Quasi-normal modes of near-extremal black holes in generalized spherically symmetric spacetime and strong cosmic censorship conjecture

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 $$C^{1}$$ C 1 version of the SCC is always valid.

Quasi-normal Modes of near-extremal black holes in Generalized spherically symmetric spacetime and Strong Cosmic Censorship Conjecture

“…The subscript χ represents an extremal horizon whose surface gravity is positive. Similar to the black hole case, the approximation formula is confirmed by utilizing AIM (for dS and AdS) and the Spectral Method (for AdS) [63]. We find that the formula works very well for ∆r/r χ < 0.02, where ∆r is the difference between the pair of near-extremal horizons.…”

“…Numerical calculations by AIM and spectral method are performed to confirm the validity of the approximation formula for asymptotic dS and AdS cases in Ref. [63].…”

A critical assessment of black hole solutions with a linear term in their redshift function

“…The parameter β, which makes this solution different from the Schwarzschild-(anti-)de Sitter one, leads to a modified Newtonian dynamics (MOND) [28] which has been investigated in regard of deviations in the trajectories of massive bodies in the solar system which would follow from an entropic force [29], of possible phase transitions [30], and as a solution of the galaxy rotation curves problem [21]. Studies of the quasi-normal frequencies of vibrations of this black hole [31,32], and of their anomalous behavior [33], have showed that the strong cosmic censorship conjecture can be violated for some choices of the black hole parameters [34].…”

Strong cosmic censorship in near-extremal Kerr-Sen-de Sitter spacetime

“…Although SCC has been inspected extensively for spherically black holes perturbed by scalar, fermion, electromagnetic, and gravitational field perturbations (see, for example, Refs. [20][21][22][23][24][25][25][26][27][28][29][30][31][32][33][34][35][36][37]), the investigations of the rotating cases seem to be limited [38][39][40][41][42]. Moreover, although the SCC of spacetimes in Einstein gravity has been investigated comprehensively, there is much that needs to be done in the modified gravities, being corrections to GR, following previous trials [43,44].…”