Äîêóìåíò âçÿò èç êýøà ïîèñêîâîé ìàøèíû. Àäðåñ îðèãèíàëüíîãî äîêóìåíòà : http://qfthep.sinp.msu.ru/talks/sa100913.pdf Äàòà èçìåíåíèÿ: Sun Sep 12 21:46:32 2010 Äàòà èíäåêñèðîâàíèÿ: Mon Oct 1 19:36:07 2012 Êîäèðîâêà: IBM-866 Ïîèñêîâûå ñëîâà: orbit

The XIXth International Workshop on High Energy Physics and Quantum Field Theory September 8-15, 2010, Golitsyno, Moscow, Russia

Brane Black Holes
S.Alexeyev
Sternberg Astronomical Institute, Moscow

D.Starodubseva
Ural State University, Ekaterinburg


References
§ N.Dadhich, R.Maartens, P.Papadopoulos,V.Rezania, Phys. Lett. B487, 1 (2000); § De-Chang Dai, D.Stojkovic, http://arxiv.org/abs/1004.3291; § T. Tanaka, Prog.Theor.Phys.Suppl. 148, 307 (2003); § R. Emparan, A. Fabbri and N. Kaloper, JHEP 0208, 043 (2002); § S.Alexeyev, D.Starodubtseva, JETP 138, (2010), accepted for October issue


Randal-Sundrum 2

Cosmology solutions

Black hole solutions


5D bulk equations

G

AB

g

2



AB

( ) A B g




A B T





4D brane equations with extra dimensions contribution

G



g



T S
2

4








Black hole solution on the brane
dr 2 2 2 ds ( r ) dt r d sin d (r)
2 2 2 2



where ( r ) 1 , í constants,


r




r
2

2 M / M q/M
2 pl

2 pl

q íëtidal charge¨


BH solution with < 0
contains only one horizon

4 M pl M rh 2 1 1 q 2 M pl MM

2 pl




Limitation on ëtidal charge¨ value
from N.Dadhich, R.Maartens, P.Papadopoulos,V.Rezania (2000)

M q § Gravitational potential: 2 M pl r 2 M 2 r pl

2

§ Requirement: correction term must be much less than Schwarzschild one at Sun mass range, therefore

where

M2 3 pl M pl 4

M

pl


Time-like geodesics
Could be established from

du E 1 u u u 2 u 3 u 4 f (u ) 2 d L2 L
2 2

2

by solving the equation: f (u ) 0


Solutions f (u ) 0
§ Schwarzschild BH § BH with ëtidal charge¨


Solutions f (u ) 0
§ Schwarzschild BH 3 roots § BH with ëtidal charge¨ 4 roots, but minimum one of them is negative no new types of circular orbits


Last stable circular orbit
is defined by the equation

8 u 9u 3 uc 0
23 c 2 c 2

where uc 1 / rc , rc í radius of a stable circular orbit


ëTidal charge¨ contribution
Dimensionless notations:

a í normalized Schwarzschild mass at Sun mass range, a ~ 1 b í normalized ëtidal charge¨


Limitations on normalized ëtidal charge¨ value
§ From N.Dadhich, R.Maartens, P.Papadopoulos, V.Rezania (2000) § From the equation for last stable circular orbit:

§

For Sun mass range: |b| << 106

where § according to astronomical data real BH are Kerr-like ones, therefore, the conditions of a-terms leading contribution in last stable circular orbit equation in Sun mass range leads to

|b| << 1


Conclusions
§ The "tidal charge" changes geodesic equations, but at the range of Sun and larger masses the presence of this one must not introduce new types of geodesics to avoid contradictions with the current astrophysical data. The suggested limit on "tidal charge" value makes impossible the possibility of its direct observation. Perhaps, the indirect consequences of "tidal charge" could be established in high energy physics. § Finally, the Black hole solution from RS2 model, discussed here has no any contradictions with astrophysical observational data at the chosen parameter values range. More strong limitation on "tidal charge" value than suggested by N.Dadhich, R.Maartens, P.Papadopoulos,V.Rezania could be obtained from last stable circular orbits analysis.


Thank you for your attention!!!


And for the questions!!!