1. Kaluza-Klein Black Holes in 5-dim. Einstein-Maxwell Theory
hep-th/ , hep-th/
Hideki Ishihara
with
M.Kimura, K.Matsuno, S.Tomizawa
Department of Physics, Osaka City University
2019/1/17

2. 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.

3. 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

4. Action
Equation of motion

5. Solutions
: Extension of Dobiash-Maison solution

6. Structure
Squashing
Horizon
Singularity
Asymptotic structure

7. Squashing

8. Foliation

9. Shape of Horizon

10. Singularities
Point-like singularity
Spindle-like singularity

11. Asymptotic Behavior
Coordinate tr.

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

13. Mass and Charge
Komar integral

14. Physical Parameters

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

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

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

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

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

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

21. Horizon Topology
NUT singularities transmute to Black holes

22. 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.

23. 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)