Stellar modeling within regularized 4D Einstein-Gauss-Bonnet gravity in light of current astrophysical constraints

TL;DR

This paper investigates interior solutions for isotropic compact stars in the framework of regularized four-dimensional Einstein-Gauss-Bonnet gravity, using a CFL9 quark-matter EoS to model dense stellar matter. By solving the modified TOV equations that arise from the regularized GB action, the authors quantify how the GB coupling $\alpha$ alters mass-radius sequences, compactness, and the $M(\rho_c)$ relation. They find that GB corrections tend to make stars less compact while permitting moderately higher maximum masses, with $\alpha$ in the range of $5$–$10$ $\text{km}^{2}$ yielding 9.7%–19.9% increases in $M_{\max}$ and 1.3%–2.4% increases in radii, all compatible with multi-messenger constraints including GW190814 and NICER measurements. These results support regularized GB corrections as a plausible extension of GR in strong-field regimes and motivate further work on tidal deformability and rotating configurations.

Abstract

In this study we obtain interior solutions and investigate structural properties of isotropic compact stars in the framework of four-dimensional regularized Einstein-Gauss-Bonnet (4DEGB) gravity. For stellar matter content, we adopt a widely used quark-matter model that approximates a realistic equation of state (EoS). By numerically integrating the modified Tolman-Oppenheimer-Volkoff equations, we obtain interior solutions for static, spherically symmetric fluid spheres. The resulting sequences are compared directly with the predictions of General Relativity (GR). Our analysis focuses on three diagnostic indicators: (i) the mass-radius profiles under GR and three representative choices of the Gauss-Bonnet coupling; (ii) the stellar compactness factor, $C \equiv M/R$; and (iii) the relation between stellar mass and central energy density. Recent observational studies suggest that the maximum masses inferred from the mass-radius relation may be larger than previously expected. To address this, we include a comparative set of constraints from multi-messenger astrophysical observations, including gravitational-wave event GW190814, as well as X-ray measurements from NICER for PSR~J0740+6620 and PSR~J0030+0451. These data provide stringent, astrophysically grounded tests of the viability of the models discussed here. Our results indicate that compact stars within 4DEGB gravity are systematically less compact and achieve moderately higher maximum masses compared to the GR case. This trend is consistent with recent theoretical analyses of compact stars in higher-curvature gravity theories and with constraints from multi-messenger astrophysics. Together, these findings suggest that regularized Gauss-Bonnet corrections constitute a plausible extension of GR in the strong-field regime.

Figures (2)

• Figure 1: Stellar mass in solar masses versus stellar radius in km assuming $\alpha=5.00$ (solid brown line), $\alpha=7.50$ (solid red line), and $\alpha=10.0$ (solid blue line). For comparison reasons, we have also shown the mass-to-radius relationship for the case of GR $(\alpha=0)$ (dashed black line). We have included one horizontal strip around 2.5 solar masses. The light-blue band corresponds to the GW event 190814 LIGOScientific:2020zkf. In addition, there are four regions corresponding to: a) the light HESS compact object (purple region) Doroshenko:2022nwp, b) the pulsar J0740+6620 (cyan region) Miller:2021qhaRiley:2021pdl, c) the pulsar J0030+0451 (red region), Miller:2019cac, and d) the light HESS compact object (purple region) Choudhury:2024xbk. The intensity of the color represents 65$\%$, 90$\%$ and 99$\%$ confidence levels (CLs) from darker to lighter color, delineating the observationally allowed mass-radius parameter space for each compact object.
• Figure 2: Left panel: Factor of compactness, $C\equiv M/R$, versus stellar mass (in solar masses), considering the same meaning of the color code as in the previous figure. Right panel: Stellar mass as a function of the (normalized) central energy density of quark matter, considering the same meaning of the color code as in the previous figure.