"General relativity"의 두 판 사이의 차이
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imported>Pythagoras0 |
imported>Pythagoras0 |
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* [[energy-momentum tensor]] | * [[energy-momentum tensor]] | ||
* [[Hamiltonian formulation of GR]] | * [[Hamiltonian formulation of GR]] | ||
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| + | ==expositions== | ||
| + | * http://arxiv.org/abs/1411.3997 | ||
| + | * http://arxiv.org/abs/1411.3930 | ||
2014년 11월 16일 (일) 17:42 판
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
\[R_{\mu \nu} - {1 \over 2}g_{\mu \nu}\,R + g_{\mu \nu} \Lambda = {8 \pi G \over c^4} T_{\mu \nu}\]