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General Relativity and Quantum Cosmology, gr-qc
Abstract:
We propose a new parametric framework to describe in generic metric theories
of gravity the spacetime of spherically symmetric and slowly rotating black
holes. In contrast to similar approaches proposed so far, we do not use a
Taylor expansion in powers of M/r, where M and r are the mass of the black hole
and a generic radial coordinate, respectively. Rather, we use a
continued-fraction expansion in terms of a compactified radial coordinate. This
choice leads to superior convergence properties and allows us to approximate a
number of known metric theories with a much smaller set of coefficients. The
measure of these coefficients via observations of near-horizon processes can be
used to effectively constrain and compare arbitrary metric theories of gravity.
Although our attention is here focussed on spherically symmetric black holes,
we also discuss how our approach could be extended to rotating black holes.
