Tidal Deformation and Dissipation of Rotating Black Holes. (arXiv:2010.07300v1 [gr-qc])
<a href="http://arxiv.org/find/gr-qc/1/au:+Chia_H/0/1/0/all/0/1">Horng Sheng Chia</a>
We show that rotating black holes do not experience any tidal deformation
when they are perturbed by a weak and adiabatic gravitational field. The tidal
deformability of an object is quantified by the so-called “Love numbers”, which
describe the object’s linear response to its external tidal field. In this
Letter, we compute the Love numbers of Kerr black holes and find that they
vanish identically. We also compute the dissipative part of the black hole’s
tidal response, which is non-vanishing due to the absorptive nature of the
event horizon. Our results hold for arbitrary values of black hole spin, for
both the electric-type and magnetic-type perturbations, and to all orders in
the multipole expansion of the tidal field. The boundary conditions at the
event horizon and at asymptotic infinity are incorporated in our study, as they
are crucial for understanding the way in which these tidal effects are mapped
onto gravitational-wave observables. In closing, we address the ambiguity issue
of Love numbers in General Relativity, which we argue is resolved when those
boundary conditions are taken into account. Our findings provide essential
inputs for current efforts to probe the nature of compact objects through the
gravitational waves emitted by binary systems.
We show that rotating black holes do not experience any tidal deformation
when they are perturbed by a weak and adiabatic gravitational field. The tidal
deformability of an object is quantified by the so-called “Love numbers”, which
describe the object’s linear response to its external tidal field. In this
Letter, we compute the Love numbers of Kerr black holes and find that they
vanish identically. We also compute the dissipative part of the black hole’s
tidal response, which is non-vanishing due to the absorptive nature of the
event horizon. Our results hold for arbitrary values of black hole spin, for
both the electric-type and magnetic-type perturbations, and to all orders in
the multipole expansion of the tidal field. The boundary conditions at the
event horizon and at asymptotic infinity are incorporated in our study, as they
are crucial for understanding the way in which these tidal effects are mapped
onto gravitational-wave observables. In closing, we address the ambiguity issue
of Love numbers in General Relativity, which we argue is resolved when those
boundary conditions are taken into account. Our findings provide essential
inputs for current efforts to probe the nature of compact objects through the
gravitational waves emitted by binary systems.
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