The zero mass limit of Kerr and Kerr-(anti-)de-Sitter space-times: exact solutions and wormholes

Abstract

Heun-type exact solutions emerge for both the radial and the angular equations for the case of a scalar particle coupled to the zero mass limit of both the Kerr and Kerr-(anti)de-Sitter spacetime. Since any type D metric has Heun-type solutions, it is interesting that this property is retained in the zero mass case. This work further refutes the claims that M going to zero limit of the Kerr metric is both locally and globally the same as the Minkowski metric.

Correction to: The zero mass limit of Kerr and Kerr-(anti-)de-Sitter space-times: exact solutions and wormholes

“…This was the equation we got after changing our variable to v = u + 3 a 2 and investigated the behavior beyond the event horizon. We noted that the solution of this equation is very similar to the one given in [1], Eqs. (19-26) on page 4.…”

“…Here we want to report an unfortunate misprint in the last equation, Eq. (28), in our paper The zero mass limit of Kerr and Kerr-(anti-)de-Sitter space-times: exact solutions and wormholes, which was published in General Relativity and Gravitation, [1]. Our Eq.…”

Dirac Equation on Kerr--Newman spacetime and Heun functions

“…In view of the parameters in (33), it turns out that only the component multiplied by C 1 gets a polynomial expression, the energy ω having the real and imaginary parts given by…”

Dirac Equation on the Kerr–Newman Spacetime and Heun Functions

“…By imposing the necessary condition for a polynomial form of the Heun confluent functions [18,19], we obtain the resonant frequencies, which are of crucial importance for getting information on the black holes interacting with different quantum fields [24]. In the last years, the Heun functions in either their general or confluent forms have been obtained by many authors, for example, [25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40] and the references therein.…”