Spacetime symmetries and geometric diffusion

M. Basquens, A. Lasanta, E. Mompó, V. Varo, E.J. S. Villaseñor

Journal of Physics A: Mathematical and Theoretical Vol. 57, nº. 28, pp. 285204-1 - 285204-29

Resumen:

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.

Palabras Clave: diffusion Lorentzian manifolds, covariant Fokker-Planck equation, spacetime symmetries

Índice de impacto JCR y cuartil WoS: 2,000 - Q2 (2023)

Referencia DOI: https://doi.org/10.1088/1751-8121/ad5a57

Publicado en papel: Julio 2024.

Publicado on-line: Junio 2024.

Cita:
M. Basquens, A. Lasanta, E. Mompó, V. Varo, E.J. S. Villaseñor, Spacetime symmetries and geometric diffusion. Journal of Physics A: Mathematical and Theoretical. Vol. 57, nº. 28, pp. 285204-1 - 285204-29, Julio 2024. [Online: Junio 2024]