Anisotropic compact stars in $D\rightarrow 4$ limit of Gauss-Bonnet gravity

TL;DR

This paper derives a new interior solution for anisotropic compact stars within the $D o 4$ Gauss-Bonnet gravity framework, demonstrating stability and consistency with observational data of pulsars.

Contribution

It introduces a novel spherically symmetric interior solution in 4D Gauss-Bonnet gravity, incorporating specific metric potentials and matching observational data.

Findings

Energy-momentum tensor components are finite at the star's center and surface.

The equations of state exhibit nonlinear behavior influenced by the Gauss-Bonnet term.

The model remains stable under static conditions and aligns with pulsar data.

Abstract

In the frame of Gauss-Bonnet gravity and in the limit of $D\to 4$, based on the fact that spherically symmetric solution derived using any of regularization schemes will be the same form as the original theory \cite{Banerjee:2020yhu,Hennigar:2020lsl,Casalino:2020kbt,Aoki:2020lig}, we derive a new interior spherically symmetric solution assuming specific forms of the metric potentials that have two constants . Using the junction condition we determine these two constants. By using the data of the star EXO $1785-248 $, whose mass is $ { M=1.3\pm0.2 \,{\textrm M}_\odot}$ and radius $ { l=8.849\pm0.4\,{\textrm km}}$, we calculate the numerical values of these constants, in terms of the dimensionful coupling parameter of the Gauss-Bonnet term, and eventually, we get real values for these constants. In this regard, we show that the components of the energy-momentum tensor has a finite value at the center of the star as well as a smaller value to the surface of the star. Moreover, we show that the equations of the state behave in a non-linear way due to the impact of the Gauss-Bonnet term. Using the Tolman-Oppenheimer-Volkoff equation, the adiabatic index, and stability in the static state we show that the model under consideration is always stable. Finally, the solution of this study is matched with observational data of other pulsars showing satisfactory results