Traceless stress-energy and traversable wormholes

TL;DR

This paper presents a family of Einstein solutions with traceless energy-momentum tensors, revealing conditions under which traversable wormholes, naked singularities, or Schwarzschild black holes occur based on a parameter.

Contribution

It introduces a new one-parameter family of solutions demonstrating how traceless energy-momentum tensors can produce different spacetime geometries, including traversable wormholes.

Findings

Traversable wormholes occur for parameter β in (0,1)

Naked singularities occur for β < 0 or β > 1

Schwarzschild black hole corresponds to β = 1

Abstract

A one-parameter family of static and spherically symmetric solutions to Einstein equations with a traceless energy-momentum tensor is found. When the nonzero parameter $\beta$ lies in the open interval $(0,1)$ one obtains traversable Lorentzian wormholes. One also obtains naked singularities when either $\beta < 0$ or $\beta > 1$ and the Schwarzschild black hole for $\beta = 1$.