Unique quasi-topological theories with first-order equations are found for Taub-NUT, NHEK, swirling and related 4D symmetric metrics, enabling closed-form solutions and regular black holes from high-order curvature corrections.
Classification of Six Derivative Lagrangians of Gravity and Static Spherically Symmetric Solutions
2 Pith papers cite this work. Polarity classification is still indexing.
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abstract
We classify all the six derivative Lagrangians of gravity, whose traced field equations are of second or third order, in arbitrary dimensions. In the former case, the Lagrangian in dimensions greater than six, reduces to an arbitrary linear combination of the six dimensional Euler density and the two linearly independent cubic Weyl invariants. In five dimensions, besides the independent cubic Weyl invariant, we obtain an interesting cubic combination, whose field equations for static spherically symmetric spacetimes are of second order. In the later case, in arbitrary dimensions we obtain two combinations, which in dimension three, are equivalent to the complete contraction of two Cotton tensors. Moreover, we also recover all the conformal anomalies in six dimensions. Finally, we present some static, spherically symmetric solutions for these Lagrangians.
fields
gr-qc 2years
2026 2representative citing papers
The Reall–Santos extremalization method is extended to perturbations around Einstein–Gauss–Bonnet backgrounds, reproducing known quasi-topological black-hole thermodynamics without solving the perturbed metric.
citing papers explorer
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Quasi-topological gravity for 4-dimensional Taub-NUT, near-horizon extreme Kerr, and swirling symmetries
Unique quasi-topological theories with first-order equations are found for Taub-NUT, NHEK, swirling and related 4D symmetric metrics, enabling closed-form solutions and regular black holes from high-order curvature corrections.
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Extremalization approach to black hole thermodynamics: perturbations around higher-derivative gravities
The Reall–Santos extremalization method is extended to perturbations around Einstein–Gauss–Bonnet backgrounds, reproducing known quasi-topological black-hole thermodynamics without solving the perturbed metric.