2013/07/25 by Michael Tsamparlis, Andronikos Paliathanasis, Spyros Basilakos +1
Physics and Astronomy · #Advanced Differential Geometry Research #Black Holes and Theoretical Physics #Conformal map #Cosmology #Cosmology and Gravitation Theories #Differential geometry #Field (mathematics) #Field equation #Hamiltonian (control theory) #Scalar (mathematics) #Scalar field #astro-ph.CO #gr-qc #hep-th
paper · pdf · doi:10.1007/s10714-013-1575-0
13 pages, to appear in Gen. Rel. Grav
arxiv created 2013/07/25 · openalex publication_date 2013/08/03 · arxiv updated 2015/06/16 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
Conformally related metrics and Lagrangians are considered in the context of scalar-tensor gravity cosmology. After the discussion of the problem, we pose a lemma in which we show that the field equations of two conformally related Lagrangians are also conformally related if and only if the corresponding Hamiltonian vanishes. Then we prove that to every non-minimally coupled scalar field, we may associate a unique minimally coupled scalar field in a conformally related space with an appropriate potential. The latter result implies that the field equations of a non-minimally coupled scalar field are the same at the conformal level with the field equations of the minimally coupled scalar field. This fact is relevant in order to select physical variables among conformally equivalent systems. Finally, we find that the above propositions can be extended to a general Riemannian space of n-dimensions.