Dynamics of Colliding Branes and Black Brane Production

Dynamics of Colliding Branes and Black Brane Production

Yu-ichi Takamizu (Waseda univ, Japan)

With Hideaki Kudoh and Kei-ichi Maeda@ Sussex, August 21 2007

◆ Introduction Brane or domain wall

Brane - an interesting object in string theory

BPS domain wall

Interesting and “realistic” objects in early (higher dimensional) universe and in strings/SUGRA theory

Collision of branes

One of interesting and fundamental topics

Creation of Big bang universe

Black brane solution They could be formed by such collision ?

◆ 　 Colliding walls and mechanism of black brane production

◆ 　 Colliding walls and mechanism of black brane production

t

Z(5th dimension )

Production Mechanism of black branes Analogy to gravitational collapse Bubbles collision They might fragment into black holes

(PBHs?)

u v

If this is a general scenario of colliding branes,

creation of big bang universe may not be possible ?

(Ekpyrotic, cyclic universe, “Relaxing to 3-

brane”)

◆ 　 Brane Gas Cosmology

Karch and Randall 05 ‘Relaxing to 3-brane’

• They say that 10D cosmological evolution would lead D3 and D7 branes to dominate.

• It may be applied to the initial setting of KKLT model

4+4<10D3 brane would not intersect and survive in 10D space-time volume

● Main idea is similar to String Gas Cosmology （ Brandenberger & Vafa 89

） Annihilation of two branes plays an important role

Collision of two branes is very interesting topic in string theory.

◆ Why is our world three spatial dimensions ?

◆ How many dimensions expand (or stay at the string length) ?

◆ Dimensionality problem

( Randall-sumdrum model, AdS/CFT correspondance)

◆ Modeling of Colliding walls◆ Modeling of Colliding walls

Scalar field:

Metric:

　 Width of brane

Asymptotically

AdS

5D

Minkowski

Single BPS domain wall sol. in 5D SUGRA (Arai, et. al. PLB ’03) Two walls are located far away with each other Initial velocity is provided by boosting the walls

● Asymptotically AdS spacetime

◆ Black hole formation is a generic consequence of collisions.

5D BPS solution (Arai et al 03) 　

Natural brane (soliton) sol from 5D SUGRA theory

Extending 4D BPS sol (Eto et al 05) to 5D solution

Y.T , H.Kudoh and K.Maeda (07)

Asymptotically 　 AdS

Two examples

TM case

Arai case

Parameter indicating effect of AdS

MetricScalar field

Y.T and K.Maeda (06)

◆ Symmetric or Asymmetric collision with different width, speeds and effect of AdS

● Symmetric ● Asymmetric

Arai case

Energy density of scalar field increases at the collsion point

Curvature and Kretschmann scalar diverge→ Singularity formation

◆ Results The wall’s tension increases during the collision because the induced universes on the walls are contracting.

Singularity emerges after the collision

A portion of energy is stored in this region.

For the wide range of initial parameters, this basic picture is a similar and generic.

However, the singularity does not appear for ‘norelativistic’ case

Two walls just pass through and the final configurations

are well described by the initial ones.

● Horizon formation■ Double-null coordinate ：

Can follow the collision even when a singularity appears

● Symmetric ● Asymmetric

Irrespective of the initial speed, the final

speed after collision goes to light speed

Walls are trapped nearby horizon

◆ Black hole formation covered by event horizon

■ Speed of Wall

Production of higher dimensional black hole (brane)

◆ Results

Black brane is produced by the collision.

Walls are trapped around the surface of horizon.

The bulk outside the two walls asymptotes to AdS and the walls are accelerating outside.

The result is very generic and similar for the wide

range of initial data in both two cases. For asymmetric collision, an interesting difference is that

the kink wall escapes from the horizon.

5D

Gregory-Laflamme instability

Multiple BHs are produced

Producing primordial BH and

Gravitational waves in an early universe

~ 5D AdS-Schwarzschild BH

3D●Symmetric ●Asymmetric

● Black brane is prduced in generic case

expect for ‘nonrelativistic case’

Horizon has three homogeneous spatial directions

Later evolution

◆ 　 Summary & Remarks We have considered a system of colliding BPS domain walls

in 5D asymptotically spacetime.

The role of gravity can drastically change the picture of ‘silent’ collisions without self-gravity.

Horizon formation (and singularity behind it) is a generic phenomena in the collision of walls.

The bulk outside the two walls is approximated by the AdS.

A study of the effects and roles of other fields in supergravity. Fermions on colliding branes (G. Gibbons, K. Maeda and Y.T 06)