Gravitational Decoupling in Higher Order Theories

Gravitational decoupling via the Minimal Geometric Deformation (MGD) approach has been used extensively in General Relativity (GR), mainly as a simple method for generating exact anisotropic solutions from perfect fluid seed solutions. Recently this method has also been used to generate exact spheri...

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Main Author: Joseph Sultana
Format: Article
Language:English
Published: MDPI AG 2021-08-01
Series:Symmetry
Subjects:
Online Access:https://www.mdpi.com/2073-8994/13/9/1598
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author Joseph Sultana
author_facet Joseph Sultana
author_sort Joseph Sultana
collection DOAJ
description Gravitational decoupling via the Minimal Geometric Deformation (MGD) approach has been used extensively in General Relativity (GR), mainly as a simple method for generating exact anisotropic solutions from perfect fluid seed solutions. Recently this method has also been used to generate exact spherically symmetric solutions of the Einstein-scalar system from the Schwarzschild vacuum metric. This was then used to investigate the effect of scalar fields on the Schwarzschild black hole solution. We show that this method can be extended to higher order theories. In particular, we consider fourth order Einstein–Weyl gravity, and in this case by using the Schwarzschild metric as a seed solution to the associated vacuum field equations, we apply the MGD method to generate a solution to the Einstein–Weyl scalar theory representing a hairy black hole solution. This solution is expressed in terms of a series using the Homotopy Analysis Method (HAM).
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spelling doaj.art-ec0d38c88b274e998ba7eab14ce93dc22023-11-22T15:27:12ZengMDPI AGSymmetry2073-89942021-08-01139159810.3390/sym13091598Gravitational Decoupling in Higher Order TheoriesJoseph Sultana0Department of Mathematics, Faculty of Science, University of Malta, MSD 2080 Msida, MaltaGravitational decoupling via the Minimal Geometric Deformation (MGD) approach has been used extensively in General Relativity (GR), mainly as a simple method for generating exact anisotropic solutions from perfect fluid seed solutions. Recently this method has also been used to generate exact spherically symmetric solutions of the Einstein-scalar system from the Schwarzschild vacuum metric. This was then used to investigate the effect of scalar fields on the Schwarzschild black hole solution. We show that this method can be extended to higher order theories. In particular, we consider fourth order Einstein–Weyl gravity, and in this case by using the Schwarzschild metric as a seed solution to the associated vacuum field equations, we apply the MGD method to generate a solution to the Einstein–Weyl scalar theory representing a hairy black hole solution. This solution is expressed in terms of a series using the Homotopy Analysis Method (HAM).https://www.mdpi.com/2073-8994/13/9/1598Einstein–Weyl gravitygravitational decouplingblack holes
spellingShingle Joseph Sultana
Gravitational Decoupling in Higher Order Theories
Symmetry
Einstein–Weyl gravity
gravitational decoupling
black holes
title Gravitational Decoupling in Higher Order Theories
title_full Gravitational Decoupling in Higher Order Theories
title_fullStr Gravitational Decoupling in Higher Order Theories
title_full_unstemmed Gravitational Decoupling in Higher Order Theories
title_short Gravitational Decoupling in Higher Order Theories
title_sort gravitational decoupling in higher order theories
topic Einstein–Weyl gravity
gravitational decoupling
black holes
url https://www.mdpi.com/2073-8994/13/9/1598
work_keys_str_mv AT josephsultana gravitationaldecouplinginhigherordertheories