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 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

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).

Higher Dimensional Spacetime: ADD-model

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

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

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

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

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

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)

The same form of this metric in 4D describes a cosmic string 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

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?

String(conical singularity) 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)

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!!

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-

What is the physics of these 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?

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

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

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

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

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

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

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

New Solutions: Lump of dark radiation Radiation density radius

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)

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