General relativity

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 matter field equation

• Einstein field equation

\[R_{\mu \nu} - {1 \over 2}g_{\mu \nu}\,R + g_{\mu \nu} \Lambda = {8 \pi G \over c^4} T_{\mu \nu}\]

related items

• cosmological constant
• Einstein field equation
• energy-momentum tensor
• Hamiltonian formulation of GR

expositions

• Iorio, Lorenzo. ‘Editorial for the Special Issue 100 Years of Chronogeometrodynamics: The Status of the Einstein’s Theory of Gravitation in Its Centennial Year’. arXiv:1504.05789 [astro-Ph, Physics:gr-Qc, Physics:physics], 21 April 2015. http://arxiv.org/abs/1504.05789.
• Straumann, Norbert. “Einstein’s `Z"urich Notebook’ and His Journey to General Relativity.” Annalen Der Physik 523, no. 6 (June 9, 2011): 488–500. doi:10.1002/andp.201110467.
• Casadio, Roberto, Jorge Ovalle, and Roldao da Rocha. “Classical Tests of General Relativity: Brane-World Sun from Minimal Geometric Deformation.” arXiv:1503.02316 [gr-Qc, Physics:hep-Th], March 8, 2015. http://arxiv.org/abs/1503.02316.
• Berti, Emanuele, Enrico Barausse, Vitor Cardoso, Leonardo Gualtieri, Paolo Pani, Ulrich Sperhake, Leo C. Stein, et al. ‘Testing General Relativity with Present and Future Astrophysical Observations’. arXiv:1501.07274 [astro-Ph, Physics:gr-Qc, Physics:hep-Ph, Physics:hep-Th], 28 January 2015. http://arxiv.org/abs/1501.07274.
• Deser, S. “The Legacy of ADM.” arXiv:1501.03522 [gr-Qc, Physics:hep-Th, Physics:physics], January 14, 2015. http://arxiv.org/abs/1501.03522.
• 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.
• Ashtekar, Abhay, Beverly K. Berger, James Isenberg, and Malcolm A. H. MacCallum. “General Relativity and Gravitation: A Centennial Perspective.” arXiv:1409.5823 [astro-Ph, Physics:gr-Qc, Physics:hep-Th, Physics:math-Ph], September 19, 2014. http://arxiv.org/abs/1409.5823.
• General relativity:a very weird world