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

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, β. In a braneworld scenario with one extra spatial dimension, the extra dimension is expected to manifest itself through -(a) negative values of β, 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 β correspond to a diminishing imaginary part of the quasinormal 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 β) of the frequency and damping time of the least-damped = 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, β < ∼ −0.05, providing a conservative limit on the tidal charge parameter. Implications and future directions are discussed.

Implications of the quantum nature of the black hole horizon on the gravitational-wave ringdown

“…In this section, we shall discuss the opposite scenario where the background spacetime inherits quantum corrections, while the membrane remains classical. Such a scenario naturally arises in the context of braneworld BHs [38,53] whose various observational signatures have been studied in [54][55][56][57][58][59][60]. We shall first provide the spacetime geometry of the braneworld BH, and then discuss the quantum origin of such a solution.…”

Gravitational radiation from a binary system in odd-dimensional spacetime

“…(IV. 35) is contained in the prefactor, proportional to the inverse distance 1/r, and in the retarded time t.…”

“…(II. 35) is separately divergent on the light cone, the resulting field is finite [65]. Let us briefly discuss the regularisation procedure used to make the finiteness of the field explicit.…”

“…As well, extra dimensions manifest themselves in the quasinormal modes of the black holes, which determine the spectrum of the gravitational radiation of the binary system at the final stage of its merger [34]. Particularly, presence of extra dimensions significantly increases the damping time of the quasinormal oscillations of the black holes, providing the rigorous constraints on the parameters of corresponding theories [35]. Another promising tool to probe extra dimensions is the photographs of the black holes shadows.…”

Odd-dimensional gravitational waves from a binary system on a three-brane

“…Recent successes of the gravitational-wave astronomy give us the new tool for exploring extra dimensions [5][6][7][8][9][10] . Some constraints on their size, number and geometry have already been extracted [11][12][13][14][15][16] . Another new tool relevant to extra dimensions is shadow of a black hole [17][18][19] .…”