Janis-Newman-Winicour and Wyman solutions are the same

TL;DR

This paper demonstrates that the Wyman and Janis-Newman-Winicour solutions are identical, providing insights into their energy properties and confirming their equivalence in describing static, spherically symmetric scalar field spacetimes.

Contribution

The paper proves the equivalence of two historically distinct solutions to Einstein's equations with scalar fields and analyzes their energy characteristics.

Findings

Wyman and Janis-Newman-Winicour solutions are identical.

Total energy for the scalar field case is zero.

Confirmed the solutions describe the same spacetime geometry.

Abstract

We show that the well-known most general static and spherically symmetric exact solution to the Einstein-massless scalar equations given by Wyman is the same as one found by Janis, Newman and Winicour several years ago. We obtain the energy associated with this spacetime and find that the total energy for the case of the purely scalar field is zero.