Generalised spheroidal spacetimes in 5-D Einstein--Maxwell--Gauss--Bonnet gravity

TL;DR

This paper derives and analyzes exact solutions for static 5-dimensional Einstein--Maxwell--Gauss--Bonnet gravity, extending spheroidal models and examining their physical viability, including effects of the Gauss--Bonnet term on pressure and density profiles.

Contribution

It introduces a generalized spheroidal ansatz in 5-D Einstein--Maxwell--Gauss--Bonnet gravity and explores its physical implications, including special cases and the impact of the Gauss--Bonnet term.

Findings

Gauss--Bonnet term corrects pressure and sound speed issues

Higher densities are achievable compared to Einstein gravity

Solutions satisfy physical and energy conditions

Abstract

The field equations for static EGBM gravity are obtained and transformed to an equivalent form through a coordinate redefinition. A form for one of the metric potentials that generalises the spheroidal ansatz of Vaidya--Tikekar superdense stars and additionally prescribing the electric field intensity yields viable solutions. Some special cases of the general solution are considered and analogous classes in the Einstein framework are studied. In particular the Finch--Skea ansatz is examined in detail and found to satisfy the elementary physical requirements. These include positivity of pressure and density, the existence of a pressure free hypersurface marking the boundary, continuity with the exterior metric, a subluminal sound speed as well as the energy conditions. Moreover, the solution possesses no coordinate singularities. It is found that the impact of the Gauss--Bonnet term is to correct undesirable features in the pressure profile and sound speed index when compared to the equivalent Einstein gravity model. Furthermore graphical analyses suggest that higher densities are achievable for the same radial values when compared to the 5--dimensional Einstein case. The case of a constant gravitational potential, isothermal distribution as well as an incompressible fluid are studied. All exact solutions derived exhibit an equation of state explicitly.