Gravity with a generalized conformal scalar field: Theory and solutions

Abstract

We naturally extend the theory of gravity with a conformally coupled scalar field by only requiring conformal invariance of the scalar field equation of motion and not of the action. The classically extended theory incorporates a scalar-Gauss-Bonnet sector and has second-order equations of motion, belonging to the Horndeski class. Remarkably, the theory features a purely geometrical field equation that allows for closed-form black hole solutions and cosmologies to be easily found. These solutions permit investigations of in-vogue scalar-Gauss-Bonnet corrections to the gravitational action without the need of resorting to approximations or numerical methods. We discuss on the connection to the recently formulated 4D Einstein-Gauss-Bonnet theory of gravity.

A New Gravitational Action For The Trace Anomaly

“…It is encouraging that such a different principle gave rise to the action of [17], which was derived in the present work based on the consistency of the effective field theory of gravity with the quantum trace anomaly. The anomaly perspective of the present work is essential: its outcome is that GR needs to be amended by a scalar degree of freedom -as it is done in the trace anomaly action (22) -in order for GR to be consistently coupled to a QFT with the trace anomaly.…”

“…Comments added: After this article appeared in the arXiv, Pedro Fernandes communicated that the action which he derived in [17] using different principles, is equivalent to the action given above in (22) (up to some obvious terms). Indeed, if one transforms the action (22) from the Jordan frame to the Einstein frame, and then changes the field σ to −φ, one obtains the respective terms in the action ( 14) of [17]. Moreover, the "duality" discussed in the present work in Section 2, transforms the action (22) into the action (14) of ref.…”

“…Moreover, the "duality" discussed in the present work in Section 2, transforms the action (22) into the action (14) of ref. [17].…”

“…The action in ref. [17] was derived based on purely classical principles, by answering the question: what is the most general scalar-tensor theory of gravity with the second order equations of motion that has the scalar equation invariant under the conformal transformations, even if the action is not conformally invariant? Furthermore, the invariance of the scalar equation of motion enabled Fernandes to find exact analytic solutions of the theory [17].…”

On Thermal Stability of Hairy Black Holes

“…Such deformations are only formally known, through recursive relations order by order in perturbation theory. A final example is the (3+1)-dimensional extended GB gravity [58], which includes coupling of a conformal scalar to a GB curvature combination.…”