BSSN formalism

G_{\mu \nu} + \Lambda g_{\mu \nu}= {8\pi G\over c^4} T_{\mu \nu}

Fundamental concepts

Phenomena

Spacetime
Kepler problem Gravitational lensing Gravitational waves Frame-dragging Geodetic effect Event horizon Singularity Black hole
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

Scientists

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]

References

↑ Jinho Kim (2008-07-28). "General Relativistic Hydrodynamics Using BSSN formalism" (PDF). Seoul National University. Retrieved 2009-10-19.
↑ Masaru Shibata (October 2004). "Status of numerical relativity" (PDF). Indian Academy of Sciences. Retrieved 2009-10-19.
↑ Takashi Nakamura (2006). "Formation of black hole and emission of gravitational waves". Japan Academy. Retrieved 2009-10-19.

Relativity

Special
relativity

Background	Principle of relativity Introduction to special relativity Special relativity

Foundations	Relative motion Frame of reference Speed of light 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	Minkowski spacetime World line Spacetime diagrams Light cone

General
relativity

Background	Introduction Mathematical formulation Resources

Fundamental concepts	Special relativity Equivalence principle World line Riemannian geometry Minkowski diagram

Phenomena	Two-body problem Lenses Waves Frame-dragging Geodetic effect Event horizon Singularity Black hole

Equations	Linearized gravity Post-Newtonian formalism Einstein field equations Geodesic equation Friedmann equations ADM formalism BSSN formalism Hamilton–Jacobi–Einstein equation

Advanced theories	Kaluza–Klein Quantum gravity Brans–Dicke theory

Solutions	Schwarzschild Reissner–Nordström Gödel Kerr Kerr–Newman Kasner Taub–NUT Milne Robertson–Walker pp-wave van Stockum dust

Scientists

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BSSN formalism

See also

References