The generally covariant meaning of space distances
Department of Physics “E. Pancini”, University of Napoli “Federico II”, via Cinthia, 80126, Napoli, Italy
2 Istituto Nazionale di Fisica Nucleare (INFN), Sez. di Napoli, via Cinthia 9, 80126, Napoli, Italy
3 Scuola Superiore Meridionale, Largo S. Marcellino 10, 80138, Napoli, Italy
4 Department of Mathematics, University of Torino, via Carlo Alberto 10, 10123, Torino, Italy
5 Istituto Nazionale di Fisica Nucleare (INFN), Sez. di Torino (Italy), via P. Giuria 1, 10125, Torino, Italy
Accepted: 25 November 2020
Published online: 5 December 2020
We propose a covariant and geometric framework to introduce space distances as they are used by astronomers. In particular, we extend the definition of space distances from the one used between events to non-test bodies with horizons and singularities so that the definition extends through the horizons and it matches the protocol used to measure them. The definition we propose can be used in standard general relativity although it extends directly to Weyl geometries to encompass a number of modified theories, extended theories in particular.
© The Author(s) 2020
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