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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.
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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
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Type IIB
(R,) NS-NS (Two form as Connection)
(R,,) Define: Define:
Define: (Torsion)
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Irreducible Gauge Curvatures
)
Where;
) K=
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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)
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D4-brane Action
Equation of Motion:
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Alternate D4-brane ActionEquivalently:
Equation of Motion:
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Emergent Gravity &dS5 Geometry
Emergent Gravity
Anstaz:
de-Sitter geometry
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D4-brane on
Where, Equation of Motion:
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𝑫𝟒→ (𝑫𝑫 )𝟑
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Charged Black hole SolutionAnstaz:
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Rotating charged black hole
Anstaz:
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Einstein Cartan Theory
)
“Cartan Curvature in addition to Riemannian curvature”
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Conclusions
1. .
2. Braneworld ( rotating & charged BH sol.)
3. Point charge Non linear extended charge.
4. Cartan curvature in addition to Riemannian curvature.