Neutron Stars in f(R) Gravity with Perturbative Constraints

TL;DR

This paper studies neutron stars in $f(R)$ gravity under perturbative constraints to retain a fundamentally second-order, gauge-invariant framework. It derives the modified Tolman-Oppenheimer-Volkoff equations and demonstrates that the exterior solution remains Schwarzschild–de Sitter, while interior structure is computed for a polytropic equation of state with $f(R)=R^2$ as representative. The results indicate that variations in the mass-radius relation can mimic changes in the equation of state, illustrating a gravity–EOS degeneracy for purely structural observables. However neutron-star cooling—sensitive to central density—offers a promising avenue to bound the theory’s parameter and the study outlines future work to quantify such cooling-based constraints.

Abstract

We study the structure of neutron stars in f(R) gravity theories with perturbative constraints. We derive the modified Tolman-Oppenheimer-Volkov equations and solve them for a polytropic equation of state. We investigate the resulting modifications to the masses and radii of neutron stars and show that observations of surface phenomena alone cannot break the degeneracy between altering the theory of gravity versus choosing a different equation of state of neutron-star matter. On the other hand, observations of neutron-star cooling, which depends on the density of matter at the stellar interior, can place significant constraints on the parameters of the theory.

Figures (4)

• Figure 1: The mass of a neutron star as a function of its central density in an $f(R)= R^2$ gravity theory for different values of the small parameter $\bar{\alpha}$. The index of the polytropic equation of state was set to $\Gamma = 9/5$.
• Figure 2: The ratio $\xi$ (see Eq. \ref{['eq:xi']}) as a function of the parameter $\bar{\alpha}$, for stars with central densities $\log \bar{\rho}_c =\; -2,\;-3,\;-4$ (dotted, solid and dashed lines respectively). The ratio $\xi$ measures the degree of perturbative validity of the stellar models. A necessary condition for perturbative validity is $\xi < 1$.
• Figure 3: The mass-radius relation of neutron stars for a polytropic equation of state with $\Gamma=9/5$, in an $f(R)=\alpha R^2$ gravity for different values of the parameter $\bar{\alpha}$.
• Figure 4: The central density $\bar{\rho}$ of neutron stars with different masses $\bar{M}$ as a function of the parameter $\bar{\alpha}$. Larger positive deviations from general relativity require larger central densities for the same neutron-star mass and, therefore, lead to shorter cooling times. On the other hand, larger negative deviations require smaller central densities and lead to longer cooling time.