Schwarzschild black hole in dark energy background

TL;DR

This paper derives an exact solution of Einstein's equations describing a Schwarzschild black hole embedded in a dark energy background, revealing unique geometric and energetic properties including violation of the strong energy condition.

Contribution

It provides a novel exact solution for a Schwarzschild black hole in dark energy, analyzing its geometric structure, energy conditions, and horizon properties.

Findings

The solution is a non-vacuum Petrov type D spacetime.

The energy-momentum tensor violates the strong energy condition.

The black hole exhibits expanding, accelerating, and shearing properties.

Abstract

In this paper we present an exact solution of Einstein's field equations describing the Schwarzschild black hole in dark energy background. It is also regarded as an embedded solution that the Schwarzschild black hole is embedded into the dark energy space producing Schwarzschild-dark energy black hole. It is found that the space-time geometry of Schwarzschild-dark energy solution is non-vacuum Petrov type $D$ in the classification of space-times. We study the energy conditions (like weak, strong and dominant conditions) for the energy-momentum tensor of the Schwarzschild-dark energy solution. We also find that the energy-momentum tensor of the Schwarzschild-dark energy solution violates the strong energy condition due to the negative pressure leading to a repulsive gravitational force of the matter field in the space-time. It is shown that the time-like vector field for an observer in the Schwarzschild-dark energy space is expanding, accelerating, shearing and non-rotating. We investigate the surface gravity and the area of the horizons for the Schwarzschild-dark energy black hole.