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 2019/1/17

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.

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 S1

Action Equation of motion

Solutions : Extension of Dobiash-Maison solution

Structure Squashing Horizon Singularity Asymptotic structure

Squashing

Foliation

Shape of Horizon

Singularities Point-like singularity Spindle-like singularity

Asymptotic Behavior Coordinate tr.

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

Mass and Charge Komar integral

Physical Parameters

Squashed Black Hole Near horizon: fully 5-dim. Far zone: 4-dim. with twisted S1

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

Critical Charge In the limit 4-dim. BH with a constant S1 Singularity is ring-like

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

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

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

Horizon Topology NUT singularities transmute to Black holes

Summary We investigate 5-dim. charged static squashed black holes with horizons of S3 topology. In near zone, the geometry is fully 5-dimensional, while in far zone, S1 bundle on 4-dim. black hole.

Rich Structure Twisted S1 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)