White Dwarf Structure in $f(Q)$ Gravity

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, $f(Q)=Q+αQ^{2}$, where $α$ 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 $α$ 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 $α$ were explored, they lead to unstable or nonphysical configurations at high densities; therefore, the analysis is restricted to non-negative values of $α$. Our results show that nonmetricity corrections produce significant deviations from the general relativistic predictions in the high-density regime. In particular, increasing $α$ 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 $α= 5\times10^{18}\,\mathrm{cm^2}$, 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.

Figures (10)

• Figure 1: Radial profile of the metric function $A(r)$ inside the white dwarf for different positive values of the parameter $\alpha$ in $f(Q)$ gravity. The function increases smoothly from the stellar center toward the surface, with larger values of $\alpha$ corresponding to more extended stellar configurations compared to the general relativistic case ($\alpha=0$).
• Figure 2: Radial profile of the metric function $B(r)$ inside the white dwarf for different positive values of the parameter $\alpha$ in $f(Q)$ gravity. The function increases smoothly from the stellar center toward the surface, with larger values of $\alpha$ leading to lower values of $B(r)$ compared to the general relativistic case ($\alpha=0$).
• Figure 3: Radial profile of the nonmetricity scalar $Q(r)$ inside the white dwarf for different positive values of the parameter $\alpha$ in $f(Q)$ gravity. The scalar $Q(r)$ is nearly zero at the center, reaches a negative minimum in the interior, and approaches zero toward the stellar surface. Increasing $\alpha$ reduces the magnitude of this minimum compared to the general relativistic case ($\alpha=0$).
• Figure 4: Radial profile of the pressure $P(r)$ inside the white dwarf for different positive values of the parameter $\alpha$ in $f(Q)$ gravity. The pressure decreases monotonically from its central value to zero at the stellar surface, while increasing $\alpha$ leads to more extended configurations compared to the general relativistic case ($\alpha=0$).
• Figure 5: Radial profile of the density $\rho(r)$ inside the white dwarf for different positive values of the parameter $\alpha$ in $f(Q)$ gravity. The density decreases monotonically from the central value toward the stellar surface, while increasing $\alpha$ leads to more extended configurations compared to the general relativistic case ($\alpha=0$).