Late Time Behaviors of an Inhomogeneous Rolling Tachyon

TL;DR

This paper derives an exact solution describing the late-time decay of an inhomogeneous unstable D-brane with tachyon and electromagnetic fields, revealing energy conversion into electric flux and tachyon matter.

Contribution

It presents a novel exact solution for inhomogeneous D-brane decay with time and spatial dependence, advancing understanding of late-time tachyon dynamics.

Findings

Energy density distribution can be controlled by parameters.

The solution shows energy conversion into electric flux and tachyon matter.

Momentum density remains zero throughout spacetime.

Abstract

We study an inhomogeneous decay of an unstable D-brane in the context of Dirac-Born-Infeld~(DBI)-type effective action. We consider tachyon and electromagnetic fields with dependence of time and one spatial coordinate, and an exact solution is found under an exponentially decreasing tachyon potential, $e^{-|T|/\sqrt{2}}$, which is valid for the description of the late time behavior of an unstable D-brane. Though the obtained solution contains both time and spatial dependence, the corresponding momentum density vanishes over the entire spacetime region. The solution is governed by two parameters. One adjusts the distribution of energy density in the inhomogeneous direction, and the other interpolates between the homogeneous rolling tachyon and static configuration. As time evolves, the energy of the unstable D-brane is converted into the electric flux and tachyon matter.