2015/06/30 by Maximilian Demmel, Andreas Nink · 1 citation
Physics and Astronomy · Mathematics · #gr-qc #hep-th #math-ph #math.MP
paper · pdf · doi:10.1103/physrevd.92.104013
published as Phys. Rev. D 92, 104013 (2015) · 15 pages, 3 figures (V2: more clarifying remarks in sections IV and V. V3: additional comment in section IV, version published in PRD)
arxiv created 2015/11/09 · arxiv updated 2015/11/11
We argue that the exponential relation gμν = gμρ(eh)ρν is the most natural metric parametrization since it describes geodesics that follow from the basic structure of the space of metrics. The corresponding connection is derived, and its relation to the Levi-Civita connection and the Vilkovisky-DeWitt connection is discussed. We address the impact of this geometric formalism on quantum gravity applications. In particular, the exponential parametrization is appropriate for constructing covariant quantities like a reparametrization invariant effective action in a straightforward way. Furthermore, we reveal an important difference between Euclidean and Lorentzian signatures: Based on the derived connection, any two Euclidean metrics can be connected by a geodesic, while this does not hold for the Lorentzian case.