Black branes in four-dimensional conformal equivalent theories

Alex Giacomini,N. Dimakis,Andronikos Paliathanasis

doi:10.1140/epjc/s10052-018-6241-y

Abstract

The physical properties of static analytic solutions which describe black brane geometries are discussed. In particular we study the similarities and differences of analytic black brane/string solutions in the Einstein and Jordan frames. The comparison is made between vacuum power law f(R) gravity solutions and their conformal equivalents in the Einstein frame. In our analysis we examine how the geometrical and physical properties of these analytic axisymmetric solutions—such as singularities, the temperature and the entropy—are affected as we pass from one frame to the other.

Highlights

The need to determine a mechanism which provides a theoretical prediction on the recent observable phenomena in cosmology, such as the late-time acceleration phase of the universe [1,2,3,4,5], has led cosmologists to introduce gravitational theories which are defined in the Jordan frame [6] instead of the Einstein frame of General Relativity [7,8,9,10]
In this work we have studied analytical solutions of black branes which are related through conformal transformations
According to our knowledge this is the first examples where black brane solutions are compared between the Jordan and the Einstein frame

Summary

Introduction

The need to determine a mechanism which provides a theoretical prediction on the recent observable phenomena in cosmology, such as the late-time acceleration phase of the universe [1,2,3,4,5], has led cosmologists to introduce (alternative/modified) gravitational theories which are defined in the Jordan frame [6] instead of the Einstein frame of General Relativity [7,8,9,10]. Scalar–tensor theories are conformally equivalent to General Relativity [21,32,33,34] The latter is just a mathematical equivalence between the Jordan and the Einstein frame on the solution space of the field equations. The conformal equivalency of scalar–tensor theories with General Relativity is true only in the case where there are not any specific conditions imposed from an extra matter source, that is except of the scalar field; we refer the reader to a recent discussion in [35]. In this work we use the results obtained in [88] so as to construct the analytical solution of General Relativity with a minimally coupled scalar field for a four-dimensional static axisymmetric spacetime.

Conformal transformations

Field equations in static axisymmetric spacetime

Black branes in the Jordan frame

Black branes in the Einstein frame

Temperature and entropy

Conclusions