From the Janis-Newman-Winicour naked singularities to Einstein-Maxwell phantom wormholes

TL;DR

This paper explores the relationships between Janis-Newman-Winicour naked singularities, wormholes, and dilaton black holes, revealing that certain parameter choices lead to physically forbidden solutions, thus questioning their physical viability.

Contribution

It establishes connections between naked singularities, wormholes, and dilaton black holes through complex transformations and parameter analysis, clarifying the physical meaning of key parameters.

Findings

Janis-Newman-Winicour solution relates to dilaton black holes with negative mass.

Wormhole solutions are derived from naked singularities via complex transformations.

Certain parameter values imply physically forbidden negative mass black holes.

Abstract

The Janis-Newman-Winicour spacetime corresponds to a static spherically symmetric solution of Einstein equations with the energy momentum tensor of a massless quintessence field. It is understood that the spacetime describes a naked singularity. The solution has two parameters, $b$ and $s$. To our knowledge, the exact physical meaning of the two parameters is still unclear. In this paper, starting from the Janis-Newman-Winicour naked singularity solution, we first obtain a wormhole solution by a complex transformation. Then let the parameter $s$ approaching infinity, we obtain the well-known exponential wormhole solution. After that, we embed both the Janis-Newman-Winicour naked singularity and its wormhole counterpart in the background of de Sitter or anti-de Sitter Universe with the energy momentum tensor of massive quintessence and massive phantom fields, respectively. To our surprise, the resulting quintessence potential is actually the dilaton potential found by one of us. It hints us that, by modulating the parameters in the charged dilaton black hole solutions we can get the Janis-Newman-Winicour solution. Furthermore, a charged wormhole solution is obtained by performing complex transformation on the charged dilaton black hole solutions in the background of de Sitter or anti-de Sitter Universe. We eventually find that $s$ is actually related to the coupling constant of dilaton field to Maxwell field and $b$ is related to a negative mass for the dilaton black holes. A negative black hole mass is physically forbidden. Therefore, we conclude that the Janis-Newman-Winicour naked singularity solution is not physically allowed.