Static Spherically Symmetric Kerr-Schild Metrics and Implications for the Classical Double Copy

TL;DR

This paper explores the physical sources of static spherically symmetric Kerr-Schild metrics, revealing they often violate energy conditions and are linked to electric charge densities via the classical double copy framework.

Contribution

It provides a detailed analysis of the stress-energy tensors sourcing Kerr-Schild metrics and clarifies their relation to electric charge density in the classical double copy context.

Findings

Sources without singularities or horizons violate energy conditions.

Stress-energy tensors are generally not perfect fluids and include shear stresses.

Electric charge density is associated with the Komar energy density in the double copy.

Abstract

We discuss the physical interpretation of stress-energy tensors that source static spherically symmetric Kerr-Schild metrics. We find that the sources of such metrics with no curvature singularities or horizons do not simultaneously satisfy the weak and strong energy conditions. Sensible stress-energy tensors usually satisfy both of them. Under most circumstances these sources are not perfect fluids and contain shear stresses. We show that for these systems the classical double copy associates the electric charge density to the Komar energy density. In addition, we demonstrate that the stress-energy tensors are determined by the electric charge density and their conservation equations.