2020/05/31 by Alessandro Pesci, A. Pesci
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Classical mechanics #Cosmology and Gravitation Theories #Curvature #General relativity #Geodesic #Gravitation #Mathematical analysis #Mathematical physics #Mathematics #Mathematics of general relativity #Maxwell's equations in curved spacetime #Minkowski space #Noncommutative and Quantum Gravity Theories #Numerical relativity #Physics #Quantum field theory in curved spacetime #Quantum gravity #Quantum mechanics #Scalar (mathematics) #Scalar field #Spacetime #Stationary spacetime #Theoretical physics #gr-qc
paper · pdf · doi:10.1088/1361-6382/ac0310
published as Class. Quantum Grav. 38 (2021) 145007 · 17 pages; v2: some corrections/editing/clarifications, reference added, it corresponds to the published version
openalex publication_date 2021/05/19 · arxiv created 2021/06/21 · arxiv updated 2021/06/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Abstract We study the recently reported qmetric (or zero-point-length) expressions of the Ricci (bi)scalar R ( q ) (namely, expressions of the Ricci scalar in a spacetime with a limit length L 0 built in), focusing specifically on the case of null separated events. A feature of these expressions is that, when considered in the coincidence limit p → P , they generically exhibit a dependence on the geodesic along which the varying point p approached P , sort of memory of how p went to P . This fact demands a deeper understanding of the meaning of the quantity R ( q ) , for this latter tells about curvature of spacetime as a whole at P and would not be supposed to depend on whichever vector we might happen to consider at P . Here, we try to search for a framework in which these two apparently conflicting aspects might be consistently reconciled. We find a tentative sense in which this could be achieved by endowing spacetime of a specific operational meaning. This comes, however, at the price (or with the benefit) of having a spacetime no longer arbitrary but, in a specific sense, constrained. The constraint turns out to be in the form of a relation between spacetime geometry in the large scale (as compared to L 0 ) and the matter content, namely as sort of field equations. This comes thanks to something which happens to coincide with the expression of balance of (matter and spacetime) exchanged heats, i.e. the thermodynamic variational principle from which the field equations have been reported to be derivable. This establishes a link between (this specific, operational understanding of) the meaning of the limit expression of R ( q ) on one side and the (large-scale) field equations on the other, this way reconnecting (once more) the latter to a quantum feature.