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General Relativity and Quantum Cosmology, gr-qc
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.
