Geometric D-branes, Torsion & Emergent (Anti) de Sitter Black holes.

NSM 2011, Department of Physics & Astrophysics, University of Delhi 7th December 2011

Abhishek K. SinghDept of Physics & Astrophysics

University of Delhi

Based on:1) 2010; Curved D-braneworld Action in 4D and Black Holes; World

Scientific, page no. 559-566.2) 2010; D-braneworld Black Holes; World Scientific, page no: 567-574.3) Under Progress, with Supriya Kar, Kumar Priyabrat Pandey & Sunita Singh.

Plan of Talk Type IIB NS-NS Geometric -brane. () (static gauge) (Torsion)

Irreducible curvature( NS-NS two form)

(geometric) dS5 (near horizon lt.) (geometric) brane(anti-brane)

Cartan Curvature

Type IIB

(R,) NS-NS (Two form as Connection)

(R,,) Define: Define:

Define: (Torsion)

Irreducible Gauge Curvatures

)

Where;

) K=

Covariantly constant Two form

If (R, d (R,d (Static Gauge) (R, d

Cancellation of curvatures

Curvatures left Dynamical Object

R AdS B H , R (Geometric) , R (Geometric)

D4-brane Action

Equation of Motion:

Alternate D4-brane ActionEquivalently:

Equation of Motion:

Emergent Gravity &dS5 Geometry

Emergent Gravity

Anstaz:

de-Sitter geometry

D4-brane on

Where, Equation of Motion:

𝑫𝟒→ (𝑫𝑫 )𝟑

Charged Black hole SolutionAnstaz:

Rotating charged black hole

Anstaz:

Einstein Cartan Theory

)

“Cartan Curvature in addition to Riemannian curvature”

Conclusions

1. .

2. Braneworld ( rotating & charged BH sol.)

3. Point charge Non linear extended charge.

4. Cartan curvature in addition to Riemannian curvature.