Radiation from a D-dimensional collision of shock waves: numerical methods

Abstract

We present a pedagogical introduction to the problem of evolving a head on collision of two Aichelburg-Sexl gravitational shock waves in D-dimensions, using perturbative techniques. We follow a constructive approach with examples, going in some detail through: the set up of the exact initial conditions and their properties; perturbative methods in flat space-time with Green function solutions; and numerical strategies to evaluate the integral solutions. We also discuss, briefly, radiation extraction methods adapted to this problem, together with some of the results for this system.

Lecture notes from the NRHEP spring school held at IST-Lisbon, March 2013. Extra material and notebooks available online at http://blackholes.ist.utl.pt/nrhep2/ To be published by IJMPA (V. Cardoso, L. Gualtieri, C. Herdeiro and U. Sperhake, Eds., 2013)

References in corpus (5)

• The high-energy collision of two black holes
• BlackMax: A black-hole event generator with rotation, recoil, split branes and brane tension
• Ultrarelativistic black hole formation
• Critical comment on the recent microscopic black hole search at the LHC
• Radiation from a D-dimensional collision of shock waves: higher order set up and perturbation theory validity

Cited by in corpus (5)

• Initial Conditions for Numerical Relativity -- Introduction to numerical methods for solving elliptic PDEs
• Lecture Notes: Numerical Relativity in higher dimensional spacetimes
• Radiation from a $D$-dimensional collision of shock waves: proof of first order formula and angular factorisation at all orders
• Bremsstrahlung and black hole production from collisions of ultra-boosted particles at non-zero impact parameter
• Radiation from a D-dimensional collision of shock waves: Two dimensional reduction and Carter-Penrose diagram