Charged black holes in a five-dimensional Kaluza-Klein universe

Abstract

We examine an exact solution which represents a charged black hole in a Kaluza-Klein universe in the five-dimensional Einstein-Maxwell theory. The spacetime approaches to the five-dimensional Kasner solution that describes expanding three dimensions and shrinking an extra dimension in the far region. The metric is continuous but not smooth at the black hole horizon. There appears a mild curvature singularity that a free-fall observer can traverse the horizon. The horizon is a squashed three-sphere with a constant size, and the metric is approximately static near the horizon.

Black holes in an expanding universe and supersymmetry

“…Using these dualized quantities, one can uplift the fourdimensional solution (2.10) back to five dimensions by ds 2 5 (1) . The dualized solution then reads [31]…”

“…where the base space ds 2 GH = h mn dx m dx n is the timedependent Gibbons-Hawking space [30], [31]. Recently, Ishihara, Kimura and Matsuno pointed out that the metric (2.15) with H = 1 + Q/r, U = 0 can be interpreted as a black string in the fivedimensional Kasner universe [32].…”

“…Q/r and U = Q/r[31]. In spite of the striking similarity to the canonical form of the metric in the timelike class[3], the metric (2.15) fails to preserve any supersymmetries within the framework of minimal supergravity.…”

Charged black strings in a five-dimensional Kasner universe

“…In the case of hyper-Kähler base space, the solutions are supersymmetric. As generalizations of four-dimensional time-dependent multi-black hole solutions [35][36][37], higher-dimensional solutions including a cosmological constant [38][39][40][41][42][43] and without cosmological constant [44][45][46][47][48] are obtained by using harmonics.…”

A pair of extremal charged black holes on Kerr–Taub-bolt space

“…In such cases, we can obtain exact Kaluza-Klein black hole solutions easily. A family of five-dimensional squashed Kaluza-Klein black hole solutions [1][2][3][4][5][6][7][8][9][10][11][12][13][14] asymptote to effective four-dimensional spacetimes with a twisted S 1 as an extra dimension at infinity, and represent fully five-dimensional black holes near the squashed S 3 horizons (See [15] as a review).…”