Black holes and a scalar field in an expanding universe

TL;DR

This paper models an inhomogeneous universe with black holes and a scalar field within Brans-Dicke gravity, analyzing black hole mass evolution and its dependence on universe curvature, providing insights into scalar-tensor gravity effects.

Contribution

It constructs a novel inhomogeneous universe model with scalar fields in Brans-Dicke gravity, analyzing black hole mass evolution and its relation to universe curvature.

Findings

Black hole mass evolves adiabatically in late universe stages.

Mass increases, remains constant, or decreases depending on universe curvature.

Mass in Einstein frame exhibits time dependence.

Abstract

We consider a model of an inhomogeneous universe including a massless scalar field, where the inhomogeneity is assumed to consist of many black holes. This model can be constructed by following Lindquist and Wheeler, which has already been investigated without including scalar field to show that an averaged scale factor coincides with that of the Friedmann model. In this work we construct the inhomogeneous universe with an massless scalar field, where we assume that the averaged scale factor and scalar field are given by those of the Friedmann model including a scalar field. All of our calculations are carried out in the framework of Brans-Dicke gravity. In constructing the model of an inhomogeneous universe, we define the mass of a black hole in the Brans-Dicke expanding universe which is equivalent to ADM mass if the mass evolves adiabatically, and obtain an equation relating our mass to the averaged scalar field and scale factor. As the results we find that the mass has an adiabatic time dependence in a sufficiently late stage of the expansion of the universe, and that the time dependence is qualitatively diffenrent according to the sign of the curvature of the universe: the mass increases decelerating in the closed universe case, is constant in the flat case and decreases decelerating in the open case. It is also noted that the mass in the Einstein frame depends on time. Our results that the mass has a time dependence should be retained even in the general scalar-tensor gravitiy with a scalar field potential. Furthermore, we discuss the relation of our results to the uniqueness theorem of black hole spacetime and gravitational memory effect.