Kasner-type singularities and solitons with Lifshitz asymptotics

TL;DR

This paper constructs exact Einstein-Maxwell-dilaton solutions exhibiting Kasner-type singularities and Lifshitz asymptotics, including a regular soliton case, with implications for photon trapping and geodesic behavior.

Contribution

It introduces new exact solutions with Kasner and Lifshitz features, including a regular soliton, expanding understanding of anisotropic singularities and Lifshitz spacetimes.

Findings

Null geodesics can be trapped by infinite potential barriers.

Existence of periodic null geodesics in the solutions.

A regular soliton solution with Lifshitz scaling.

Abstract

We present an exact solution in Einstein-Maxwell-dilaton gravity describing a spacetime with an anisotropic Kasner-type singularity and Lifshitz asymptotics. This configuration can also be supported by a phantom scalar while still satisfying the Null Energy Condition. For certain parameters of this solution, null geodesics can have an infinitely deep effective potential, thus trapping photons in a finite region along the radial direction. Some examples of periodic null geodesics are obtained. A particularly interesting special case of this solution is a regular, soliton-type metric that retains its Lifshitz scaling in the time coordinate.