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 Ø One of interesting and fundamental topics Ø Creation of Big bang universe Black brane solution Ø They could be formed by such collision ?

◆ Colliding walls and mechanism of black brane production t Production Mechanism of black branes Ø Ø Ø 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 Z (5 th dimension ) ? (Ekpyrotic, cyclic universe, “Relaxing to 3 -brane”)

◆ Brane Gas Cosmology ● Main idea is similar to String Gas Cosmology（Brandenberger & Vafa 89） Annihilation of two branes plays an important role ◆ Dimensionality problem ◆ Why is our world three spatial dimensions ? ◆ How many dimensions expand (or stay at the string length) ? Karch and Randall 05 ‘Relaxing to 3 -brane’ D 3 brane would not intersect and survive in 10 D 4+4<10 space-time volume • They say that 10 D cosmological evolution would lead D 3 and D 7 branes to dominate • It may be applied to the initial setting of KKLT model Collision of two branes is very interesting topic in string theory.

◆ Modeling of Colliding walls p Single BPS domain wall sol. in 5 D SUGRA (Arai, et. al. PLB ’ 03) p Two walls are located far away with each other Initial velocity is provided by boosting the walls p ● Asymptotically Ad. S spacetime ( Randall-sumdrum model, Ad. S/CFT correspondance) 5 D Scalar field: Width of brane Metric: y l l a tic o t p m y S As Ad Minkowski

◆ Black hole formation is a generic consequence of collisions. Two examples Y. T , H. Kudoh and K. Maeda (07) Ø 5 D BPS solution (Arai et al 03) Arai case Natural brane (soliton) sol from 5 D SUGRA theory Ø Extending 4 D BPS sol (Eto et al 05) to 5 D solution Metric Y. T and K. Maeda (06) TM case Scalar field Asymptotically Ad. S Parameter indicating effect of Ad. S

◆ Symmetric or Asymmetric collision with Arai case different width, speeds and effect of Ad. S ● Symmetric ● Asymmetric Ø Energy density of scalar field increases at the collsion point Ø Curvature and Kretschmann scalar diverge→ Singularity formation

◆ Results Ø The wall’s tension increases during the collision because the induced universes on the walls are contracting. Ø Singularity emerges after the collision Ø 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 Ø Two walls just pass through and the final configurations are well described by the initial ones.

● Horizon formation ■ Double-null coordinate： Ø Can follow the collision even when a singularity appears ● Symmetric ● Asymmetric

◆Black hole formation covered by event horizon Production of higher dimensional black hole (brane) ■ Speed of Wall Irrespective of the initial speed, the final speed after collision goes to light speed Ø Ø Walls are trapped nearby horizon

◆ Results Ø Black brane is produced by the collision. Ø Walls are trapped around the surface of horizon. Ø The bulk outside the two walls asymptotes to Ad. S and the walls are accelerating outside. The result is very generic and similar for the wide range of initial data in both two cases. Ø For asymmetric collision, an interesting difference is that the kink wall escapes from the horizon.

● Black brane is prduced in generic case expect for ‘nonrelativistic case’ Ø Horizon has three homogeneous spatial directions 5 D ~ 5 D Ad. S-Schwarzschild BH Later evolution ●Symmetric Ø Gregory-Laflamme instability Ø Multiple BHs are produced Ø Producing primordial BH and Gravitational waves in an early universe 3 D ●Asymmetric

◆ Summary & Remarks We have considered a system of colliding BPS domain walls in 5 D asymptotically spacetime. The role of gravity can drastically change the picture of ‘silent’ collisions without self-gravity. Ø Horizon formation (and singularity behind it) is a generic phenomena in the collision of walls. Ø The bulk outside the two walls is approximated by the Ad. S. A study of the effects and roles of other fields in supergravity. Fermions on colliding branes (G. Gibbons, K. Maeda and Y. T 06)