KaluzaKlein Black Holes in 5 dim EinsteinMaxwell Theory

Kaluza-Klein Black Holes in 5 -dim. Einstein-Maxwell Theory hep-th/0510094, hep-th/0605030 Hideki Ishihara with M. Kimura, K. Matsuno, S. Tomizawa Department of Physics, Osaka City University 1 9/29/2020

Introduction If spacetime has extra-dimensions with sub-millimeter scale Black holes would be created in an accelerator ・central zone of accelerator spacetime is fully higher dimensional ・far zone spacetime is effectively 4 -dimensional. 2

Kaluza-Klein Black Hole Higher dim. BH with compact dimensions P. D. Dobiash&D. Maison, G. W. Gibbons&D. L. Wiltshire, R. C. Myers…. . B. Kol, T. Harmark, N. Obers, T. Wiseman, H. Kudoh…. 5 -dim. Kaluza-Klein black hole Near horizon: ~ 5 -dim. BH Far region: ~ 4 -dim. BH x S 1 3

Action Equation of motion 4

Solutions : Extension of Dobiash-Maison solution 5

Structure Squashing n Horizon n Singularity n Asymptotic structure n 6

Squashing 7

Foliation 8

Shape of Horizon 9

Singularities Point-like singularity Spindle-like singularity 10

Asymptotic Behavior Coordinate tr. 11

Whole Structure Point-like singularity Spindle-like singularity Spatial infinity 12

Mass and Charge Komar integral 13

Physical Parameters 14

Squashed Black Hole Near horizon: fully 5 -dim. Far zone: 4 -dim. with twisted S 1 15

Spindle Black Hole 16 Like a 4 -dim. Black hole with a compact dim. in far zone

Critical Charge In the limit 4 -dim. BH with a constant S 1 Singularity is ring-like 17

Three Types of Singularity Point-like Ring-like Spindle-like Black Hole Charge 18 Black holes with similar outer structure with very different inner structure

Extreme Limit BH on the NUT singularity Gross-Perry-Sorkin Monopole 19

Multi-Black Hole Solutions Multi-NUT space Black holes are on NUT singularities 20 hep-th/0605030

Horizon Topology NUT singularities transmute to Black holes 21

Summary We investigate 5 -dim. charged static squashed black holes with horizons of S 3 topology. In near zone, the geometry is fully 5 -dimensional, while in far zone, S 1 bundle on 4 -dim. black hole. 22

Rich Structure Twisted S 1 over asymptotic flat 4 -dim. (Kaluza-Klein type) • Singularity of black hole is one of point-like, ring-like, or spindle-like. • A set of physical parameters admits both BH and Naked singularity solutions. • Multi-BHs with degenerate horizon are possible. Topology of each horizon is the lens space. c. f. Black ring (Emparan&Realｌ) 23