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BTZ LikeString on Codimension2 Brane

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Title: 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

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

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

11
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)

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????