Curvature invariants of static spherically symmetric geometries

Details Curvature invariants of static spherically symmetric geometries Curvature invariants of static spherically symmetric geometries

2005-05-10

arxiv.org/abs/gr-qc/0505039v1

Class.Quant.Grav.22:3315-3324,2005

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

14 pages

Scientific paper

10.1088/0264-9381/22/16/012

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.

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