Exact solutions of Einstein's equations with ideal gas sources

摘要: We derive a new class of exact solutions characterized by the Szekeres-Szafron metrics (of I), admitting in general no isometries. The source is fluid with viscosity but zero heat flux (adiabatic irreversible evolution) whose equilibrium state variables satisfy equations of: (a) an ultra-relativistic ideal gas; (b) non-relativistic (c) mixture and (b). Einstein's field reduce to quadrature that integrable terms elementary functions (cases (c)) elliptic integrals (case (b)). Necessary sufficient conditions are provided for viscous dissipative stress be consistent theoretical framework extended thermodynamics kinetic theory Maxwell-Boltzmann radiative gases. Energy regularity discussed. prove smooth matching can performed along spherical boundary Friedmann-Lemaitre-Robertson-Walker (FLRW) cosmology or Vaidya exterior solution. Possible applications briefly outlined.