New models in general relativity and Einstein-Gauss-Bonnet gravity.

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.