Collision of localized shocks in AdS${}_5$ as a series expansion in transverse gradients

Abstract

We introduce a computational framework to more efficiently calculate the collision of localized shocks in five dimensional asymptotically Anti-de Sitter space. We expand the Einstein equations in transverse gradients and find that our numerical results agree well with exact solutions already at first order in the expansion. Moreover, the Einstein equations at first order in transverse gradients can be decoupled into two sets of differential equations. The bulk fields of one of these sets has only a negligible contribution to boundary observables, such that the computation on each time slice can be simplified to the solution of several planar shockwave equations plus four further differential equations for each transverse plane `pixel'. At the cost of errors of $\lesssim 10\%$ at the hydrodynamization time and for low to mid rapidities, useful numerical solutions can be sped up by roughly one order of magnitude.

29 pages, 12 figures

References in corpus (4)

• Nonlinear Fluid Dynamics from Gravity
• Holography and colliding gravitational shock waves in asymptotically AdS_5 spacetime
• Holographic thermalization with radial flow
• Particle spectra and HBT radii for simulated central nuclear collisions of C+C, Al+Al, Cu+Cu, Au+Au, and Pb+Pb from Sqrt(s)=62.4-2760 GeV