https://doi.org/10.1140/epjp/s13360-020-00968-7
Regular Article
The generally covariant meaning of space distances
1
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
Received:
3
November
2020
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
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
