On the time dependent Schwarzschild - de Sitter spacetime

TL;DR

This paper investigates the properties of a time-dependent Schwarzschild-de Sitter spacetime filled with an imperfect cosmic fluid, analyzing its energy flux, kinematics, and singularities.

Contribution

It provides a detailed analysis of the energy flux and kinematic quantities in a non-static Schwarzschild-de Sitter spacetime with an imperfect fluid.

Findings

Energy density is positive with pressure equal to negative energy density.

Scalar expansion remains time-independent but diverges at the singularity.

Heat flux near the central mass is independent of Newton's constant G.

Abstract

An imperfect cosmic fluid with energy flux is analyzed. Even though its energy density $\rho$ is positive, the pressure $p = -\rho$ due to the fact that the metric is asymptotically de Sitter. The kinematical quantities for a nongeodesic congruence are computed. The scalar expansion is time independent but divergent at the singularity $r = 2m$. Far from the central mass $m$ and for a cosmic time $\bar{t} << H^{-1}$, the heat flux $q$ does not depend on Newton's constant $G$.