Analogies between self-duality and stealth matter source

TL;DR

This paper explores a self-dual scalar field system in three-dimensional BTZ spacetime, establishing conditions under which the matter action is bounded and vanishes for self-dual solutions, revealing deep analogies with self-duality concepts.

Contribution

It demonstrates the equivalence of a nonminimally coupled scalar field system to a self-dual set of equations in BTZ spacetime, identifying the self-dual point and action bounds.

Findings

Self-dual equations are derived for the scalar field system.

The matter action is bounded and vanishes at the self-dual point.

Conditions for the self-dual point involve fixing coupling constants.

Abstract

We consider the problem of a self-interacting scalar field nonminimally coupled to the three-dimensional BTZ metric such that its energy-momentum tensor evaluated on the BTZ metric vanishes. We prove that this system is equivalent to a self-dual system composed by a set of two first-order equations. The self-dual point is achieved by fixing one of the coupling constant of the potential in terms of the nonminimal coupling parameter. At the self-dual point and up to some boundary terms, the matter action evaluated on the BTZ metric is bounded below and above. These two bounds are saturated simultaneously yielding to a vanishing action for configurations satisfying the set of self-dual first-order equations.