Generating Moving Field Initial Conditions with Spatially Varying Boost

TL;DR

This paper presents a versatile algorithm for creating initial conditions with specific velocity profiles by locally boosting fields, enabling advanced simulations across physics disciplines including cosmology and condensed matter.

Contribution

The paper introduces a generic spatially varying boost algorithm that can generate relativistic initial conditions for any field type without restrictions.

Findings

Successfully boosted solitons to ultra-relativistic speeds for collision studies.

Generated relativistic transverse Proca fields with random velocities.

Set up spin-1 Schrödinger-Poisson fields with realistic dark matter perturbations.

Abstract

We introduce a novel class of algorithms, the ``spatially varying boost'', for generating dynamical field initial conditions with prescribed bulk velocities. Given (non-moving) initial field data, the algorithm generates new initial data with the given velocity profile by performing local Lorentz boosts. This algorithm is generic, with no restriction on the type of the field, the equation of motion, and can endow fields with ultra-relativistic velocities. This algorithm enables new simulations in different branches of physics, including cosmology and condensed matter physics. For demonstration, we used this algorithm to (1) boost two Sine-Gordon solitons to ultra-relativistic speeds for subsequent collision, (2) generate a relativistic transverse Proca field with random velocities, and (3) set up a spin-$1$ Schr\"{o}dinger-Poisson field with velocity and density perturbations consistent with dark matter in matter dominated universe.