Reissner-Nordstrom black hole in dark energy background

Abstract

In this paper we propose a stationary solution of Einstein's field equations describing Reissner-Nordstrom black hole in dark energy background. It is to be regarded as the Reissner-Nordstrom black hole is embedded into the dark energy solution producing Reissner-Nordstrom-dark energy black hole. We find that the space-time geometry of Reissner-Nordstrom-dark energy solution is Petrov type $D$ in the classification of space-times. It is also shown that the embedded space-time possesses an energy-momentum tensor of the electromagnetic field interacting with the dark energy having negative pressure. We find the energy-momentum tensor for dark energy violates the the strong energy condition due to the negative pressure, whereas that of the electromagnetic field obeys the strong energy condition. It is shown that the time-like vector field for an observer in the Reissner-Nordstrom-dark energy space is expanding, accelerating, shearing and non-rotating. We investigate the surface gravity of the horizons for the embedded dark energy black hole. The characteristic properties of relativistic dark energy based on the de Sitter solution is discussed in an appendix.