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

TL;DR

This paper explores how gravitational-wave data constrains higher-dimensional theories with extra dimensions, finding that such models are largely unconstrained and that Kaluza-Klein modes are suppressed, with revised calculations of black hole Love numbers.

Contribution

It demonstrates that higher-dimensional models with flat extra dimensions are not constrained by gravitational-wave observations and provides new calculations of black hole Love numbers in higher dimensions.

Findings

KK modes are highly suppressed and not excited in typical GW signals.

Gravitational-wave data do not constrain models with flat large extra dimensions.

Recomputed Love numbers differ in magnitude and sign from previous results.

Abstract

Gravitational-wave (GW) 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 inspiralling 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 set-ups 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 $\sim 10^{11}$. Finally, we re-compute 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.