Yunes, Nicolas, Pani, Paolo and Cardoso, Vitor (2012), "Gravitational waves from quasicircular extreme mass-ratio inspirals as
probes of scalar-tensor theories", PHYSICAL REVIEW D, 85, 10.
Abstract: A stellar-mass compact object spiraling into a supermassive black hole,
an extreme mass-ratio inspiral, is one of the targets for future
space-based gravitational-wave detectors. Such inspirals offer a unique
opportunity to learn about astrophysics and test general relativity in
the strong field. Here we study whether scalar-tensor theories in
asymptotically flat spacetimes can be further constrained with these
inspirals. In the extreme mass-ratio limit, and assuming analyticity of
the coupling functions entering the action, we show that all
scalar-tensor theories universally reduce to massive or massless
Brans-Dicke theory. We also show that in this limit, black holes do not
emit dipolar radiation to all orders in post-Newtonian theory. For
massless theories and quasicircular orbits, we calculate the scalar
energy flux in the test-particle Teukolsky formalism to all orders in
post-Newtonian theory and fit it to a high-order post-Newtonian
expansion. We then derive the post-Newtonian corrections to the
scalar-tensor modified, Fourier transform of the gravitational-wave
response function and map it to the parametrized post-Einsteinian
framework. With the Teukolsky flux at hand, we use the
effective-one-body framework adapted to extreme mass-ratio inspirals to
calculate the scalar-tensor 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 Brans-Dicke coupling parameter that are worse than current Solar
System ones. This is because Brans-Dicke theory modifies the weak field,
leading to deviations in the energy flux that are largest at small
velocities. For massive theories, superradiance can produce resonances
in the scalar energy flux that can lead to quasicircular 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 a LISA-like mission,
they would lead to a large dephasing (typically similar to 10(6) rads)
that would prevent detection of such modified inspirals using general
relativity templates. A detection that is consistent with general
relativity would then rule out the presence of floating resonances at
frequencies lower than the lowest inspiral frequency observed, allowing
for the strongest constraints yet on massive scalar-tensor theories.
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