Abstract
We find a new family of exact solutions to the Einstein system of equations with an anisotropic fluid distribution for a spherically symmetric spacetime containing a conformal Killing vector. Simple analytic expressions describe the matter variables and the metric functions which are regular at the centre and the interior of the body. We demonstrate that the new class of exact solutions is physically reasonable and may be utilized to model a compact object. A detailed graphical analysis of the matter variables shows that the criteria for physical acceptability are satisfied. The energy conditions are satisfied, causality is not violated, and the body is stable in terms of cracking, the Harrison–Zeldovich–Novikov stability criterion, and the adiabatic index inequality. It is, therefore, possible to geometrically describe a compact object with a conformal symmetry for an astrophysical application.
Highlights
It is necessary to solve the nonlinear Einstein field equations to describe physical systems in relativistic astrophysics
We have pursued the solution of the Einstein field equations with anisotropies by imposing a conformal Killing vector
This has been pursued by Mateos and Trancanelli [36] for strong coupled anisotropic plasmas, by Jain et al [37] for anisotropic fluids from dilaton driven holography, and Giataganas et al [38] for Einstein-axiondilaton systems. These results provide a path to obtain such gravity solutions which have been useful in explaining properties of strongly coupled plasmas in the papers of Giataganas [39] and Chernicoff et al [40]. We expect that this alternate approach may lead to useful insights in studying stellar systems that have been analyzed in this paper with conformal motions
Summary
It is necessary to solve the nonlinear Einstein field equations to describe physical systems in relativistic astrophysics. Several stellar models with spherical symmetry in general relativity have been generated with a conformal Killing vector, see for example the recent paper of Kileba Matondo et al [13]. Finding an exact solution to the Einstein field equations do not always lead to a physically acceptable model for a relativistic star. Physical criteria such as causality and regularity at the centre should be satisfied. 2, we present the appropriate Einstein field equations with an anisotropic fluid distribution for a spherically symmetric spacetime containing a conformal Killing vector.
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