Abstract
We construct shock waves for Lifshitz-like geometries in four- and fivedimensional effective theories as well as in D3-D7 and D4-D6 brane systems. The solutions to the domain wall profile equations are found. Further, the study makes a connection with the implications for the quark-gluon plasma formation in heavy-ion collisions. According to the holographic approach, the multiplicity of particles produced in heavy-ion collisions can be estimated by the area of the trapped surface formed in shock wave collisions. We calculate the areas of trapped surfaces in the geometry of two colliding Lifshitz domain walls. Our estimates show that for five-dimensional cases with certain values of the critical exponent the dependence of multiplicity on the energy of colliding ions is rather close to the experimental data $$ \mathrm{\mathcal{M}} $$ ∼ s 0.15 observed at RHIC and LHC.
Highlights
Duality between gravitation and field theories with a Lifshitz scaling symmetry has recently received much attention
According to the holographic approach, the multiplicity of particles produced in heavy-ion collisions can be estimated by the area of the trapped surface formed in shock wave collisions
We have considered Lifshitz-like metrics arising in four- and five-dimensional effective theories with a non-positive cosmological constant and gauge fields, as well as in intersecting brane systems of supergravities IIA and IIB
Summary
To find solutions to (2.24) with (2.29) looks to be rather complicated. In works [53, 56] a simpler form of shock waves called domain walls was suggested. To derive the equation for the profile, one should consider the mass of a point-like source averaged over the domainwall. The profile of the domain wall has the dependence only on the holographic coordinate z and obeys the equation. The solution to eq (2.32) for the domain wall profile can be written down in the following form φ = φaΘ(z∗ − z) + φbΘ(z − z∗),. It is worth noting that the solution (2.34) decreases in both directions from the point z∗. The point z∗ can be considered as the center of the shock domain wall
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