New models in general relativity and Einstein-Gauss-Bonnet gravity.
Date
2021
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Abstract
We generate the Einstein-Gauss-Bonnet field equations in five dimensions for a spherically symmetric static spacetime. The matter distributions considered are both neutral
and charged. The introduction of a coordinate transformation brings the condition of
isotropic pressure to a single master ordinary differential equation that is an Abel equation of the second kind. We demonstrate that the master equation can be reduced to
a first order nonlinear canonical differential equation. Firstly, we consider uncharged
gravitating matter. Several new classes of exact solutions are found in explicit and
implicit forms. One of the potentials is determined completely. The second potential
satisfies a constraint equation. Secondly, we study charged gravitating matter with
Maxwell’s equations. We find new classes of exact charged solutions in explicit and implicit forms using two approaches. In the first approach, we can find new exact models
without integration. In the second approach the Abelian pressure isotropy equation has
to be integrated, which we demonstrate is possible in a number of cases. The inclusion
of the electromagnetic field provides an extra degree of freedom that leads to viable
exact solutions. An interesting feature characterising the new models is that a general
relativity limit does not exist. Our new solutions exist only in Einstein-Gauss-Bonnet
gravity. In addition, we have considered the dynamics of a shear-free fluid in Einstein
gravity in higher dimensions with nonvanishing heat flux in a spherically symmetric
manifold. This endeavour generates new exact models, being a generalisation of models
developed in earlier treatments.
Description
Masters Degree. University of KwaZulu-Natal, Durban.