1. p-branes on the charged background
Dmitry G. Orlov (NCU; VNIIMS, Russia)
8th January
2008 Taitung International School/Workshop on Cosmology and Gravitation

2. Dilatonic black holes
System consists of gravity, form field and scalar field:
S-duality

3. case of one charge (magnetically charged brane)
dilatonic black holes
case of one charge (magnetically charged brane)
dyonic case

4. asymptotically flat (AF) on the linear dilaton background (LDB)
dilatonic black holes
For investigated system exist
only two type solutions black hole solution:
asymptotically flat (AF)
on the linear dilaton background (LDB)
D.Gal'tsov, S.Klevtsov, DO and G.Clement,
``More on general p-brane solutions'’,
Int. J. Mod. Phys.A21,3575(2006) ; hep-th/
G.Clement, D.Gal'tsov, C.Leygnac and DO,
``Dyonic branes and linear dilaton background'’
Phys.Rev. D73, (2006); hep-th/

5. asymptotycally flat solution - dilatonic black p-brane
dilatonic black holes - one charge - AF
asymptotycally flat solution - dilatonic black p-brane
where
and

6. First law of thermodynamics:
dilatonic black holes - one charge - AF
- mass
- temperature
- entropy
- magnetic charge
First law of thermodynamics:
We have charged black brane on neutral background.

7. black brane on linear dilaton background (LDB)
dilatonic black holes - one charge - LDB
black brane on linear dilaton background (LDB)
Scalar
curvature:

8. So we have neutral solution on the charged background !
dilatonic black holes - one charge - LDB
- dependence only from scale factor, so do not
give deposit in the first law.
First law of thermodynamics:
So we have neutral solution on the charged background !

9. asymptotycally flat solution - dyonic black p-brane
dilatonic black holes - dyonic case - AF
asymptotycally flat solution - dyonic black p-brane
We have dyonic charged black brane
on neutral background.

10. dyonic solution - black brane on LDB
dilatonic black holes - dyonic case - LDB
dyonic solution - black brane on LDB
- depends only from scale factor
We have charged black brane on charged background !

11. dyonic solution - black brane on LDB
dilatonic black holes - dyonic case - LDB
dyonic solution - black brane on LDB
Neutral solution on dyonic charged background.

12. Summarize 1. Uniqueness theorem (by construction):
For spherical symmetrical p-brane solution exist only two type:
AF and LDB.
2. Linear dilaton background has non-trivial charge, so it’s possible:
- neutral brane on charged background
- charged brane on charged background
- neutral brane on dyonic charged background
3. LDB solution is general class of black hole solution (was checked
for ultimate cases (instanton) and (domain wall)).