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Mohamed Anber HEP Bag Lunch April 1st With Lorenzo Sorbo

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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

- 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

- 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).

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

- 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

- Holography (Bekenstein, Susskind, ‘t Hooft, Bousso)

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

Randall-Sundrum model provides

a naturla set up to study

AdS/CFT

On the RS brane: gravity+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)

- 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

- 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?

- 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)

- 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!!

- 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-

- 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?

- We take
- The induced metric on this brane reads (after suitable parameter transformations)

In the bulk

On the brane

This metric describes accelerating BHs

This is the first accelerating BH solution on a brane

- What is the CFT picture?

Tr T=0

CFT

Cosmological constant on brane

- This black hole is accelerating, there must be a string (adge on the brane) that can provide such acceleration

- F=mA+ O(mAG)

Classical force

Quantum effect

- 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

- The energy momentum tensor

Cosmological constant

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

Radiation density

radius

- This is a lump of radiation on top of conical geometry
- No horizon, No quantum cosmic censorship! (this is time-dependent solution)

- 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