ON THE BLACK HOLE SPECIES

Transcription

1 Paris ON THE BLACK HOLE SPECIES (by means of natural selection) Maria J. Rodriguez Dumitru Astefanesei and MJR ( to appear) Marco Calderelli, Roberto Emparan and MJR ( [hep-th] ) Henriette Elvang, and MJR ( [hep-th] ) Roberto Emparan, Troels Harvmark, Niels Obers, Vasilis Nirchos and MJR ( [hep-th] )

2 On the Black Hole Species (by means of natural selection) Introduction Motivation: interest on black holes (BH) in D>4 Context Status of known BH solutions/species in D>4 Black Holes species in more detail Black Rings in D>5 AdS Black Rings in D>4 Other Black Holes Introduction Method and Results Introduction Method and Results D=5 SUSY black rings? Multi black holes e.g. Bycicling Black Rings Future directions and Conclusions

3 Introduction I. Motivation: interest on BH in D>4 II. Context III. Status of known BH solutions/species in D>4 Why are we interested in higher dimensional Black Holes? string/m theory These solutions are contained in lower energy effective theory, namely GR in D>4. as solutions of a AdS/CFT In the context the asymptotically AdS black holes are particularly interesting solutions. In general relativity these solutions are interesting on its own. Experimentally they could form at LHC during particle collisions

4 Introduction I. Motivation: interest on BH in D>4 II. Context III. Status of known BH solutions/species in D>4 What are we looking for? [*] Stationary black hole solutions that satisfy Einstein's equations are non-singular on and outside event horizons with specified boundary conditions Asymptotically Flat, AdS or ds in D dimensions of space-time [*] The inclusion of the second equality complicates the theory.

5 Introduction I. Motivation: interest on BH in D>4 II. Context III. Status of known BH solutions/species in D>4 Uni horizon BHs A topological classification of known BHs n=d-4 Multi horizon BHs Black Saturn Di Ring Bicycling Black Ring Pomeransky, Sen kov, Elvang, Mishima, Iguchi, Hollands, Yazadjiev, Evslin, Emparan, Camps, Giusto, Saxena, Figueras, Kleihaus, Harmark, Obers, Radu, Ishibashi, Kunz, MJR,

6 Introduction I. Motivation: interest on BH in D>4 II. Context III. Status of known BH solutions/species in D>4 D=4 has one black hole Kerr black hole Asympt. Flat b.c. where The phase diagram ah 1 j Angular momenta bounded from above J GM 2 Spherical horizon topology S 2 To compare solutions we need to fix a common scale Classical GR We'll fix the mass M equivalently factor it out to get dimensionless quantities ah j 2 ω

7 Introduction I. Motivation: interest on BH in D>4 II. Context III. Status of known BH solutions/species in D>4 D=5 has three black holes (uni horizon) Myers -Perry black hole Myers and Perry (1986) What are the known solutions of black holes in D=5? Two topologies: Spherical horizon topology S 3 Black Ring thin branch fat branch Emparan and Reall (2001) Non-spherical horizon topology S 1 x S 2 The phase diagram of BHs with ONE angular momenta ah Myers -Perry black hole Angular momenta bounded from above Black Ring j 1 Angular momenta bounded from below 1 j 2 For each value of M and j there are three solutions The generalization of these solutions with TWO angular momentums is known

8 Introduction I. Motivation: interest on BH in D>4 II. Context III. Status of known BH solutions/species in D>4 D>5 Seems to have??? black holes Myers Perry black hole where ah The phase diagram of BHs with ONE angular momentum Always a horizon Angular momenta unbounded Ultra-spinning black hole 1 j Are there other black hole solutions? Answer: Yes Black Rings.

9 Black rings in D>5 I. Introduction II. Method and results What The is techniques a qualitative and way methods to construct used to of find black new rings BHs in solutions are not? successfully extended to higher dimensions D=5 Balance in D=5 S 2 at each point selfgravitation + tension Singular + rotation black rings Black rings

10 Black rings in D>5 I. Introductio II. Method and results Can we use a similar qualitative construction of black rings in D>5? Balance in D>5 S D-3 at each point selfgravitation + tension + rotation Thin Black Rings Then the thin black ring is expected to approach locally the boosted black string if we find a way to guarantee this balance.

11 Black rings in D>5 I. Introductio II. Method and results We approximate the black ring by a distributional source of energy-momentum. Distributional sources for the black string in the weak field regime The general form of the equations of motion in absence of external forces is Carter (2001) If it is satisfied then the linear distribution of energy-momentum will be in equilibrium

12 Black rings in D>5 I. Introductio II. Method and results The equilibrium conditions translates into a very specific condition for the boost parameter The balance condition where For building the explicit solution for the thin black ring we used the Matched asymptotic expansion The basic idea, in a problem with two widely separate scales, is that one can build approximate solutions to the equation in the two zones and match at an intermediate zone where both approximations are valid.

13 Black rings in D>5 I. Introduction II. Method and results ah Some phases D>5: analitical results D>5 It seems that there is an infinite number of BHs. j

14 AdS Black rings in D>4 I. Introduction II. Method and results The only known solutions Kerr-Ads BHs Do Anti de Sitter Black Rings exist in higher dimensions? Hawking and Taylor. Gibbons, Lu, Page and Pope Asympt. AdS b.c. Balance in D>4 selfgravitation + tension + rotation + centripetal pull Thin Black Rings

15 AdS Black rings in D>4 I. Introduction II. Method and results Do de Sitter Black Rings exist in higher dimensions? Yes Asympt. ds b.c. Do ( Anti ) de Sitter Black Saturns exist in higher dimensions? Yes Yes

16 AdS Black rings in D>4 I. Introduction II. Method and results Start from global AdS coordinates The ring is placed at Balance condition where AdS BR AdS BS Flat BR We change to a coordinate system adapted to the problem Balance condition

17 AdS Black rings in D>4 I. Introduction II. Method and results AH D>5 AH The patterns (*) are compressed to the range J M. D=5 J max < M J max = M J (*) GL instabilities and membrane behaviour J max = M J

18 Other Black Holes I. D=5 SUSY Black Rings II. Multi BHs e.g. Bycicling Black Rings Do SUSY AdS Back Rings exist? No The sources of Black String of ungauged SUGRA If we use this to build the AdS SUSY Black Ring with the same technique The balance is never achieved conical singularities will appear

19 Other Black Holes I. D=5 SUSY Black Rings II. Multi BHs e.g. Bycicling Black Rings Find a rod structure and use the inverse scattering method What is a Bicycling Black ring? S 1 x S 2 A balance condition is required to select the physical black hole solution If not imposed there are disks of conical singularities

20 Future directions and conclusions Is there a dynamical balance condition for thin and fat black rings? Which is the physical interpretation for this more general condition? Conclusions We reviewed known asymptotically flat, AdS and ds black holes in higher dimensions. We investigated in more detail the solutions of thin black rings in D>4 We extended the methods and proved the existence of BR D>4 in curved backgrounds We found a strong tool to identify regular black hole solutions: a dynamical balance condition A lot remains to be done and we expect in the future to contribute further to the subject of black objects in more than four dimensions Thank You!