Speaker
Description
We present a classification of four-dimensional gravitational theories exhibiting integrability properties similar to quasi-topological gravity, focusing on metrics that share the symmetries of Schwarzschild and Taub–NUT solutions with spherical, hyperbolic, and planar horizons, as well as their double Wick–rotated counterparts, including B-metrics, the near-horizon extremal Kerr geometry, and the swirling universe. These symmetry classes exhaust all cases with four Killing vectors and three-dimensional group orbits that admit consistent symmetry reductions at the level of the Lagrangian, in the sense of the principle of symmetric criticality. Restricting to theories constructed solely from the Riemann tensor, we demonstrate that analyticity in the Riemann tensor is compatible only with theories leading to third-order field equations, which reduce to second order after a trivial integration.