Possible existence of super Chandrasekhar mass limit in the matter-curvature coupled gravity

Abstract

We investigate white dwarfs in the framework of f(R,L_m) and f(R,L_m,T) gravity to explore the Chandrasekhar Limit. We have considered two functional forms of f(R,L_m) and one functional form of f(R,L_m,T) gravity. Considering the matter Lagrangian L_m=p, we calculate modified TOV equations for each of the forms. By employing the fully degenerate electron gas equation of state in the modified TOV equations, we derive the mass-radius relation for each functional form of both f(R,L_m) and f(R,L_m,T) gravity. Our models imply modifications in the Chandrasekhar mass limit that deviate significantly from the GR and the Newtonian cases. In the f(R,L_m, T)$ gravity, the new mass limit of the white dwarf can reach upto 1.537\,\mathrm{M}_\odot while in f(R,L_m) with the quadratic extension can goes upto 1.52\,\mathrm{M}_\odot and with exponential extension upto 2.08\,\mathrm{M}_\odot. Further, we analyze the static stability criterion, the gravitational redshift, and the adiabatic indices. For the power-law form of f(R,L_m) and the non-linear form of f(R,L_m,T) gravity, significant variations are observed at higher densities (ρ_c > 10^{10}\, \mathrm{g/cm^3}), while substantial changes are noted at much lower central densities in the case of exponential form of f(R,L_m) gravity. We also calculate compactness and gravitational redshift, which are much lower than those of neutron stars and black holes. Stability is also confirmed by adiabatic indices, which show that all models yield Γ> 4/3 throughout the interiors of WDs. Overall, our models provide a viable framework for the existence of super-Chandrasekhar mass limit, extending beyond the classical predictions in the Newtonian and/or GR cases.

Figures (9)

• Figure 1: $M-R$ plot for WDs within $f(\mathcal{R}, \mathcal{L}_m)$ gravity power-law form. The solid black curve represents the predictions of GR, while the colored curves depict various values of the coupling parameter $\sigma$, which range from $-1.50\eta$ to $+3.0\eta$, with $\eta$ approximately equal to $1.8 \times 10^{-32}\,\mathrm{cm}^2\,/\mathrm{dyne}$.
• Figure 2: $M-R$ diagram for WDs in the $f(\mathcal{R},\mathcal{L}_m)$ gravity with an exponential form. For simplification purposes, we set the value of $\beta=2$ with units of $\mathrm{cm}^2\,\mathrm{dyne}^{-1}$ while considering values of $\gamma$ from $-2.0 \zeta$ to $5.50\zeta$. The solid black line represents the predictions from GR, while the dashed lines represent various values of the coupling parameter $\gamma$, measured in dimensionless units with the value of $\zeta=10^{-1}$.
• Figure 3: $M-R$ plot for WDs within the non-linear model of $f(\mathcal{R}, \mathcal{L}_m, \mathcal{T})$ gravity. The solid black curve represents the predictions of GR, while the colored curves depict various values of the coupling parameter $\alpha$, which range from $-3.0\chi$ to $+2.0\chi$, with $\chi$ approximately equal to $1.6 \times 10^{-12}\,\mathrm{cm}^3\,/\mathrm{g}$.
• Figure 4: $M-\rho_c$ plots within the framework of the power-law and exponential models of $f(\mathcal{R,L}_m)$ gravity. The solid black line represents the GR, while colored curves represent the different values of $\sigma$ and $\gamma$.
• Figure 5: $M-\rho_c$ plots within the non-linear model of $f(\mathcal{R,L}_m,\mathcal{T})$ gravity. The solid black lines represent the GR, whereas the colored curves represent the various values of the coupling parameter $\alpha$.