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

• http://arxiv.org/abs/1411.3997
• http://arxiv.org/abs/1411.3930