BSSN formalism

General relativity
Introduction History Mathematical formulation Tests
Fundamental concepts Equivalence principle Special relativity World line Riemannian geometry
Phenomena Kepler problem Gravitational lensing Gravitational waves Frame-dragging Geodetic effect Event horizon Singularity Black hole Spacetime Spacetime diagrams Minkowski spacetime Einstein–Rosen bridge
Equations Formalisms Equations Linearized gravity Einstein field equations Friedmann Geodesics Mathisson–Papapetrou–Dixon Hamilton–Jacobi–Einstein Formalisms ADM BSSN Post-Newtonian Advanced theory Kaluza–Klein theory Quantum gravity
Solutions Schwarzschild (interior) Reissner–Nordström Gödel Kerr Kerr–Newman Kasner Lemaître–Tolman Taub-NUT Milne Robertson–Walker pp-wave van Stockum dust Weyl−Lewis−Papapetrou
Scientists Einstein Lorentz Hilbert Poincaré Schwarzschild de Sitter Reissner Nordström Weyl Eddington Friedman Milne Zwicky Lemaître Gödel Wheeler Robertson Bardeen Walker Kerr Chandrasekhar Ehlers Penrose Hawking Raychaudhuri Taylor Hulse van Stockum Taub Newman Yau Thorne others

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

Relativity
Special relativity	Background Principle of relativity Special relativity Foundations Frame of reference Speed of light Hyperbolic orthogonality Rapidity Maxwell's equations Formulation Galilean relativity Galilean transformation Lorentz transformation Consequences Time dilation Relativistic mass Mass–energy equivalence Length contraction Relativity of simultaneity Relativistic Doppler effect Thomas precession Relativistic disks Spacetime Light cone World line Spacetime diagram Biquaternions Minkowski space
General relativity	Background Introduction Mathematical formulation Fundamental concepts Special relativity Equivalence principle World line Riemannian geometry Minkowski diagram Phenomena Black hole Event horizon Frame-dragging Geodetic effect Lenses Singularity Waves Ladder paradox Twin paradox Two-body problem Equations ADM formalism BSSN formalism Einstein field equations Geodesic equation Friedmann equations Linearized gravity Post-Newtonian formalism Hamilton–Jacobi–Einstein equation Advanced theories Brans–Dicke theory Kaluza–Klein Mach's principle Quantum gravity Solutions Schwarzschild (interior) Reissner–Nordström Gödel Kerr Kerr–Newman Kasner Taub–NUT Milne Robertson–Walker pp-wave van Stockum dust Weyl−Lewis−Papapetrou
Scientists	Einstein Lorentz Hilbert Poincaré Schwarzschild de Sitter Reissner Nordström Weyl Eddington Friedmann Milne Zwicky Lemaître Gödel Wheeler Robertson Bardeen Walker Kerr Chandrasekhar Ehlers Penrose Hawking Taylor Hulse Stockum Taub Newman Yau Thorne Weiss Bondi Misner others