Constraining extra dimensions using observations of black hole quasi-normal modes

TL;DR

This paper investigates how extra dimensions influence black hole quasi-normal modes, using numerical methods and gravitational wave data to constrain the tidal charge parameter, thereby testing braneworld scenarios.

Contribution

It provides the first numerical analysis of gravitational perturbations in braneworld black holes and constrains the tidal charge parameter using gravitational wave observations.

Findings

Negative tidal charge reduces damping of quasi-normal modes.

Tidal charge parameter constrained to be greater than approximately -0.05.

Results support the absence of significant extra-dimensional effects in GW150914 data.

Abstract

The presence of extra dimensions generically modify the spacetime geometry of a rotating black hole, by adding an additional hair, besides the mass $M$ and the angular momentum $J$, known as the `tidal charge' parameter, $\beta$. In a braneworld scenario with one extra spatial dimension, the extra dimension is expected to manifest itself through -- (a) negative values of $\beta$, and (b) modified gravitational perturbations. This in turn would affect the quasi-normal modes of rotating black holes. We numerically solve the perturbed gravitational field equations using the continued fractions method and determine the quasi-normal mode spectra for the braneworld black hole. We find that increasingly negative values of $\beta$ correspond to a diminishing imaginary part of the quasi-normal mode, or equivalently, an increasing damping time. Using the publicly available data of the properties of the remnant black hole in the gravitational wave signal GW150914, we check for consistency between the predicted values (for a given $\beta$) of the frequency and damping time of the least-damped $\ell=2,m=2$ quasi-normal mode and measurements of these quantities using other independent techniques. We find that it is highly unlikely for the tidal charge, $\beta \lesssim -0.05$, providing a conservative limit on the tidal charge parameter. Implications and future directions are discussed.