A new solution for dilaton-Maxwell gravity
type: Item
instance of: scholarly article
title: A new solution for dilaton-Maxwell gravity
zbMATH Open document ID: 0843.53066
DOI: 10.1007/BF02113080
author: Slava G. Turyshev
published in: General Relativity and Gravitation
publication date: 1995-11-30T00:00:00Z
review text: It is known that the inclusion of a scalar field in the theory of general relativity leads to a violation of the equivalence principle and to a modification of large scale gravitational phenomena. Moreover, some of the scalar fields in tensor multiscalar theories might contain non-positively defined kinetic terms. The purpose of this paper is to explore the behaviour of the static gravity coupled to a scalar field with a negative kinetic term in the presence of the electromagnetic field. In the string theory the action is given by \[ S=- {1\over {16\pi}} \int \sqrt {-g} (R+ 2g^{mn} \nabla_m \varphi \nabla_n \varphi+ e^{-2 \varphi} g^{mn} g^{kl} F_{mk} F_{nl} )d^4 x. \] Applying the variational principle to this functional, a set of field equations is obtained. The solution of this equation is sought under the following requirements: a) covariant de Donder gauge condition; b) assumption that the static spherically symmetric fields are everywhere radial. It is noted that if the scalar field is absent \((\varphi =0)\) the solution resulting from the minimization of the action describes a charged black hole with mass \(\mu_0\) and electromagnetic charge \(Q\). The obtained solution is in general singular, but by choosing a parameter entering in the solution, the author avoids the singularity. In this case the solution is a modification of the Fock solution in the presence of the dilaton and electromagnetic field. It is labeled by means of two parameters, \(\mu\) and \(Q\), and has two regular event horizons \((r_\pm)\) which correspond to the physical mass \(\mu_0\) and the electric charge \(Q\) of the hole \[ r_\pm= \mu_\pm= {\textstyle {1\over 2}} (\mu_0 \pm \sqrt {\mu_0^2- 2Q^2}). \] Other related quantities computed in this paper are: a) the Riemann curvature \(R\); b) the scalar curvature \(R_s\) in the general case and in the extreme regime \((\mu_0= 2Q^2)\). At the end of the paper the author quotes a negative result that he obtained: The negative kinetic term \(…
reviewed by: Serban Misicu
Mathematics Subject Classification ID: 53Z05
Mathematics Subject Classification ID: 83C22
Mathematics Subject Classification ID: 83C20
Mathematics Subject Classification ID: 83C60
zbMATH DE Number: 811244
zbMATH Keywords: Einstein-Maxwell equations
zbMATH Keywords: dilaton
zbMATH Keywords: equivalence principle
zbMATH Keywords: scalar field
zbMATH Keywords: Riemann curvature
zbMATH Keywords: scalar curvature
MaRDI profile type: Publication
cites work: Black holes as elementary particles
cites work: Tensor-multi-scalar theories of gravitation
cites work: Relativistic theory of gravitation
cites work: Q3256906
cites work: Q4029819
description: scientific article; zbMATH DE number 811244