Nicolas Yunes, Paolo Pani, Vitor Cardoso
A stellar-mass compact object spiraling into a supermassive black hole, an
extreme-mass-ratio inspiral (EMRI), is one of the targets of future
gravitational-wave detectors and it offers a unique opportunity to test General
Relativity (GR) in the strong-field. We study whether generic scalar-tensor
(ST) theories can be further constrained with EMRIs. We show that in the EMRI
limit, all such theories universally reduce to massive or massless Brans-Dicke
theory and that black holes do not emit dipolar radiation to all orders in
post-Newtonian (PN) theory. For massless theories, we calculate the scalar
energy flux in the Teukolsky formalism to all orders in PN theory and fit it to
a high-order PN expansion. We derive the PN ST corrections to the Fourier
transform of the gravitational wave response and map it to the parameterized
post-Einsteinian framework. We use the effective-one-body framework adapted to
EMRIs to calculate the ST modifications to the gravitational waveform. We find
that such corrections are smaller than those induced in the early inspiral of
comparable-mass binaries, leading to projected bounds on the coupling that are
worse than current Solar System ones. Brans-Dicke theory modifies the
weak-field, with deviations in the energy flux that are largest at small
velocities. For massive theories, superradiance can lead to resonances in the
scalar energy flux that can lead to floating orbits outside the innermost
stable circular orbit and that last until the supermassive black hole loses
enough mass and spin-angular momentum. If such floating orbits occur in the
frequency band of LISA, they would lead to a large dephasing (~1e6 rads),
preventing detection with GR templates. A detection that is consistent with GR
would then rule out floating resonances at frequencies lower than the lowest
observed frequency, allowing for the strongest constraints yet on massive ST
theories.
View original:
http://arxiv.org/abs/1112.3351
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