Novel finite-differencing techniques for numerical relativity: application to black hole excision
Gioel Calabrese, Luis Lehner, David Neilsen, Jorge Pullin, Oscar, Reula, Olivier Sarbach, Manuel Tiglio
TL;DR
This paper develops stable finite-difference methods for numerical relativity, specifically for black hole excision, and demonstrates their effectiveness through 3D scalar field simulations around a Schwarzschild black hole.
Contribution
It introduces rigorous finite-difference schemes tailored for hyperbolic equations in bounded domains, advancing numerical relativity techniques for black hole simulations.
Findings
Stable 3D scalar field simulations around Schwarzschild black holes
Finite-difference schemes ensure numerical stability in black hole excision
Application of hyperbolic PDE analysis to numerical relativity
Abstract
We use rigorous techniques from numerical analysis of hyperbolic equations in bounded domains to construct stable finite-difference schemes for Numerical Relativity, in particular for their use in black hole excision. As an application, we present 3D simulations of a scalar field propagating in a Schwarzschild black hole background.
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