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Mohamed Anber HEP Bag Lunch April 1st With Lorenzo Sorbo

New exact solutions on the Randall-Sundrum 2-brane: lumps of dark radiation and accelerated black holes. Mohamed Anber HEP Bag Lunch April 1st With Lorenzo Sorbo. Outline. Higher dimensional spacetime: ADD, Randall-Sundrum models AdS/CFT

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Mohamed Anber HEP Bag Lunch April 1st With Lorenzo Sorbo

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  1. New exact solutions on the Randall-Sundrum 2-brane: lumps of dark radiation and accelerated black holes Mohamed Anber HEP Bag Lunch April 1st With Lorenzo Sorbo

  2. Outline • Higher dimensional spacetime: ADD, Randall-Sundrum models • AdS/CFT • Building black holes on branes (Emparan, Horwoitz and Myers construction) • New solutions on RS 2-Brane: Lump of radiation and accelerated black holes • AdS/CFT interpretation

  3. Higher Dimensional Spacetime • Kaluza–Klein theory(1921): compactified extra dimensions, used extensively in unified field theories (string theory, M-theory ) • Large extra dimensions (ADD model-1998): Hierarchy problem (elevate it).

  4. Higher Dimensional Spacetime: ADD-model

  5. Randall-Sundrum model • Randall-Sundrum (I & II) models (1999): Hierarchy problem, SM lives on a brane in AdS space. • Model I: 2 branes

  6. Randall-Sundrum model • Model II: single brane (the world lives on the Plank brane), the extra dimension is infinite but we have 4-D gravity on brane!! • String implementation for Add and RS models

  7. AdS/CFT • Holography (Bekenstein, Susskind, ‘t Hooft, Bousso)

  8. AdS/CFT • Maldacena conjecture (AdS/CFT) (1997) • Conformal=scale invariance, Roughly speaking

  9. AdS/CFT Randall-Sundrum model provides a naturla set up to study AdS/CFT On the RS brane: gravity+CFT

  10. AdS/CFT • Black holes localized on RS-branes: great opportunity to study BH evaporation (classical BH+CFT corrections) • This is important to shed some light on quantum gravity • But no localized BH on RS 3-brane (4+1 D spacetime) so far!! • Emparan, Horowitz and Myers (EHM) (1999) found BH on RS-2 brane (3+1 D)

  11. EHM construction • First we need to understand gravity in 2+1 D • Gravity is not dynamical in 2+1 D • Vacuum Solution: conical singularity, no BH The same form of this metric in 4D describes a cosmic string

  12. EHM construction • RS brane is accelerating in the AdS • If you want a BH on this brane, this BH should be accelerating as well in AdS • How to implement this picture?

  13. EHM construction • Find some solution that describes an accelerating BH in AdS background: the AdS-C metric • Then cut it with an empty brane That is it!! String(conical singularity) Root H(y)

  14. EHM construction • What we get? For flat brane (at x=0) • The conical singularity is dressed with a horizon . This horizon is quantum in nature (quantum cosmic censorship) • EHM also found that other solutions for non-flat branes (e.g. with AdS brane there is quantum corrected BTZ BH) • Are there any more allowed solutions? Yes!!

  15. New Solutions M. Anber and L. Sorbo arXiv:0803.2242 • We want the most general brane embedding in the AdS-C metric. How to do it? • Take • Compute the extrinsic curvature • Write down Israel junction condition • We find K+ K-

  16. New Solutions • But the AdS-C metric is invariant under the transformation • Then we also have • These are the only allowed solutions!! What is the physics of these new solutions?

  17. New Solutions: Accelerated BHs on RS-2 brane • We take • The induced metric on this brane reads (after suitable parameter transformations)

  18. In the bulk On the brane This metric describes accelerating BHs This is the first accelerating BH solution on a brane New Solutions: Accelerated BHs on RS-2 brane

  19. New Solutions: Accelerated BHs on RS-2 brane • What is the CFT picture? Tr T=0 CFT Cosmological constant on brane

  20. New Solutions: Accelerated BHs on RS-2 brane • This black hole is accelerating, there must be a string (adge on the brane) that can provide such acceleration

  21. New Solutions: Accelerated BHs on RS-2 brane • F=mA+ O(mAG) Classical force Quantum effect

  22. New Solutions: Lump of dark radiation • Now we take • To find the brane induced metric • With Friedman-like equation There is a conical singularity Cosmological constant Thermal radiation Hubble parameter curvature

  23. New Solutions: Lump of dark radiation • The energy momentum tensor Cosmological constant radiation

  24. New Solutions: Lump of dark radiation • This metric is very complicated • We study the limiting case with a flat barne • For m=0 we obtain • This is a flat metric! • The energy momentum tensor to first order of m

  25. New Solutions: Lump of dark radiation Radiation density radius

  26. New Solutions: Lump of dark radiation • This is a lump of radiation on top of conical geometry • No horizon, No quantum cosmic censorship! (this is time-dependent solution)

  27. Conclusion • We have presented new solutions on RS-2 brane • We hope to learn something about the higher dimensional case • AdS/CFT is very exciting , recently many applications have been proposed: QCD plasma, superconductivity, etc.. • It would be great to see what applications one can find in the case of RS-2 brane

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