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Covariant perturbations of Schwarzschild black holes. (English) Zbl 1054.83018
This work introduces a new covariant and gauge-invariant perturbation formalism for spacetimes with a spherically symmetric background. Compared to the usual $$1+3$$ -splitting using a timelike vector $$u^a$$, the $$1+1+2$$ formalism presented here is based on a further splitting of the spacetime using a radial vector $$n^a$$. In this way the Bianchi and Ricci identities split into systems of first order ODEs plus constraints. This new approach is applied to the background Schwarzschild solution. The main equations governing perturbations of the spacetime (Regge-Wheeler and Zerilli) can also be derived in this setting. The paper closes with an outlook on promising applications to the study of gravitational waves.

##### MSC:
 83C57 Black holes 83C25 Approximation procedures, weak fields in general relativity and gravitational theory 83C35 Gravitational waves
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