White Dwarf Structure in $f(Q)$ Gravity

TL;DR

This paper explores how modifications in $f(Q)$ gravity affect white dwarf structures, revealing deviations from general relativity and potential observational signatures in maximum mass and radius.

Contribution

It introduces a detailed numerical analysis of white dwarf equilibrium configurations within $f(Q)$ gravity, highlighting the impact of nonmetricity corrections on stellar properties.

Findings

Nonmetricity corrections significantly alter high-density white dwarf structure.

Increasing $eta$ reduces the maximum white dwarf mass below Chandrasekhar limit.

Results are consistent with observational data of ultra-massive white dwarfs.

Abstract

In this work, we investigate the equilibrium structure of white dwarfs within the covariant formulation of symmetric teleparallel $f(Q)$ gravity, in which gravity is described by the nonmetricity scalar $Q$ instead of spacetime curvature. We consider static and spherically symmetric stellar configurations composed of cold, fully degenerate electron matter and adopt a quadratic form of the gravitational Lagrangian, $f(Q)=Q+\alpha Q^{2}$, where $\alpha$ quantifies deviations from general relativity. The corresponding modified stellar structure equations are solved numerically in conjunction with the Chandrasekhar equation of state. We examine the impact of the parameter $\alpha$ on the internal structure and global properties of white dwarfs, including the radial profiles of the metric potentials, pressure, density, nonmetricity scalar, and enclosed mass, as well as the mass--radius relation. While negative values of $\alpha$ were explored, they lead to unstable or nonphysical configurations at high densities; therefore, the analysis is restricted to non-negative values of $\alpha$. Our results show that nonmetricity corrections produce significant deviations from the general relativistic predictions in the high-density regime. In particular, increasing $\alpha$ modifies the equilibrium configurations and leads to a reduction in the maximum mass relative to the Chandrasekhar limit, accompanied by corresponding changes in the stellar radius and interior profiles. For $\alpha = 5\times10^{18}\,\mathrm{cm^2}$, we obtain a maximum mass $M_{\max}=1.3519\,M_{\odot}$ and radius $R=2228.85\,\mathrm{km}$, which are consistent with the observational constraints of the ultra-massive white dwarf ZTF J1901+1458. These findings suggest that white dwarfs can provide a complementary astrophysical probe for testing the viability of $f(Q)$ gravity in the strong-field regime.