Modified TOV in gravity's rainbow: properties of neutron stars and dynamical stability conditions

TL;DR

This study explores how gravity's rainbow modifies neutron star properties, including mass, radius, and stability, by incorporating rainbow functions and the cosmological constant, and compares theoretical predictions with observational data.

Contribution

It extends hydrostatic equilibrium equations to higher dimensions in gravity's rainbow and analyzes the impact of rainbow functions on neutron star characteristics and stability.

Findings

Rainbow functions significantly affect mass-radius relations.

Neutron stars remain dynamically stable under gravity's rainbow.

Theoretical results align with observational data.

Abstract

In this paper, we consider a spherical symmetric metric to extract the hydrostatic equilibrium equation of stars in $(3+1)-$dimensional gravity's rainbow in the presence of cosmological constant. Then, we generalize the hydrostatic equilibrium equation to $d$-dimensions and obtain the hydrostatic equilibrium equation for this gravity. Also, we obtain the maximum mass of neutron star using the modern equations of state of neutron star matter derived from the microscopic calculations. It is notable that, in this paper, we consider the effects of rainbow functions on the diagrams related to the mass-central mass density ($M$-$\rho _{c}$) relation and also the mass-radius ($M$-$R$) relation of neutron star. We also study the effects of rainbow functions on the other properties of neutron star such as the Schwarzschild radius, average density, strength of gravity and gravitational redshift. Then, we apply the cosmological constant to this theory to obtain the diagrams of $M$-$\rho _{c}$ (or $M$-$R$) and other properties of these stars. Next, we investigate the dynamical stability condition for these stars in gravity's rainbow and show that these stars have dynamical stability. We also obtain a relation between mass of neutron stars and Planck mass. In addition, we compare obtained results of this theory with the observational data.