2014/06/30 by Dawood Kothawala · 21 citations
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Conformal map #Context (archaeology) #Cosmology and Gravitation Theories #Differential geometry #Geodesic #Geometric Analysis and Curvature Flows #Metric (unit) #Point (geometry) #Scalar (mathematics) #Scalar field #Scaling #Spacetime #gr-qc #math-ph #math.MP
paper · pdf · doi:10.1007/s10714-014-1836-6
published in General Relativity and Gravitation 46(12) (Springer Science+Business Media) · 8 pages, 1 figure; Sec IV now includes a more refined expression for Ricci scalar completely in terms of conformal (3-)geometry, and discusses a couple of applications; to appear in Gen. Rel. Grav._
arxiv created 2014/11/13 · openalex publication_date 2014/11/19 · arxiv updated 2014/11/24 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We consider metrics related to each other by functionals of a scalar field φ(x) and it's gradient ∇ φ(x), and give transformations of some key geometric quantities associated with such metrics. Our analysis provides useful and elegant geometric insights into the roles of \it conformal and \it non-conformal metric deformations in terms of intrinsic and extrinsic geometry of φ-foliations. As a special case, we compare \it conformal and \it disformal transforms to highlight some non-trivial scaling differences. We also study the geometry of \it equi-geodesic surfaces formed by points p at constant geodesic distance σ(p,P) from a fixed point P, and apply our results to a specific disformal geometry based on σ(p,P) which was recently shown to arise in the context of spacetime with a minimal length.