2018/02/28 by Dawood Kothawala
Mathematics · Physics and Astronomy · #Action (physics) #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Einstein #Euclidean geometry #Euclidean space #Geodesic #Geometry #Hypersurface #Interpretation (philosophy) #Lambda #Mathematical analysis #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Order (exchange) #Physics #Pure mathematics #Quantum mechanics #Sigma #Tensor (intrinsic definition) #gr-qc #hep-th
paper · pdf · doi:10.1103/physrevd.97.124062
published as Phys. Rev. D 97, 124062 (2018) · 6 pages, 2 figures, added comments and expanded discussion of some implications, matches version accepted in Phys. Rev. D
openalex publication_date 2018/06/26 · arxiv created 2018/06/27 · arxiv updated 2018/06/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We give a local description of the Euclidean regime (M,\mathbitg,\mathbitu) of Lorentzian spacetimes (M,\mathbitg) based on timelike geodesics \mathbitu passing through an arbitrary event p0\ensuremath∈M. We show that, to leading order, the Euclidean Einstein-Hilbert action IE is proportional to the Einstein tensor \mathbitG[\mathbitg](\mathbitu,\mathbitu). The positivity of IE follows if \mathbitG[\mathbitg](\mathbitu,\mathbitu)>0 holds. We suggest an interpretation of this result in terms of the amplitude A[\mathrm\ensuremathΣ0]=exp[\ensuremath-IE] for a single spacelike hypersurface \mathrm\ensuremathΣ0\ensuremath∈I+(p0) to emerge at a constant geodesic distance \ensuremathλ0 from p0. Implications for classical and quantum gravity are discussed.