Apply Moving Puncture Method to Adm Formalism

Details Apply Moving Puncture Method to Adm Formalism Apply Moving Puncture Method to Adm Formalism

Apr 2010

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2010gras.conf..233c&link_type=abstract

GRAVITATION AND ASTROPHYSICS. Proceedings of the Ninth Asia-Pacific International Conference. Held 29 June-2 July 2009 in Wuhan,

Astronomy and Astrophysics

Astrophysics

Numerical Relativity, Adm Formalism, Moving Puncture Method, Gauge Condition

Scientific paper

It is well known that moving puncture method and the specific gauge condition are critically important for successful simulation of binary black hole merging. On the contrary, the importance of formalism for numerical relativity is not very clear yet. Both generalized harmonic formalism and BSSN formalism work very well. So the simplicity of Einstein's equations in ADM formalism stimulates us to investigate a naive but interesting problem--can ADM formalism work as stably as BSSN formalism does with the moving puncture method and the advanced gauge condition, which were proved critical important for BSSN formalism's success. We apply this idea to Schwarzschild black hole simulation as a test example. Unfortunately, our result implies that ADM formalism has its intrinsic instable character which may be introduced by the property of the corresponding equations themselves instead of the gauge condition. And more, we find that the so called advanced gauge condition even make the situation worse. So we conclude that one gauge condition works well in one numerical formalism does not mean it works well also in other formalism. Through concrete examples, we give readers a primary sense on the roles that formalism, gauge condition, numerical method and other issues play in the problem of stability of numerical relativity.

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