Einstein's Equations in Matter

Understand

Einstein's equations in matter are gravitational analogues of Maxwell's equations in matter, providing an effective classical description of gravitational fields.

• We derive Einstein's equations in matter for relativistic fluids, and use them to illustrate how the Tolman-Oppenheimer-Volkoff equations are modified by the matter's response to curvature.
• For a gas of massive fermions, we evaluate how the effective Newton's constant and other susceptibilities depend on the temperature and density.
• In anti-de Sitter space, we study the $O(1/(T\ell)^2)$ corrections to the geometries sourced by perfect fluids, and illustrate the breakdown of hydrostatics in AdS at small temperatures.