Curvature invariants of static spherically symmetric geometries

Abstract

We construct all independent local scalar monomials in the Riemann tensor at arbitrary dimension, for the special regime of static, spherically symmetric geometries. Compared to general spaces, their number is significantly reduced: the extreme example is the collapse of all invariants ~ Weyl^k, to a single term at each k. The latter is equivalent to the Lovelock invariant L_k. Depopulation is less extreme for invariants involving rising numbers of Ricci tensors, and also depends on the dimension. The corresponding local gravitational actions and their solution spaces are discussed.

arXiv comment14 pages

References in corpus (6)

• On the Relationship between Yang-Mills Theory and Gravity and its Implication for Ultraviolet Divergences
• Dimensionally Continued Black Holes
• Shortcuts to high symmetry solutions in gravitational theories
• Tree Amplitudes and Two-loop Counterterms in D=11 Supergravity
• Graviton-Graviton Scattering, Bel-Robinson and Energy (Pseudo)-Tensors
• Graviton-Form Invariants in D=11 Supergravity

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