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Ge ometric D- branes , Torsion & Emergent (Anti) de Sitter B lack holes.

NSM 2011, Department of Physics & Astrophysics, University of Delhi 7 th December 2011 Abhishek K. Singh Dept of Physics & Astrophysics University of Delhi Based on: 2010 ; Curved D- braneworld Action in 4D and Black Holes; World Scientific, page no . 559-566.

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Ge ometric D- branes , Torsion & Emergent (Anti) de Sitter B lack holes.

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  1. NSM 2011, Department of Physics & Astrophysics, University of Delhi 7th December 2011 Abhishek K. Singh Dept of Physics & Astrophysics University of Delhi Based on: 2010; Curved D-braneworld Action in 4D and Black Holes; World Scientific, page no. 559-566. 2010; D-braneworld Black Holes; World Scientific, page no: 567-574. Under Progress, with SupriyaKar, Kumar PriyabratPandey & Sunita Singh. Geometric D-branes, Torsion & Emergent (Anti) de Sitter Black holes.

  2. 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

  3. Type IIB (R,) NS-NS (Two form as Connection) (R,,) Define: Define: Define: (Torsion)

  4. Irreducible Gauge Curvatures ) Where; ) K=

  5. Covariantly constant Two form If (R, d (R,d (Static Gauge) (R, d

  6. D4-brane Action Equation of Motion:

  7. Alternate D4-brane Action Equivalently: Equation of Motion:

  8. Emergent Gravity &dS5 Geometry Emergent Gravity Anstaz: de-Sitter geometry

  9. D4-brane on Where, Equation of Motion:

  10. Charged Black hole Solution Anstaz:

  11. Rotating charged black hole Anstaz:

  12. Einstein Cartan Theory ) “Cartan Curvature in addition to Riemannian curvature”

  13. Conclusions • . • Braneworld ( rotating & charged BH sol.) • Point charge Non linear extended charge. • Cartan curvature in addition to Riemannian curvature.

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