Relativistic stars in f(R) gravity

Abstract

We study the strong gravity regime in viable models of so-called f(R) gravity that account for the observed cosmic acceleration. In contrast with recent works suggesting that very relativistic stars might not exist in these models, we find numerical solutions corresponding to static star configurations with a strong gravitational field. The choice of the equation of state for the star is crucial for the existence of solutions. Indeed, if the pressure exceeds one third of the energy density in a large part of the star, static configurations do not exist. In our analysis, we use a polytropic equation of state, which is not plagued with this problem and, moreover, provides a better approximation for a realistic neutron star.

Figures (4)

• Figure 1: Potential $V$ (in units of $M_P^2 {R_0}$) as a function of $\phi$ (in Planck units) for $n=1$ and $x_\infty=3.6$. The lower black dot corresponds to the de-Sitter attractor while the upper-right dot shows the curvature singularity.
• Figure 2: Energy density ${\tilde{\rho}}$ (upper solid line), pressure ${\tilde{P}}$ (lower solid line) and the combination ${\tilde{\rho}}-3{\tilde{P}}$ (dashed line), in units of the central density $\rho_c$, as functions of the radial coordinate $r$ (in units of $M_P\tilde{\rho}_c^{-1/2}$).
• Figure 3: Profile of the scalar field $\phi$ (in Planck units), shown by solid (blue) line, as a function of the radius (in units of $M_P\tilde{\rho}_c^{-1/2}$), for the model (\ref{['staro']}) with $n=1$, $x_\infty=3.6$ and $v_0=10^{-4}$. The value $\phi_{\rm min}$ for the minimum of the effective potential is plotted by dashed (gray) line.
• Figure 4: Effective potential $U(\phi)=-V(\phi)$ in which the scalar field $\phi$ "moves" under the action of the force ${\cal F}$, in the picture of the classical mechanic analogy.