Gravitational waves and higher dimensions: Love numbers and Kaluza-Klein excitations

Gravitational-wave observations provide a wealth of information on the nature and properties of black holes. Among these, tidal Love numbers or the multipole moments of the inspiraling and final objects are key to a number of constraints. Here, we consider these observations in the context of higher-dimensional scenarios, with flat large extra dimensions. We show that - as might be anticipated, but not always appreciated in the literature - physically motivated setups are unconstrained by gravitational-wave data. Dynamical processes that do not excite the Kaluza-Klein (KK) modes lead to a signal identical to that in four-dimensional general relativity in vacuum. In addition, any possible excitation of the KK modes is highly suppressed relative to the dominant quadrupolar term; given existing constraints on the extra dimensions and the masses of the objects seen in gravitational-wave observations, KK modes appear at post-Newtonian order ∼1011. Finally, we recompute the tidal Love numbers of spherical black holes in higher dimensions. We confirm that these are different from zero, but comparing with previous computations we find a different magnitude and sign.