Ergoregion instability and echoes for braneworld black holes: Scalar, electromagnetic, and gravitational perturbations

Ramit Dey, Shauvik Biswas, and Sumanta Chakraborty

Phys. Rev. D 103, 084019 – Published 12 April 2021

Abstract

In the context of the higher dimensional braneworld scenario, we have argued that the occurrence of horizonless exotic compact objects, as an alternative to classical black holes, is more natural. These exotic compact objects carry a distinctive signature of the higher dimension, namely a tidal charge parameter, related to the size of the extra dimension. Due to the absence of any horizon, rotating exotic compact objects are often unstable because of superradiance. Interestingly, these higher dimensional exotic compact objects are more stable than their four-dimensional counterpart, as the presence of the tidal charge reduces the size of the extra dimension and hence results in a stronger gravitational field on the brane. A similar inference is drawn by analyzing the static modes associated with these exotic compact objects, irrespective of the nature of the perturbation, i.e., it holds true for scalar, electromagnetic and also gravitational perturbation. The postmerger ringdown phase of the exotic compact object in the braneworld scenario, which can be described in terms of the quasinormal modes, holds a plethora of information regarding the nature of the higher dimension. In this connection we have discussed the analytical computation of the quasinormal modes as well as their numerical estimation for perturbations of arbitrary spin, depicting existence of echoes in the ringdown waveform. As we have demonstrated, the echoes in the ringdown waveform depend explicitly on the tidal charge parameter and hence its future detection can provide constraints on the tidal charge parameter, which in turn will enable us to provide a possible bound on the size of the extra dimension.

Received 31 October 2020
Accepted 26 February 2021

DOI:https://doi.org/10.1103/PhysRevD.103.084019

Physics Subject Headings (PhySH)

Alternative gravity theories General relativity Gravitational waves Gravity in dimensions other than four Quantum aspects of black holes

Gravitation, Cosmology & Astrophysics

Authors & Affiliations

Ramit Dey ^*, Shauvik Biswas^†, and Sumanta Chakraborty ^‡

School of Physical Sciences, Indian Association for the Cultivation of Science, Kolkata-700032, India

^*ramitdey@gmail.com
^†intsb6@iacs.res.in
^‡sumantac.physics@gmail.com

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Vol. 103, Iss. 8 — 15 April 2021

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Images

Figure 1
The above figure demonstrates the relevant boundary conditions associated with QNMs in the context of a black hole as well as for braneworld ECO. As evident, for black hole spacetime, the perturbation of the angular momentum barrier leads to outgoing mode at infinity and ingoing mode at the horizon. For braneworld ECO, the perturbation leads to outgoing mode at infinity (similar to black hole spacetime) while for the near-horizon regime, there will be both ingoing and outgoing modes, in contrast to black hole spacetime. See the text for more discussions.
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Figure 2
The above figure presents the relevant boundary condition associated with the phenomenon of superradiance in the case of a black hole as well as a braneworld ECO. In the case of a black hole, the ingoing wave gets scattered by the angular momentum barrier and goes to infinity while a part of it is transmitted. The scattered wave carries out more energy if the frequency of the mode satisfies the condition $ω < m Ω_{+}$ . On the other hand, for braneworld ECO, there are both ingoing and outgoing modes in the near-horizon regime, leading to possible runaway amplification of the amplitude of the ingoing wave from infinity, referred to as the ergoregion instability.
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Figure 3
The amplification factor ${{}_{s}Z}_{ℓ m}$ is plotted against the frequency both from the analytical expression and numerical estimation, for different values of the dimensionless tidal charge parameter $(Q / M^{2})$ . The plot of the amplification factor ${{}_{s}Z}_{ℓ m}$ for the scalar case ( $s = 0$ ) is plotted to the left and for the gravitational case ( $s = - 2$ ) is plotted to the right. We see from the above plots that with an increase in the tidal charge parameter $Q$ , the ergoregion instability is suppressed. This is because the critical frequency up to which the amplification happens decreases, as well as the maximum amplification factor also decreases drastically. Though at a given frequency, the amplification in the presence of extra dimension is slightly larger compared to the case of the Kerr black hole. See the text for more discussions.
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Figure 4
The absorption cross section $σ_{abs}$ of the surface of the ECO is plotted against the frequency of the perturbation modes for different values of the reflectivity and the tidal charge. The zero crossing of the absorption cross section corresponds to the superradiance bound $ω = m Ω_{+}$ . See the text for more discussions.
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Figure 5
The postmerger time-domain ringdown signal has been presented for braneworld ECOs having dimensionless tidal charge parameters, $(Q / M^{2}) = 0$ and $(Q / M^{2}) = 1$ , respectively. The above plot is for an ECO of having $a = 0.67$ , $l = 2$ , $m = 2$ . As evident, after the primary ringdown signal, we can see that there are additional signals considered as echo of the original signal arising out of reflection at the surface of the ECO. For nonzero values of the tidal charge parameter, these echoes are differently spaced, as the echo time delay would depend on the tidal charge for a braneworld ECO. See the text for more discussion.
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Figure 6
The basic structure of an ECO has been presented with a quantum structure in the near-horizon region which would partially reflect the ingoing waves incident on the merged ECO. These reflected waves would partially transmit through the angular momentum barrier and reach a distant observer as an echo of the primary signal with a time delay $Δ t_{echo}$ . The echo time delay is determined by the position of the reflective membrane placed in front of the would-be horizon and the maxima of the angular momentum barrier. See the text for further discussions.
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