Generalized spheroidal spacetimes in 5-D Einstein–Maxwell–Gauss–Bonnet gravity

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 generalizes 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 FinchSkea 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.

Static conformal models for anisotropic charged fluids

“…Pandya et al [27] found models with geometry consistent with observed radii and masses for dense stars. The Finch-Skea geometry has also been studied for higher dimensional gravitational geometries [28][29][30][31] and trace-free gravity [32].…”

Relativistic compact stars with charged anisotropic matter

“…Plugging in the typical values from Eqs. (23)(24)(25), and using the above expressions, we get the different forces in a straightforward way, which leads to:…”

Exploring Physical Properties of Gravitationally Decoupled Anisotropic Solution in 5D Einstein‐Gauss‐Bonnet Gravity

“…The EGB facilitates a natural generalization of GR to higher dimensions. [ 26 ] This is achieved by including higher curvature while preserving the fundamental elements of GR such as the conservation laws via the Bianchi identities, diffeomorphism invariance and quasi‐linear, second order equations of motion. It is well‐known that the EGB theory is a special case of the Lovelock [ 27 ] theory arising from the order Lovelock Lagrangian.…”