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 Sussex, August

◆ 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 t Z (5th dimension ) Production Mechanism of black branes  Analogy to gravitational collapse  Bubbles collision  They might fragment into black holes (PBHs?) uv 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<10 D3 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 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 Metric Scalar 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.  H orizon formation (and singularity behind it) is a generic phenomena in the collision of walls.  T he 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)