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, $$\beta $$ β . In a braneworld scenario with one extra spatial dimension, the extra dimension is expected to manifest itself through – (a) negative values of $$\beta $$ 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 $$\beta $$ β 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 $$\beta $$ β ) of the frequency and damping time of the least-damped $$\ell =2,m=2$$ ℓ = 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, $$\beta \lesssim -0.05$$ β ≲ - 0.05 , providing a conservative limit on the tidal charge parameter. Implications and future directions are discussed.

Horizon-scale tests of gravity theories and fundamental physics from the Event Horizon Telescope image of Sagittarius A ∗

“…We now consider one of the most well-motivated high-energy physics models: the Randall-Sundrum II (RSII) brane-world model, which has been tested over a wide range of scales and using an enormous variety of probes (see e.g. [712][713][714][715][716][717][718][719][720][721][722][723][724][725][726]). This is an AdS 5 brane-world model where the extra dimension has an infinite size and negative bulk cosmological constant [727].…”

Gravitational wave from extreme mass-ratio inspirals as a probe of extra dimensions

“…This implies EMRI observation can put much tighter constraints on the tidal charge parameter than black hole shadow observation or the gravitational wave from the coalescence of comparable mass binaries. In particular, [53] put an upper bound on the tidal charge parameter Q 0.05 through gravitational wave observation, while [51] found the bound as Q 0.004 through shadow observations. Thus, LISA is much better suited for probing the existence of higher dimensions.…”

“…However, these black holes carry tidal charges, which can take negative values, unlike the electric charge of Reissner-Nordström black holes. 1 The observational consequences of tidal-charged black holes have been discussed in the literature in the context of black hole shadow and gravitational wave observations [46][47][48][49][50][51][52][53][54][55][56][57][58]. In the present context, we consider the effect of tidal charge on the EMRI waveform and check whether LISA observation can put a tighter constraint on this parameter and, consequently, on the extra dimensions.…”

Transition from inspiral to plunge for braneworld EMRI

“…All of these modifications lead to corrections to the background geometry and also modify the near horizon behaviour of the spacetime. Implications on the stability of the braneworld geometry, due to such modified near horizon behaviour, for both rotating and nonrotating spacetimes have already been explored [30][31][32][33][34][35]. Further, the effect of such corrections on the tidal properties of compact objects, as well as on the quasi-normal mode frequencies, have been computed and contrasted with the real GW data from GW150914 and GW170817 [36][37][38].…”