may not be…
In this paper the entropy of an eternal Schwarzschild black hole is studied in the limit of infinite black hole mass. The problem is addressed from the point of view of both canonical quantum gravity and superstring theory. The entropy per…
Centered finite volume methods are considered in the context of Numerical Relativity. A specific formulation is presented, in which third-order space accuracy is reached by using a piecewise-linear reconstruction. This formulation can be…
This paper is concerned with the initial-boundary value problem for a nonlinear hyperbolic system of conservation laws. We study the boundary layers that may arise in approximations of entropy discontinuous solutions. We consider both the…
An algebraic-hyperbolic method for solving the Hamiltonian and momentum constraints has recently been shown to be well posed for general nonlinear perturbations of the initial data for a Schwarzschild black hole. This is a new approach to…
The BTZ stationary black hole solution is considered and its mass and angular momentum are calculated by means of Noether theorem. In particular, relative conserved quantities with respect to a suitably fixed background are discussed.…