Spacetime symmetries and geometric diffusion
Metadata
Show full item recordAuthor
Basquens, Marc; Lasanta Becerra, Antonio; Mompó, Emanuel; Varo, María del Valle; Sánchez Villaseñor, Eduardo JesúsEditorial
IOP Publishing
Materia
diffusion Lorentzian manifolds covariant Fokker-Planck equation spacetime symmetries
Date
2024-06-28Referencia bibliográfica
Basequens, M. et. al. 57 (2024) 285204 (28pp). [https://doi.org/10.1088/1751-8121/ad5a57]
Sponsorship
Spanish Ministerio de Ciencia Innovación y Universidades-Agencia Estatal de Investigación Grant Nos. AEI/PID2020-116567GB-C22 and PID2021-128970OA-I00; Madrid Government (Comunidad de Madrid-Spain) under the Multiannual Agreement with UC3M in the line of Excellence of University Professors (EPUC3M23), and in the context of the V PRICIT (Regional Programme of Research and Technological Innovation); FEDER/Junta de Andalucía Consejería de Universidad, Investigación e Innovación, and by the European Union, through Grants Nos. A-FQM-644-UGR20 and C-EXP-251-UGR23Abstract
We examine relativistic diffusion through the frame and observer bundles associated
with a Lorentzian manifold (M, g). Our focus is on spacetimes with a
non-trivial isometry group, and we detail the conditions required to find symmetric
solutions of the relativistic diffusion equation. Additionally, we analyze
the conservation laws associated with the presence of Killing vector fields on
(M, g) and their implications for the expressions of the geodesic spray and the vertical Laplacian on both the frame and the observer bundles. Finally, we
present several relevant examples of symmetric spacetimes.