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

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, [Formula: see text] . In a braneworld scenario with one extra spatial dimension, the extra dimension is expected to manifest itself through – (a) negative values of [Formula: see text] , 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 [Formula: see text] 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 [Formula: see text] ) of the frequency and damping time of the least-damped [Formula: see text] quasi-normal mode and measurements of these quantities using other independent techniques. We find that it is highly unlikely for the tidal charge, [Formula: see text] , providing a conservative limit on the tidal charge parameter. Implications and future directions are discussed.