Explorations in Generalized Quasi-topological Gravities

Abstract

This thesis presents a comprehensive study of Generalized Quasi-Topological Gravities (GQTGs), a broad class of higher-curvature extensions of Einstein gravity in arbitrary spacetime dimensions. These theories are distinguished by possessing second-order lin- earized field equations around maximally symmetric backgrounds and admitting static, spherically symmetric black hole solutions characterized by a single metric function f (r) obeying a second-order differential equation. We rigorously demonstrate that, at order n in curvature, exactly n − 1 inequivalent GQTG densities exist in dimensions D ≥ 5, among which only one belongs to the Quasi-topological subclass for which the field equa- tions reduce to an algebraic equation for f (r). In contrast, we find strong evidence that only a unique such density exists for each order in four dimensions, which is not of the Quasi-topological kind. We analyze the thermodynamic properties of black holes in these theories and confirm that the first law of thermodynamics is satisfied. Moreover, we provide evidence that the black hole thermodynamics is fully encoded in the same embedding function that determines the maximally symmetric vacua of the theory, offering a unified and simplified framework for studying solutions with arbitrary higher-curvature corrections. Building on this foundation, we explore the multi-critical thermodynamic behavior of uncharged AdS black holes in GQTGs. Utilizing a reformulated version of Maxwell’s equal area law, we identify a geometric criterion for the existence of multicritical (or N -tuple) points in the black hole phase diagram. Applying this criterion, we explicitly construct black hole solutions exhibiting quadruple and quintuple critical points supported by genuine GQTG densities. Finally, we uncover a novel class of traversable wormhole solutions in four-dimensional Einsteinian Cubic Gravity—a specific GQTG—including examples that are entirely vac- uum configurations with no need for exotic matter. These wormholes connect asymptoti- cally AdS regions with a geometric deficit at infinity, interpretable as a global monopole. We demonstrate that these configurations satisfy standard traversability conditions and exhibit a variety of geometries depending on the parameter space.