Volume Integral Theorem for Exotic Matter

TL;DR

This paper introduces an exact integral quantifier for exotic matter violating ANEC in general relativity, demonstrating that traversable wormholes can be supported by arbitrarily small amounts of such matter.

Contribution

It proposes a new integral quantifier for exotic matter violating ANEC and validates it against known wormhole solutions, advancing understanding of exotic matter requirements.

Findings

Quantifier is consistent with small quantities of exotic matter supporting wormholes.

Validated against static, spherically symmetric wormhole solutions.

Supports the principle that minimal exotic matter can sustain traversable wormholes.

Abstract

We answer an important question in general relativity about the volume integral theorem for exotic matter by suggesting an exact integral quantifier for matter violating Averaged Null Energy Condition (ANEC). It is checked against some well known static, spherically symmetric traversable wormhole solutions of general relativity with a sign reversed kinetic term minimally coupled scalar field. The improved quantifier is consistent with the principle that traversable wormholes can be supported by arbitrarily small quantities of exotic matter.