Conformally coupled scalar in Lovelock theory
arXiv:2302.02920 · doi:10.1103/PhysRevD.107.084050
Abstract
In arbitrary higher dimension, we consider the combination of Lovelock gravity alongside a scalar-tensor action built out of higher order operators and Euler densities. The latter action is constructed in such a way as to ensure conformal invariance for the scalar field. For the combined version of these theories, we show the existence of black hole solutions interpreted as stealth configurations within Lovelock gravity theory. The scalar field solutions are endowed with an integration constant that may be identified as a scalar charge. In particular, we show that these stealth solutions can be extended to include a time-dependent scalar field despite the underlying theory being non shift-symmetric. Finally, we present a procedure to obtain a non-conformally invariant action in even dimensions from the considered theory. For the target theory, the scalar field is not conformally coupled to gravity although the scalar field equation itself is conformally invariant. By means of this procedure, the black hole stealth configurations are converted into non-stealth black hole solutions, as discovered recently in four dimensions.
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- Asymptotically AdS black hole with a conformally-coupled scalar field in the first-order formalism of gravity
- Cosmic acceleration in Lovelock quantum gravity
- Klein-Gordon and Schrödinger solutions in Lovelock quantum gravity
- Revisiting local-scale invariant gravitational theory