Quasi-normal modes of near-extremal black holes in generalized spherically symmetric spacetime and strong cosmic censors
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Regular Article - Theoretical Physics
Quasi-normal modes of near-extremal black holes in generalized spherically symmetric spacetime and strong cosmic censorship conjecture Piyabut Burikham1,a , Supakchai Ponglertsakul1,2,b , Taum Wuthicharn1,c 1
High Energy Physics Theory Group, Department of Physics, Faculty of Science, Chulalongkorn University, Phyathai Rd., Bangkok 10330, Thailand 2 Division of Physics and Semiconductor Science, Dongguk University, Seoul 04620, Republic of Korea
Received: 27 February 2020 / Accepted: 6 October 2020 © The Author(s) 2020
Abstract A number of near-extremal conditions are utilized to simplify the equation of motion of the neutral scalar perturbations in generalized spherically symmetric black hole background into a differential equation with the Pöschl– Teller potential. An analytic formula for quasinormal frequencies is obtained. The analytic formula is then used to investigate strong cosmic censorship conjectures (SCC) of the generalized black hole spacetime for the smooth initial data. The Christodoulou version of the SCC is found to be violated for certain regions of the black hole parameter space including the black holes in general relativity while the C 1 version of the SCC is always valid.
1 Introduction A number of gravitational wave events has been detected by the Laser Interferometer Gravitational-Wave Observatory. The discovery of these gravitational waves confirms that the gravitational disturbances propagate through space at the speed of light [1,2]. These waves carry encoded information in their oscillatory modes unique to the sources. Since the source loses energy in the form of gravitational waves, it is described by the so-called quasinormal modes (QNMs) where an associated frequency consists of real and imaginary part. The real part refers to frequency of oscillation while imaginary part associates with decaying or growing (e.g. when there is superradiance) characteristic time of the wave [3]. It is possible to detect the quasinormal modes in various events such as falling of massive stars into a supermassive black hole (BH) and a merging of black holes or any highly a e-mail:
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compact objects to form a new black hole [4]. For merging binaries, the quasinormal modes of the merged object are found in the ring down and contain information about the mass, charge, spin, and other possible “hairs” of the final black hole. It is even possible to distinguish a black hole from a wormhole and other exotics from the emitted QNMs [5–7]. The study of QNMs of black hole has a long story. A vast number of black holes in asymptotically flat, de-Sitter (dS) and anti de-Sitter (AdS) spacetimes are studied in the context of QNMs (see [3,4,8] for a well-written review on this subject). Among those black hole backgrounds, extremal black holes are interesting by their own nature. An extremal black hole possesses zero surface gravity. Thus black hole’s
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