Compact stars in Einstein-scalar-Gauss-Bonnet gravity: regular and divergent scalar field configurations

Abstract

We investigate static, spherically symmetric solutions in Einstein-scalar-Gauss-Bonnet gravity non-minimally coupled to a massless real scalar field, both in vacuum and in the presence of fermionic matter. Focusing on a specific quadratic scalar-Gauss-Bonnet coupling, we identify two distinct classes of compact objects: one with a regular scalar field at the origin -- connected to general relativity in an appropriate limit -- and another {one} with a divergent scalar field at the origin but a regular geometry. We analyze both purely scalar and matter-supported (hybrid) configurations, showing that the former can describe a broad class of compact objects, while the latter can reproduce neutron star-like masses even when modeled with a simple polytropic equation of state. Furthermore, we highlight distinctive phenomenological signatures, including the ability of these stars to exceed known compactness limits and their potential to act as gravitational wave super-emitters. We also examined the motion of test particles non-minimally coupled to the scalar field and showed the existence of stable circular orbits within the Schwarzschild's ISCO and static configurations at finite radii for particles with zero angular momentum.

Figures (9)

• Figure 1: Illustrative Einstein-Gauss-Bonnet-scalar stars. Left panel: radial profile of the scalar field, showing a divergence at the origin, while the Ricci and Kretschmann scalars remain finite (see inset). Circular marker indicates the analytical value from Eqs. (\ref{['Eq.ScCurvOrig']}). Right panel: corresponding metric profiles, including Schwarzschild profiles for comparison. The parameters used to compute the boundary conditions at $r = 100$ are specified at the top. See Fig. \ref{['fig:IllExamp2']} for details.
• Figure 2: Comparison of numerical and approximate solutions. Full numerical profiles (solid lines) are compared with approximate solutions near the origin (dotted lines, Eqs. (\ref{['Sys.OrigCond']})) and at infinity (dashed lines, Eqs. (\ref{['Sys.BoundCond']})). These profiles correspond to those shown in Fig. \ref{['fig:IllExamp']}. Right panel: notice that although the boundary condition is set at $r = 100$, the numerical solution satisfies $g(r = 0) = 1$, ensuring finite curvature.
• Figure 3: Illustrative Einstein–Gauss–Bonnet hybrid stars with a regular scalar field at the origin. Left panel shows the matter pressure and scalar field profiles, scaled by their respective central values: $p_0=0.02$ and $\phi_0=0.5$ with $\beta=1.0$. Right panel displays the metric function: lapse $N(r)$ and radial component $g(r)$, both normalized to one at spatial infinity. The dashed lines represent the Schwarzschild metric components for an object of the same total mass, $M=155$ (see Eq. (\ref{['Eq.DimMass']})). The vertical lines indicate the radii where $p= 0$ (border of the baryonic component of the star).
• Figure 4: Illustrative Einstein–Gauss–Bonnet hybrid stars with a non-regular scalar field at the origin. The configuration is equivalent to that shown in Fig. \ref{['fig:MIllExamp']} in the sense that it has the same total mass $M = 155$ and baryonic radius $R = 25.7$. However, its metric, pressure, and scalar field profiles exhibit significant differences. The inset displays the Ricci and Kretschmann scalar profiles. In the right panel, we show the values used to determine the boundary conditions from the asymptotic expansion (\ref{['Sys.BoundCond']}).
• Figure 5: Mass–Radius relationship of Einstein–Gauss–Bonnet scalar stars. The left panel shows the mass-radius profiles (computed using Eq. (\ref{['Eq.DimMass']})) corresponding to selected configurations with dimensionless mass $M = 37.81$ (dotted line) displayed in the central panel. Note that for $\beta \sim 10^{-1}$, the mass becomes negative near the origin---an atypical behavior discussed in the main text. The center panel shows the mass $M_{99}$ as a function of the effective radius $R_{99}$ for configurations with $\phi_{\infty}=0.01$ and $a_1=2.0$. Each curve corresponds to a different value of $\beta$ in the range $[10^{-1}, 10^{5}]$. For comparison we also show the Einstein-Klein-Gordon family of solutions (red curve). The right panel presents the maximum compactness $C_{\textrm{max}}$ (computed using Eq. (\ref{['Eq.Compactness']})) as a function of $\beta$. We also display the following maximum compactness limits: Schwarzschild black hole ($C=1/2$), Buchdahl limit for fluid stars ($C_{\textrm{max}}=4/9$) Buchdahl:1959zz, and boson star without self-interactions ($C_{\textrm{max}}=0.1$). Configurations lying above the shaded region correspond to super-emitters, in the terminology of Ref. Palenzuela:2017kcg. For further details, see the discussion in Section \ref{['SectMR_sub_Ss']}.