# Item

ITEM ACTIONSEXPORT

Released

Journal Article

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

##### External Resource

No external resources are shared

##### Fulltext (restricted access)

There are currently no full texts shared for your IP range.

##### Fulltext (public)

2106.05558.pdf

(Preprint), 807KB

s10052-022-10788-x.pdf

(Publisher version), 598KB

##### Supplementary Material (public)

There is no public supplementary material available

##### Citation

Mishra, A. K., Ghosh, A., & Chakraborty, S. (2022). Constraining extra dimensions
using observations of black hole quasi-normal modes.* The European Physical Journal C,* *82*(9): 820. doi:10.1140/epjc/s10052-022-10788-x.

Cite as: https://hdl.handle.net/21.11116/0000-0008-B5FF-D

##### 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.

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.