Abstract
We investigate the extension of isotropic interior solutions for static self-gravitating systems to include the effects of anisotropic spherically symmetric gravitational sources by means of the gravitational decoupling realised via the minimal geometric deformation approach. In particular, the matching conditions at the surface of the star with the outer Schwarzschild space-time are studied in great detail, and we describe how to generate, from a single physically acceptable isotropic solution, new families of anisotropic solutions whose physical acceptability is also inherited from their isotropic parent.
Highlights
In a recent paper [1], the first simple, systematic and direct approach to decoupling gravitational sources in general relativity (GR) was developed from the so-called Minimal Geometric Deformation (MGD) approach
We investigate the extension of isotropic interior solutions for static self-gravitating systems to include the effects of anisotropic spherically symmetric gravitational sources by means of the gravitational decoupling realised via the minimal geometric deformation approach
The matching conditions at the surface of the star with the outer Schwarzschild space-time are studied in great detail, and we describe how to generate, from a single physically acceptable isotropic solution, new families of anisotropic solutions whose physical acceptability is inherited from their isotropic parent
Summary
In a recent paper [1], the first simple, systematic and direct approach to decoupling gravitational sources in general relativity (GR) was developed from the so-called Minimal Geometric Deformation (MGD) approach. This simple and systematic method could be conveniently exploited in a large number of relevant cases, such as the Einstein–Maxwell [20] and Einstein–Klein–Gordon system [21,22,23,24], for higher derivative gravity [25,26,27], f (R)-theories of gravity [28,29,30,31,32,33,34], Horava-aether gravity [35,36], polytropic spheres [37,38,39], among many others In this respect, the simplest practical application of the MGD-decoupling consists in extending known isotropic and physically acceptable interior solutions for spherically symmetric self-gravitating systems into the anisotropic domain, at the same time preserving physical acceptability, which represents a highly non-trivial problem [40]
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