Numerical relativity from a gauge theory perspective

I present a new method for numerical simulations of general relativistic systems that eliminates constraint violating modes without the need for constraint damping or the introduction of extra dynamical fields. The method is a type of variational integrator. It is based on a discretization of an action for gravity (the Plebański action) on an unstructured mesh that preserves the local Lorentz transformation and diffeomorphism symmetries of the continuous action. Applying Hamilton's principle of stationary action gives discrete field equations on the mesh. For each gauge degree of freedom there is a corresponding discrete constraint; the remaining discrete evolution equations exactly preserve these constraints under time-evolution. I validate the method using simulations of several analytically solvable spacetimes: a weak gravitational wave spacetime, the Schwarzschild spacetime, and the Kerr spacetime.

Department dc:contributor.department

Massachusetts Institute of Technology. Dept. of Physics.

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2010

Author dc:creator

• Farr, Will M. (Will Meierjurgen)

Advisor dc:contributor.advisor

• Edmund Bertschinger.

• Physics.

Statement dc:rights

• M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/1721.1/62871

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/62871