Emmy's letter to Santa Claus (and a reply): Vaidya geometries and scalar fields with null gradients

TL;DR

The paper discusses specific solutions in Vaidya geometries involving scalar fields with null gradients, comparing theoretical models and their physical plausibility.

Contribution

It introduces a novel exact plane wave solution sourced by a scalar field with a lightlike gradient, expanding the understanding of scalar field configurations in gravitational backgrounds.

Findings

Vaidya solutions with null gradient scalar fields are analyzed.

A new exact plane wave solution with a lightlike scalar gradient is presented.

The physical limitations of certain scalar field configurations are discussed.

Abstract

Emmy, a child prodigy, writes a letter to Santa Claus asking for a Vaidya solution sourced by a massless scalar field with null gradient for Christmas. Santa writes back explaining why such a toy cannot be built and offers an exact plane wave sourced by a scalar field with lightlike gradient as a replacement.