BSSN formalism

{{Short description|Formalism of general relativity}}

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The BSSN formalism (Baumgarte, Shapiro, Shibata, Nakamura formalism) is a formalism of general relativity that was developed by Thomas W. Baumgarte, Stuart L. Shapiro, Masaru Shibata and Takashi Nakamura between 1987 and 1999.{{cite web |url=http://www.ksc.re.kr/kcnr/Presentations/26thNR/26thNRJKim.pdf |title=General Relativistic Hydrodynamics Using BSSN formalism |date=2008-07-28 |author=Jinho Kim |publisher=Seoul National University |access-date=2009-10-19 |url-status=dead |archive-url=https://www.webcitation.org/66TbfxEOa?url=http://www.ksc.re.kr/kcnr/Presentations/26thNR/26thNRJKim.pdf |archive-date=2012-03-27 }} It is a modification of the ADM formalism developed during the 1950s.

The ADM formalism is a Hamiltonian formalism that does not permit stable and long-term numerical simulations. In the BSSN formalism, the ADM equations are modified by introducing auxiliary variables. The formalism has been tested for a long-term evolution of linear gravitational waves and used for a variety of purposes such as simulating the non-linear evolution of gravitational waves or the evolution and collision of black holes.{{cite web |url=http://www.ias.ac.in/listing/bibliography/pram/Masaru_Shibata/ |title=Status of numerical relativity |date=October 2004 |author=Masaru Shibata |publisher=Indian Academy of Sciences |access-date=2009-10-19}}{{cite journal |pmc=4338837 |title=Formation of black hole and emission of gravitational waves |year=2006 |author=Takashi Nakamura |journal=Proceedings of the Japan Academy, Series B |volume=82 |issue=9 |pages=311–327 |bibcode=2006PJAB...82..311N |doi=10.2183/pjab.82.311 |pmid=25792793}}