Einstein's Equations in Matter

Abstract

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.

arXiv commentv2: Added section on matter in thermal equilibrium in anti-de Sitter spacetime

References in corpus (15)

• Relativistic viscous hydrodynamics, conformal invariance, and holography
• Black Holes
• Constraints on Fluid Dynamics from Equilibrium Partition Functions
• Towards hydrodynamics without an entropy current
• Relativistic magnetohydrodynamics
• Spectral sum rules for the quark-gluon plasma
• Anomaly inflow and thermal equilibrium
• Kubo Formulae for Second-Order Hydrodynamic Coefficients
• General equilibrium second-order hydrodynamic coefficients for free quantum fields
• Thermodynamical second-order hydrodynamic coefficients
• Thermodynamics of polarized relativistic matter
• Kubo formulas for thermodynamic transport coefficients
• Second-order partition function of a non-interacting chiral fluid in 3+1 dimensions
• Equilibrium thermodynamic susceptibilities for a dense degenerate Dirac field
• Ricci cosmology

Cited by in corpus (9)

• Chiral hydrodynamics in strong external magnetic fields
• Hydrodynamics, spin currents and torsion
• Prospects for testing the inverse-square law and gravitomagnetism using quantum interference
• Equilibrium thermodynamic susceptibilities for a dense degenerate Dirac field
• Second order equilibrium transport in strongly coupled $\mathcal{N}=4$ supersymmetric $SU(N_c)$ Yang-Mills plasma via holography
• Determining all thermodynamic transport coefficients for an interacting large N quantum field theory
• Hydrodynamic fluctuations and long-time tails in a fluid on an anisotropic background
• Thermodynamic equilibrium condition and the first law of thermodynamics for charged perfect fluids in electromagnetic and gravitational fields
• Hydrodynamics in the Carrollian regime