Cosmological isotropic matter-energy generalizations of Schwarzschild and Kerr metrics

TL;DR

This paper introduces new time-dependent isotropic fluid solutions around Schwarzschild and Kerr black holes, analyzing their effects on spacetime horizons and cosmological expansion in an expanding universe context.

Contribution

It generalizes Schwarzschild and Kerr metrics to include isotropic matter-energy content in a cosmological setting, providing new solutions and insights into black hole behavior in expanding universes.

Findings

Time-dependent isotropic solutions around Schwarzschild black holes.

Rotating black hole solutions in an expanding universe.

Black hole presence does not alter standard cosmological scale factor laws.

Abstract

We present a time dependent isotropic fluid solution around a Schwarzschild black hole. We offer the solutions and discuss the effects on the field equations and the horizon. We derive the energy density, pressure and the equation of state parameter. In the second part, we generalize the rotating black hole solution to an expanding universe. We derive from the proposed metric the special solutions of the field equations for the dust approximation and the dark energy solution. We show that the presence of a rotating black hole does not modify the scale factor $b(t)=t^{2/3}$ law for dust, nor $b(t)=e^{\lambda\hspace{1mm}t}$ and $p=-\rho$ for dark energy.