BSSN formalism

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${\displaystyle G_{\mu \nu }+\Lambda g_{\mu \nu }={\kappa }T_{\mu \nu }}$
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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.^[1] 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.^[2][3]