Horizons, hyperbolic systems, and inner boundary conditions in numerical relativity

"We discuss several closely connected open questions central to Numerical Relativity. These involve computational, numerical, theoretical, and physical aspects of evolving and understanding dynamical black hole spacetimes. We discuss finding and understanding the event horizon (EH), which is the causal boundary separating the black hole interior from its exterior, in dynamical black hole spacetimes. In the EH studies, we formulate a set of tools for analyzing the behavior of the EH, including proposing a construction of the membrane paradigm suitable for numerical relativity. Moreover, we probe the geometry of the two black hole collision in detail, and investigate limits of the distortion of a single black hole EH interacting with a gravitational wave. We discuss both standard and hyperbolic formulations of the Einstein equations and how these are amenable to numerical treatment with modern parallel and adaptive computational techniques. In the course of this discussion, we present a three-dimensional implementation of the Bona-Massó hyperbolic system, and a three dimensional code we call ""Cactus,"" which we apply to several spacetimes. Finally, exploiting certain mathematical properties of the Bona-Massó system and the causal structure of horizons, we discuss and compare several methods to implement a (preliminary) apparent horizon boundary condition for evolving black hole spacetimes using the full three-dimensional Cactus code."

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Physics

Year dc:date

2012

Author dc:creator

• Walker, Paul

Contributors dc:contributor

• Seidel, H.E.

• numerical relativity
• black hole spacetimes
• event horizons

Statement dc:rights

• ©1998 Paul Walker

Language dc:language

en

Identifier

4162287

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/30860