Abstract
We study exact models for anisotropic gravitating stars with conformal symmetry. The gravitational potentials are related explicitly by the conformal vector. We use this relationship between the metric potentials to find new classes of exact solutions to the field equations. We identify a particular model to study the physical features and demonstrate that the model is well behaved. In particular the criteria for stability are satisfied. We regain masses, radii and surface redshifts for the compact objects PSR J1614-2230 and SAX J1808.4-3658.
Highlights
A conformal symmetry in spacetime places restrictions on the gravitational potentials. This happens because in the presence of a conformal Killing vector, null geodesics are mapped to null geodesics; the change in the metric is proportional to the metric as it is Lie dragged along a congruence of curves
Exact solutions generated in this way are useful in relativistic astrophysics and may be used to model dense stars
In our approach we have specified one of the gravitational potentials to yield an exact solution to the Einstein field equations with anisotropic matter distributions
Summary
A conformal symmetry in spacetime places restrictions on the gravitational potentials. In our approach we have specified one of the gravitational potentials to yield an exact solution to the Einstein field equations with anisotropic matter distributions. For stellar objects with high densities greater than nuclear matter density, it is required that the Tolman–Oppenheimer–Volkov equation describing the equilibrium condition for charged fluid elements subject to gravitational, electric and hydrostatic forces, to be modified because of another interaction force due to the pressure anisotropy within the star It was suggested by Usov [33] that the existence of strong electric field could be generated by the presence of anisotropy. Manjonjo et al [4] have shown that the existence of a conformal Killing vector implies a relationship relating the gravitational potentials This provides a systematic method of generating solutions of the Einstein and Einstein–Maxwell systems of field equations.
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