Speaker
Description
Understanding how higher-order curvature corrections modify black hole spacetimes is essential for exploring possible deviations from General Relativity in the strong-field regime. In this work, we investigate the gravitational effects of a power-law Gauss–Bonnet modification in four dimensions, focusing on the perturbative structure of static, spherically symmetric vacuum solutions. Starting from a general gravitational Lagrangian containing quadratic curvature invariants, we develop a first-order perturbative framework around the Schwarzschild geometry and identify the conditions under which genuinely new gravitational contributions arise.
We consider a family of models characterized by the interaction $\Psi_\eta=\ell_\lambda^{4\eta-2}\mathcal G^\eta$, where $\mathcal G$ denotes the Gauss–Bonnet invariant. Unlike Ricci-based modifications, which preserve the vacuum Einstein solutions along the analytic perturbative branch, these nonlinear curvature interactions can generate nontrivial corrections to the Schwarzschild metric. We obtain explicit analytical expressions for the metric perturbations and examine their implications for several characteristic properties of black holes, including the event horizon, innermost stable circular orbit, photon sphere, gravitational shadow, Hawking temperature, and Wald entropy.
Our results reveal a distinctive dependence on the exponent $\eta$. Within the asymptotically controlled regime (\eta>2/3), positive perturbative couplings produce an increase in the characteristic horizon and orbital radii for $2/3<\eta<1$, while the opposite behavior occurs for $\eta>1$. The special case $\eta=1$ recovers the Schwarzschild geometry, reflecting the topological character of the linear Gauss–Bonnet term in four dimensions, although a constant contribution to the entropy remains. We also explore how shadow measurements can provide sensitivity to these modifications, illustrating the potential relevance of black hole imaging for testing higher-curvature gravitational models.
These findings provide an analytical connection between the mathematical structure of modified gravity theories and potentially measurable strong-field phenomena, offering a framework for investigating departures from Einstein gravity through black hole observations.