Frozen Neutron Stars in Four-Dimensional Non-polynomial Gravities

TL;DR

This work analyzes neutron stars in four-dimensional non-polynomial gravity, solving the modified TOV equations for three representative EOS to test the persistence and properties of NS solutions under higher-curvature corrections. By examining two uniparametric forms of the characteristic function $h(ψ)$, the authors show that increasing the modification parameter $α$ yields larger radii and masses and can drive the star into a frozen state with a near-horizon surface, effectively mimicking an extremal black hole from afar. The frozen state emerges universally across EOS and can occur even at finite truncations of the infinite tower of corrections, with the mass–radius curve terminating near the black-hole branch and the EOS playing a secondary role in setting the critical density $ρ_{cr}$. Observational constraints from GW170817 and pulsar measurements still permit frozen neutron stars within the admissible $(α,ρ_c)$ range, motivating further stability analyses and discriminants (tidal deformability, QNM spectra) to distinguish these objects from true black holes in future observations.

Abstract

This paper investigates the structure and properties of neutron stars in four-dimensional non-polynomial gravities. Solving the modified Tolman-Oppenheimer-Volkoff equations for three different equations of state (BSk19, SLy4, AP4), we confirm that neutron star solutions remain in existence. As the modification parameter $α$ increases, neutron stars grow in both radius and mass. We find that, when the parameter $α$ is sufficiently large, a frozen state emerges at the end of the neutron-star sequence. In this state, the metric functions approach zero extremely close to the stellar surface, forming a critical horizon, making it nearly indistinguishable from a black hole to an external observer. Such a frozen neutron star constitutes a universal endpoint of the neutron-star sequence in this theory, independent of the choice of the equation of state. Based on our results and current observational constraints, we derive bounds on the modification parameter $α$ and show that frozen neutron stars remain allowed in the bounds.

Figures (10)

• Figure 1: The black curves $f(r)$ correspond to different configurations of the mass function $m$: the dashed curve ($m = 0.5M_{\text{cr}}$) represents a horizonless regular spacetime; the solid curve ($m = M_{\text{cr}}$), an extremal black hole with a single horizon; and the dot-dashed curve ($m = 2M_{\text{cr}}$), a regular black hole with two horizons.
• Figure 2: The left and right subplots show the radial pressure profiles for different characteristic functions ($\frac{\psi}{1-\alpha^2\psi^2}$ and $\frac{\psi}{\sqrt{1-\alpha^2\psi^2}}$) at a fixed central density $0.8\times 10^{15} \rm[g/cm^3]$, plotted for various values of the modification parameter $\alpha$. Results from the BSk19(black), SLy4(red), and AP4(blue) equations of state are compared.
• Figure 3: The left and right subplots show $N^2(r)f(r)$ ($-g_{tt}$) for different characteristic functions ($\frac{\psi}{1-\alpha^2\psi^2}$ and $\frac{\psi}{\sqrt{1-\alpha^2\psi^2}}$) at a fixed central density $0.8\times 10^{15} \rm[g/cm^3]$, plotted for various values of the modification parameter $\alpha$. Results from the BSk19(black), SLy4(red), and AP4(blue) equations of state are compared.
• Figure 4: The left and right subplots show $f(r)$ ($1/g_{rr}$) for different characteristic functions ($\frac{\psi}{1-\alpha^2\psi^2}$ and $\frac{\psi}{\sqrt{1-\alpha^2\psi^2}}$) at a fixed central density $0.8\times 10^{15} \rm[g/cm^3]$, plotted for various values of the modification parameter $\alpha$. Results from the BSk19(black), SLy4(red), and AP4(blue) equations of state are compared.
• Figure 5: The dependence of the compactness $\mathcal{C}$ and average density $\bar{\rho}$ on the modification parameter $\alpha$ is depicted in the left and right subplots for different characteristic functions ($\frac{\psi}{1-\alpha^2\psi^2}$ and $\frac{\psi}{\sqrt{1-\alpha^2\psi^2}}$). Results from the BSk19(black), SLy4(red), and AP4(blue) equations of state are compared.