Analogies between self-duality and stealth matter source

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.

6 pages. To be published in Jour. Phys. A

References in corpus (2)

• Gravitational Cheshire effect: Nonminimally coupled scalar fields may not curve spacetime
• Extended Klein-Gordon Action, Gravity and Non-Relativistic Fluid

Cited by in corpus (8)

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• Massive stealth scalar fields from field redefinition method
• A new rotating axionic AdS${}_4$ black hole dressed with a scalar field
• Electromagnetically and gravitationally stealth fields