Dark-Energy Anisotropic Compact Configurations in 4D Einstein-Gauss-Bonnet Gravity: From Structure to Observational Viability

TL;DR

This work investigates anisotropic dark-energy compact stars within regularized $4$D Einstein–Gauss–Bonnet gravity, modeling the interior with a modified Chaplygin gas and a quasi-local anisotropy closure. By numerically solving the modified TOV equations across a broad grid of GB coupling $α$ and anisotropy $β$, the authors generate mass–radius sequences, compactness, and internal profiles, and perform a multi-faceted stability analysis using the turning-point criterion, the radial adiabatic index $γ_r$, and the radial/transverse sound speeds $v_r^2$, $v_t^2$. They find that positive $α$ and $β>0$ systematically increase the maximum mass and radius, enabling configurations that can exceed $2\,M_⊙$ while respecting causality and the modified Buchdahl bound in 4DEGB. Comparisons with NICER, GW170817, GW190814, and massive pulsar data delineate observationally viable regions in $(α,β)$, suggesting anisotropic dark-energy stars in 4DEGB as viable, testable ultra-compact alternatives to neutron stars and black holes, and motivating future multi-messenger searches for higher-curvature signatures.

Abstract

We address the equilibrium configurations and stability properties of anisotropic compact stars whose interior is described by a modified Chaplygin gas (MCG) equation of state in the framework of the regularized four-dimensional Einstein-Gauss-Bonnet (4DEGB) theory. Applying a quasi-local prescription for the pressure anisotropy, we derive the modified Tolman-Oppenheimer-Volkoff (TOV) equations and integrate them numerically over a large parameter space in the Gauss-Bonnet coupling $α$ and the degree of anisotropy $β$. We provide mass-radius sequences, mass-compactness, energy density, and pressure profiles, and perform a full stability analysis based on the turning-point criterion, the radial adiabatic index $γ_r$, and the radial and transverse sound speeds $v_r^2$ and $v_t^2$. Our results show that positive $α$ and positive anisotropy $(β> 0)$ systematically increase the maximum mass and radius, enabling then configurations that exceed $2\,M_\odot$ while still obeying causality and the modified Buchdahl bound in 4DEGB gravity. A comparison with the latest astrophysical constraints (NICER, GW170817, GW190814, and massive-pulsar measurements) identifies regions of the $(α,β)$ parameter space that are observationally allowable. In conclusion, anisotropic dark-energy stars in 4DEGB gravity provide viable, observationally testable ultra-compact alternatives to normal neutron stars and black holes, and also potentially open rich avenues for further multi-messenger searches for higher-curvature effects.

Figures (7)

• Figure 1: These profiles are the energy density $\rho(r)$ (left panel) and radial pressure $p_r(r)$ (right panel) for anisotropic dark-energy stars in 4D Einstein–Gauss–Bonnet gravity with different values of the Gauss–Bonnet coupling parameter $\alpha$ in the range $[-10, +10]~\mathrm{km^2}$. The numerical integration is performed using the parameter set summarized in Table \ref{['table1']}, with the equation of state constants fixed at $A = \sqrt{0.4}$, $B = 0.23 \times 10^{-3}~\mathrm{km^{-2}}$, and $\beta = 0.5$. The solutions remain regular throughout the stellar interior, exhibit finite central values and monotonic radial behavior, and satisfy all physically acceptable energy conditions.
• Figure 2: These profiles are the energy density $\rho(r)$ (left panel) and radial pressure $p_r(r)$ (right panel) for anisotropic dark-energy stars in 4D Einstein–Gauss–Bonnet gravity with different values of the anisotropy parameter $\beta$ in the range $[-1.0, +1.0]$. The numerical solutions are obtained using the same parameter set summarized in Table \ref{['table2']}, where the equation of state constants are fixed at $A = \sqrt{0.4}$, $B = 0.23 \times 10^{-3}~\mathrm{km^{-2}}$, and $\alpha = 5~\mathrm{km^2}$. The case $\beta = 0$ corresponds to the isotropic configuration, while negative and positive values of $\beta$ represent increasingly anisotropic distributions with dominant radial and tangential pressures, respectively. The solutions remain regular throughout the stellar interior, exhibit finite central values and monotonic radial behavior, and satisfy all physically acceptable energy conditions.
• Figure 3: Mass-radius (left panel) and mass versus compactness (right panel) relations for compact stars in 4DEGB gravity with varying coupling parameter $\alpha$ (ranging from $-10$ km$^2$ to $+10$ km$^2$). The equation of state and model parameters are identical to those adopted in Figure \ref{['fig1']}. The left panel includes observational constraints from massive pulsars PSR J0952$-$0607 with $M = 2.35 \pm 0.17\,M_{\odot}$Romani:2022jhd, PSR J0740+6620 with $M = 2.08^{+0.07}_{-0.07}\,M_{\odot}$Fonseca:2021wxt, PSR J0348+0432 with $M = 2.01 \pm 0.04\,M_{\odot}$Antoniadis:2013pzd, and the low-mass compact object in HESS J1731$-$347 Doroshenko:2022nwp. Gravitational wave constraints from GW170817 LIGOScientific:2018cki and the secondary component of GW190814 with mass $2.50$--$2.67\,M_{\odot}$LIGOScientific:2020zkf are also shown. Different values of $\alpha$ demonstrate how the GB coupling modifies the stellar structure, with the General Relativity (GR) limit corresponding to $\alpha = 0$ km$^2$.
• Figure 4: Mass-radius (left panel) and mass versus compactness (right panel) relations for isotropic and anisotropic compact stars in 4DEGB gravity with varying anisotropy parameter $\beta$ (ranging from $-1.0$ to $+1.0$). The equation of state and model parameters are identical to those adopted in Figure \ref{['fig2']}, while the observational constraints are from Fig. \ref{['fig3']}. The case $\beta = 0$ corresponds to the isotropic configuration, while negative and positive values of $\beta$ represent different degrees of pressure anisotropy.
• Figure 5: Gravitational mass $M/M_{\odot}$ as a function of central energy density $\rho_c$ for anisotropic dark energy stars in 4DEGB gravity. Left: Sequences for varying GB coupling parameter $\alpha$. Right: Sequences for different anisotropy parameters $\beta$. Black dots denote maximum-mass configurations along each curve, marking the transition from stable to unstable stellar configurations according to the static stability criterion ($dM/d\rho_c < 0$). For consistency, the parameter sets listed in Tables \ref{['table1']} and \ref{['table2']} are employed in the present analysis.