All $2D$ generalised dilaton theories from $d\geq 4$ gravities
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arXiv
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| Formato: | Preprint |
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2026
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| _version_ | 1866914464455983104 |
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| author | Borissova, Johanna |
| author_facet | Borissova, Johanna |
| contents | We demonstrate that generic two-dimensional Horndeski theories can arise from the reduction of pure gravities in $d \geq 4$ dimensions, and therefore generic onshell configurations for the two-dimensional metric and scalar field correspond to genuine $d$-dimensional gravitational vacuum solutions. We discuss separately the two-dimensional Horndeski theories which can arise from the reduction of $d$-dimensional generally covariant gravitational actions built only from curvature invariants without covariant derivatives and possessing second-order equations of motion on $2 + (d-2)$ warped-product backgrounds. The discussion is subsequently extended to generic $d$-dimensional gravitational actions with this latter property. We establish a Birkhoff theorem for all gravitational theories whose reduction yields an integrable two-dimensional Horndeski theory, in which case static spherically symmetric solutions satisfy $g_{tt} g_{rr} = -1$ in Schwarzschild gauge whereby the metric function $g_{tt} = -f$ is determined by an algebraic equation. We therefore propose to refer to all such theories as quasi-topological gravities. These results can be used to show in reverse that any $d$-dimensional static spherically symmetric and asymptotically flat spacetime satisfying $g_{tt} g_{rr} = -1$ in Schwarzschild gauge with an invertible dependence of $f$ on the ADM mass can be reconstructed explicitly as a vacuum solution to a $d$-dimensional gravitational theory. We discuss examples of regular black holes such as the Bardeen spacetime, which could not be obtained from polynomial and non-polynomial quasi-topological gravities involving only curvature invariants without covariant derivatives. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_06786 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | All $2D$ generalised dilaton theories from $d\geq 4$ gravities Borissova, Johanna High Energy Physics - Theory General Relativity and Quantum Cosmology We demonstrate that generic two-dimensional Horndeski theories can arise from the reduction of pure gravities in $d \geq 4$ dimensions, and therefore generic onshell configurations for the two-dimensional metric and scalar field correspond to genuine $d$-dimensional gravitational vacuum solutions. We discuss separately the two-dimensional Horndeski theories which can arise from the reduction of $d$-dimensional generally covariant gravitational actions built only from curvature invariants without covariant derivatives and possessing second-order equations of motion on $2 + (d-2)$ warped-product backgrounds. The discussion is subsequently extended to generic $d$-dimensional gravitational actions with this latter property. We establish a Birkhoff theorem for all gravitational theories whose reduction yields an integrable two-dimensional Horndeski theory, in which case static spherically symmetric solutions satisfy $g_{tt} g_{rr} = -1$ in Schwarzschild gauge whereby the metric function $g_{tt} = -f$ is determined by an algebraic equation. We therefore propose to refer to all such theories as quasi-topological gravities. These results can be used to show in reverse that any $d$-dimensional static spherically symmetric and asymptotically flat spacetime satisfying $g_{tt} g_{rr} = -1$ in Schwarzschild gauge with an invertible dependence of $f$ on the ADM mass can be reconstructed explicitly as a vacuum solution to a $d$-dimensional gravitational theory. We discuss examples of regular black holes such as the Bardeen spacetime, which could not be obtained from polynomial and non-polynomial quasi-topological gravities involving only curvature invariants without covariant derivatives. |
| title | All $2D$ generalised dilaton theories from $d\geq 4$ gravities |
| topic | High Energy Physics - Theory General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2603.06786 |