Charged Rotating Black Hole from Five Dimensional Point of View

Abstract

Abstract. It is shown that the usual characteristics of a black hole and of the physical fields produced by it obtain a unified geometrical meaning in the five-dimensional framework. Especidly, it is demonstrated that a solution for a rotating black hole with electric and scalar charges can he generated by a boost transformation of the fifth coordinate from the Kerr solution. (feladene, rotierende schwarze Lticher aus fiinf-dimensionalor SiehtInhaltsubersicht. Es wird gezeigt, wie die iiblichen Charakteristiken schw.wzer Ljcher iind der von ihnen erzeugten physikslischen Felder eine einheitliche geometrische Bedeutung im fiinfdimensionalen Formalismus erhalten. Speziell wird vorgefuhrt, daB man eine Losung fur ein rot,ierendea schwarzea Loch mit elektrischer und skalarer Ladung durch eine ,,b~ost"-Transformatsion der funften Koordinate aus der Ken-Losung erzeugen kann.Recently, the generalization of the standard EINSTEIN theory of gravitation to more than four dimensions by KALUZA [I] and KLEIN [ 2 ] is activly considered as a possible candidate for a unified field theory. The most important applications of this theories are early stages of the evolution of the Universe as well as compact astrophysical objects llke black holes. These cases are characterised by extremly strong fields and, therefore, specific properties of the more-dimensional theory may become significant. There is an extended literature on early cosmology in the framework of KALUZA-KLEIN theory ( 8 . e.g. [3-91). Concerning compact objects, in most of the papers (s. e.g. [ 10-151 the case of nonrotating black holes is considered.I n the present paper stationary axially symmet,ric five-dimensiod spaces are analysed, which correspond to regular four-dimensional rotating charged black holes.Suppose Mb to he a five-dimensional space-time covered by the metric GLin (-4, B = 0, 1, 2, 3; 5, sgii GAB = -+ + + +) providing a Killing vector field E.4(['),A EA = 2 f A~B E A 6 B = O ,(by ":" we denote the covariant derivative with respect to the 5-metric Gain). For 5 2 = fAtA we have the following relations:

Rotating charged black hole solution in heterotic string theory

“…Surprisingly, this result is identical to the corresponding result for the rotating charged black hole in a different model discussed in ref. [9].…”

Charged dilaton black holes with unusual asymptotics

“…No explicit solutions have yet been found except for a = √ 3 [20] and for a = 1 when the string three-form H abc is included [21]. It would be interesting to add angular momentum to the string black hole solutions we obtained in section 3 and 4 to see if it is possible to extend the family of solutions we obtained to the rotating case.…”

Superradiance around rotating dilatonic black holes

“…The latter is the 4-dimensional rotating black hole solution in the 5-dimensional Kaluza-Klein theory derived by Frolov et al [3]. We call it the Kaluza-Klein black hole.…”