Paolo Pani, Caio F. B. Macedo, Luis C. B. Crispino, Vitor Cardoso
We present, in closed analytic form, a general stationary, slowly rotating
black hole, which is solution to a large class of alternative theories of
gravity in four dimensions. In these theories, the Einstein-Hilbert action is
supplemented by all possible quadratic, algebraic curvature invariants coupled
to a scalar field. The solution is found as a deformation of the Schwarzschild
metric in General Relativity. We explicitly derive the changes to the orbital
frequency at the innermost stable circular orbit and at the light ring in
closed form. These results could be useful when comparing General Relativity
against alternative theories by (say) measurements of X-ray emission in
accretion disks, or by stellar motion around supermassive black holes. When
gravitational-wave astronomy comes into force, strong constraints on the
coupling parameters can in principle be made.
View original:
http://arxiv.org/abs/1109.3996
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