Extreme Compactness, Extreme Gravity: Higher-Derivative Corrections to ECOs

Higher-derivative gravity theories offer insights into the behavior of extremely compact objects (ECOs). Focusing on Gauss-Bonnet (GB) and Einstein-dilaton-Gauss-Bonnet (EdGB) gravity, we derive the compactness scale in these models and demonstrate how higher-curvature corrections lead to deviations from the standard ECO compactness scale. The corrections are of order $\alpha \mathrm{/}{r}_0^2$ in EGB gravity and ${\alpha }^2\mathrm{/}{r}_0^4$ in EdGB gravity, where $\alpha$ is the coupling constant and $r_0$ is the horizon radius corresponding to the mass of the ECO. Observational constraints suggest these effects could be significant in certain astrophysical systems, providing a new perspective on the nature of extremely compact objects in models of modified gravity.