The BSSN 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]
See also
ADM formalism
Canonical coordinates
Canonical gravity
Hamiltonian mechanics
References
Jinho Kim (2008-07-28). "General Relativistic Hydrodynamics Using BSSN formalism" (PDF). Seoul National University. Archived from the original (PDF) on 2012-03-27. Retrieved 2009-10-19.
Masaru Shibata (October 2004). "Status of numerical relativity". Indian Academy of Sciences. Retrieved 2009-10-19.
Takashi Nakamura (2006). "Formation of black hole and emission of gravitational waves". Proceedings of the Japan Academy, Series B. 82 (9): 311–327. Bibcode:2006PJAB...82..311N. doi:10.2183/pjab.82.311. PMC 4338837. PMID 25792793.
Relativity
Special relativity
Background
Principle of relativity (Galilean relativity Galilean transformation) Special relativity Doubly special relativity
Fundamental
concepts
Frame of reference Speed of light Hyperbolic orthogonality Rapidity Maxwell's equations Proper length Proper time Relativistic mass
Formulation
Lorentz transformation
Phenomena
Time dilation Mass–energy equivalence Length contraction Relativity of simultaneity Relativistic Doppler effect Thomas precession Ladder paradox Twin paradox
Spacetime
Light cone World line Minkowski diagram Biquaternions Minkowski space
General relativity
Background
Introduction Mathematical formulation
Fundamental
concepts
Equivalence principle Riemannian geometry Penrose diagram Geodesics Mach's principle
Formulation
ADM formalism BSSN formalism Einstein field equations Linearized gravity Post-Newtonian formalism Raychaudhuri equation Hamilton–Jacobi–Einstein equation Ernst equation
Phenomena
Black hole Event horizon Singularity Two-body problem
Gravitational waves: astronomy detectors (LIGO and collaboration Virgo LISA Pathfinder GEO) Hulse–Taylor binary
Other tests: precession of Mercury lensing redshift Shapiro delay frame-dragging / geodetic effect (Lense–Thirring precession) pulsar timing arrays
Advanced
theories
Brans–Dicke theory Kaluza–Klein Quantum gravity
Solutions
Cosmological: Friedmann–Lemaître–Robertson–Walker (Friedmann equations) Kasner BKL singularity Gödel Milne
Spherical: Schwarzschild (interior Tolman–Oppenheimer–Volkoff equation) Reissner–Nordström Lemaître–Tolman
Axisymmetric: Kerr (Kerr–Newman) Weyl−Lewis−Papapetrou Taub–NUT van Stockum dust discs
Others: pp-wave Ozsváth–Schücking metric
Scientists
Poincaré Lorentz Einstein Hilbert Schwarzschild de Sitter Weyl Eddington Friedmann Lemaître Milne Robertson Chandrasekhar Zwicky Wheeler Choquet-Bruhat Kerr Zel'dovich Novikov Ehlers Geroch Penrose Hawking Taylor Hulse Bondi Misner Yau Thorne Weiss others
Categories
Theory of relativity
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