Black holes in an expanding universe

Abstract

By performing transformations on the isotropic forms of di erent metrics, new cosmological black hole solutions were obtained by generalizing the static solution, the Schwarzchild solution, the McVittie and the Kerr solutions. We present cosmological black holes solutions that satisfy the known behaviours of the scale factor through the history of our Universe, the Radiation, Matter and Dark Energy dominated eras. In the static case we presented solutions satisfying all of the energy conditions, then a time generalization and analysis of the previous isotropic solution gave us the behaviour in time of the Schwarzschild black hole solution. By a choice of parameter, we obtained a non-singular equation of state parameter even though the energy density and pressure tend to in nity at the horizon. In that case the solution suggests that in the expanding universe, the equation of state parameter is negative and may eventually be satis ed by a dark energy dominated representation of the Universe. For the classical McVittie and Kerr solutions, an inductive reasoning led us to obtain all the solutions, Radiation, Matter and Dark energy dominated eras, by introducing two conformal factors and generalizing the metrics. Finally, the Weyl curvature and the volume expansion are calculated for the cosmological black holes and the e ects, increases or decreases, of the volume expansions for all the cases are discussed. It is shown at the end that a multitude of black holes can impact the Universe as a whole by increasing or decreasing its volume.