Abstract
Using numerical holography, we study the collision, at non-zero impact parameter, of bounded, localized distributions of energy density chosen to mimic relativistic heavy ion collisions, in strongly coupled $$ \mathcal{N}=4 $$ supersymmetric Yang-Mills theory. Both longitudinal and transverse dynamics in the dual field theory are properly described. Using the gravitational description, we solve 5D Einstein equations with no dimensionality reducing symmetry restrictions to find the asymptotically anti-de Sitter spacetime geometry. Implications of our results on the understanding of early stages of heavy ion collisions, including the development of transverse radial flow, are discussed.
Highlights
Where H± is an arbitrary function of the 2D transverse wavevector k⊥ and the longitudinal variable z∓
Using numerical holography, we study the collision, at non-zero impact parameter, of bounded, localized distributions of energy density chosen to mimic relativistic heavy ion collisions, in strongly coupled N = 4 supersymmetric Yang-Mills theory
The geometry described by eqs. (2.1) and (2.3) represents a state in the dual SYM theory with a stress-energy tensor expectation value given by [10]
Summary
Our time evolution scheme [11] for asymptotically-AdS gravitational dynamics uses infalling Eddington-Finkelstein (EF) coordinates in which the spacetime metric has the form r2 L2 gμν (x, r) dxμdxν dr dt ,. To transform the geometry (2.1) to the infalling form (2.6) one must locate the same congruence of infalling radial null geodesics in FG coordinates. Let Y ≡ {yμ, s} denote the FG coordinates of some event, and let X ≡ {xμ, r} denote the EF coordinates of the event at affine parameter r along the radial infalling geodesic which begins at boundary coordinates xμ. The solution Y (X) to the geodesic equation (in FG coordinates) for the same null geodesic which begins at boundary coordinates xμ provides the required mapping between EF and FG coordinates Given this mapping, the required transformation of the FG metric components GMN (Y ) to the metric components GMN (X) in our infalling coordinates (with ds2 = GMN (X) dXM dXN = GMN (Y ) dY M dY N ) is .
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