Generalized quasitopological gravity

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Abstract
We construct the most general, to cubic order in curvature, theory of gravity whose (most general) static spherically symmetric vacuum solutions are fully described by a single field equation. The theory possesses the following remarkable properties: (i) It has a well-defined Einstein gravity limit, (ii) it admits “Schwarzschild-like” solutions characterized by a single metric function, (iii) on maximally symmetric backgrounds it propagates the same degrees of freedom as Einstein’s gravity, and (iv) Lovelock and quasitopological gravities, as well as the recently developed Einsteinian cubic gravity [Bueno and Cano Phys. Rev. D 94, 104005 (2016).] in four dimensions, are recovered as special cases. We perform a brief analysis of asymptotically flat black holes in this theory and study their thermodynamics.
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Funding Information
  • Natural Sciences and Engineering Research Council of Canada
  • Government of Canada
  • Perimeter Institute for Theoretical Physics
  • Department of Innovation, Science and Economic Development Canada
  • Ministry of Research, Innovation and Science

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