General relativity
imported>Pythagoras0님의 2014년 11월 16일 (일) 19:14 판 (→expositions)
Vacuum field equation and gravitational field equation
- gravitational potentail satisfies the following equation (Poisson's equation)
\[\nabla^2 \phi = - 4 \pi G \rho\]
- \(\rho\) is the matter density
- in relativity theory, the metric plays the role of gravitational potential
energy-momentum tensor
- also called as stress-energy tensor
- describe the densities and flows of energy and momentum
- all forms of mass-energy can be sources of gravitational fields
- the stress-energy tensor \(T_{\mu \nu}\) acts as a source of the gravitational field
relativistic Vacuum field equation
relativistic matter field equation
\[R_{\mu \nu} - {1 \over 2}g_{\mu \nu}\,R + g_{\mu \nu} \Lambda = {8 \pi G \over c^4} T_{\mu \nu}\]
expositions
- Damour, Thibault. ‘1974: The Discovery of the First Binary Pulsar’. arXiv:1411.3930 [gr-Qc, Physics:physics], 14 November 2014. http://arxiv.org/abs/1411.3930.
- Sperhake, Ulrich. ‘The Numerical Relativity Breakthrough for Binary Black Holes’. arXiv:1411.3997 [gr-Qc, Physics:physics], 14 November 2014. http://arxiv.org/abs/1411.3997.