BTZ LikeString on Codimension2 Brane

1
BTZ Like-String on Codimension-2 Brane
PLANCK 2008 From the Planck Scale to the Electro
Weak Scale

• Minas Tsoukalas (N.T.U.A.)
• work with Bertha Cuadros-Melgar, Eleftherios
  Papantonopoulos Vassilios Zamarias,
  (arxiv0712.3232)
• (to be published in
  PRL)

Barcelona 19/23-05-2008
2
Outline

• Brane World Models
• Black Holes and Codimension-1 Brane-Worlds
• Codimension-2 Brane-Worlds
• BTZ Like-String
• Conclusions

3
Brane-World Models

• String motivated models
• P.Horava E.Witten,Heterotic and type I
  string dynamics from eleven dimensions,Nucl.
  Phys. B 460 (1996) 506, (arxiv hep-ph/9510209)
• Brane World Senario
• D-dimensional space (the brane) embeded in a
  higher dimensional space (the bulk).
• All matter fields are trapped on the brane.
• Gravity propagates in the bulk space.
• If n dimensions ? to the brane
• codimension-n braneworld
• 
  Maartens, Living
  Rev.Rel.77,2004, (arxivgr-qc/0312059)

4
Arkani-Hamed,Dimopoulos Dvali model
(ADD)Randall Sundrum models (RS1-RS2)

• ADD model
• 3-brane in D4n space, with the extra dimensions
  compactified as a torus of size R
• MP2M2n Rn
• RS1 model
• RS2 model
• N.Arkani-Hamed,S.Dimopoulos G.R.Dvali,
  Phys.Lett.B429263-272,1998, (arxivhep-ph/9803315
  )
• L.Randall R.Sundrum, Phys. Rev. Lett. 83
  (1999) 3370, (arxivhep-ph/9905221)
• L.Randall R.Sundrum, Phys. Rev. Lett. 83
  (1999) 4690, (arxivhep-th /9906064)

5
Black Holes and Codimension-1 Branes

• Black String
• Instability
• 
  
  S.S.Seahra, C.Clarkson R.Maartens,
  Phys.Rev.Lett.94121302,2005, (arxivgr-qc/0408032
  )
• ?.Chablin, S.W.Hawking H.S.Reall, Phys. Rev. D
  61, (2000) 065007, (arxivhep-th/9909205)
• R.Gregory, Phys. Rev. Lett. 70, (1993)
  2837-2840, (arxivhep-th.9301052)
• R.Gregory, Class. Quant. Grav. 17L125-L132,
  (2000), (arxivhep-th/0004101)

6
Codimension-2 Brane-Worlds

• 
  
• 
  
  N.Kaloper D.Kiley, JHEP 0705045,2007,
  (arxivhep-th/0703190)
• Any matter on the brane other than tension causes
  singularities more severe than conical
• Thick branes
• Extra curvature terms
• S.Deser, R.Jackiw G.t Hooft, Anals of Phys.
  152, (1984) 220
• J.W.Chen, M.A.Luty E.Ponton, JHEP 0009 (2000)
  012, (arxivhep-th/0003067)
• J.M.Cline, J.Descheneau, M.Giovannini J.Vinet,
  JHEP 0306 (2003) 048, (arxivhep-th/0304147)

7
Gauss-Bonnet/ Induced Gravity Terms

• 
  
• ,
• d-contributions
  non-singular terms
• 
  non-singular terms
• Conical-anomaly and ß
  const.
• ,
• P.Bostock, R.Gregory, I.Navarro J.Santiago,
  Phys. Rev. Lett. 92 (2004) 221901,
  (arxivhep-th/0311074)
• E.Papantonopoulos A.Papazoglou, JCAP 0507,
  004, (2005), (arxivhep-th/0501112)

8
BTZ-Like String

• 
  
  
• 
  
  (1)
  
  
• 
  
  (2)
• 
  
  (3)

9

• non-singular terms
• non-singular
  terms
• 
  
  (4)
• Bulk Equations
  (5)

10

• Combining the (rr), (??) and (??), (??)
  components of the five dimensional Einstein
  equations we get the following set of equations
• A B
• 
  (6)
• 
  
  (7)
• C D

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Solutions

• First we consider A0,D0
  (BTZ Black Hole)(8)
• 
  
• 
  
  (9)
• A0,C0
  (10)
• i) Then from the (??) equation together with
  the fine tuning relation
  we get the following equation
• 
  (11)
• ii)
• M.Banados,C.Teitelboim J.Zanelli, Phys. Rev.
  Lett. 69, 1849 (1992), (arxivhep-th/9204099)

12

• B0,C0
  (12)
• B0,D0
  (13)
• 
  (14)
• 
  (15)
• C.Martinez J.Zanelli, Phys. Rev. D 54, 3830
  (1996), (arxivgr-qc/9604021)

13
Conclusions

• The issue of black holes in braneworld theories
  is still open both in codimension-1 and in
  codimension-2 models.
• We can have a suitable extension of the black
  hole on the brane, into the bulk for a 2-brane in
  4d or for a 3-brane in 5d.
• Higher codimension models????

14

• Searching for the Fourth
  Dimension (1979)-Salvador Dali