Tolman IV fluid sphere in bigravity

TL;DR

This paper models compact stars using Tolman IV spacetime within bigravity, analyzing how the scale parameter influences the equation of state, stability, and physical properties of the stars.

Contribution

It introduces a bigravity-based model for compact stars with a scale parameter affecting the EoS, extending previous models to include background metric effects.

Findings

Lower scale parameter k leads to stiffer EoS.

Sound speed and adiabatic index increase with lower k.

Solutions satisfy energy conditions and are stable.

Abstract

We present Tolman IV spacetime representing compact fluid sphere in bigravity. Here we have explored the effect of scale parameter $k$ in the local matter distribution of compact stars. We have model for three well-known compact stars and it shows that for lower values of $k$ leads to stiffer EoS. This claim is also supported by the graphical analysis. It can be observed that the sound speed and the adiabatic index are more for lower values of $k$. It is also seen that all the solutions of Einstein's field equations are still satisfying the field equations in the presence of a background metric $\gamma_{\mu \nu}$. However, the density and pressure does modified by extra term from the constant curvature background, thus affecting the EoS. One can also think that the parameter $\alpha \equiv 1/k^2$ as coupling constant between the $g_{\mu \nu}$ and $\gamma_{\mu \nu}$ and consequently more the coupling stiffer is the EoS. As $k\rightarrow \infty$, the background de-Sitter spacetime reduces to Minkowski's spacetime and the coupling vanishes. The solution satisfy the causality condition, all the energy conditions and equilibrium under gravity and hydrostatic forces. The stability of the local stellar structure is enhanced by reducing the scalar curvature of the background spacetime.