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C. Pfeifer, “Finsler spacetime geometry in Physics,” arXiv:1903.10185 [gr-qc]
Original
1903
Earlier work this paper cites.
M. Bartelmann, E. Kozlikin, R. Lilow, C. Littek, F. Fabis, I. Kostyuk, C. Viermann, L. Heisenberg, S. Konrad, and D. Geiss, “Cosmic Structure Formation with Kinetic Field Theory,” arXiv:1905.01179 [astro-ph.CO]
Original
1910
Earlier work this paper cites.
PhD thesis, Georg-August Universität zu Göttingen, 1918
P. Finsler, Über Kurven und Flächen in allgemeinen Räumen · 1918
Earlier work this paper cites.
W. Israel, “Relativistic kinetic theory of a simple gas,” Journal of Mathematical Physics
1963
Earlier work this paper cites.
J. K. Beem, “Indefinite Finsler spaces and timelike spaces,” Can. J. Math
1970
Earlier work this paper cites.
D. Reidel Publishing Company, 1985
G. S. Asanov, Finsler Geometry, Relativity and Gauge Theories · 1985
Earlier work this paper cites.
Amer. Math. Soc., Providence, RI, 1992
M. J. Gotay and J. E. Marsden, “Stress-energy-momentum tensors and the Belinfante-Rosenfeld formula,” in Mathematical aspects of classical field theory (Seattle, WA, 1991) · 1992
Earlier work this paper cites.
S. Rutz, “A Finsler generalisation of Einstein’s vacuum field equations,” General Relativity and Gravitation
1993
Earlier work this paper cites.
Springer, 2000
D. Bao, S. S. Chern, and Z. Shen, An Introduction to Riemann-Finsler geometry · 2000
Earlier work this paper cites.
Editura Academiei Romane, 2007
R. Miron and I. Bucataru, Finsler Lagrange geometry · 2007
Earlier work this paper cites.
H. F. Goenner, “On the History of Geometrization of Space-time: From Minkowski to Finsler Geometry,” 414 Heraeus-Seminar
Original
2008
Earlier work this paper cites.

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Then

M. Hohmann, “Extensions of Lorentzian spacetime geometry: From Finsler to Cartan and vice versa,” Phys. Rev
Original
2013
Later among the works it cites.
X. Li and Z. Chang, “Exact solution of vacuum field equation in Finsler spacetime,” Phys. Rev. D
2014
Later among the works it cites.
E. Minguzzi, “The connections of pseudo-Finsler spaces,” Int. J. Geom. Meth. Mod. Phys
Original
2015
Later among the works it cites.
M. Hohmann, “Non-metric fluid dynamics and cosmology on Finsler spacetimes,” Int. J. Mod. Phys
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2016
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M. Hohmann, “Spacetime and observer space symmetries in the language of Cartan geometry,” J. Math. Phys
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2016

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2019

Relativistic kinetic gases as direct sources of gravity

Hohmann, Manuel, Pfeifer, Christian, Voicu, Nicoleta

Understand

We propose a new model for the description of a gravitating multi particle system, viewed as a kinetic gas.

The properties of the, colliding or non-colliding, particles are encoded into a so called one-particle distribution function, which is a density on the space of allowed particle positions and velocities, i.e.
on the tangent bundle of the spacetime manifold.
We argue that an appropriate theory of gravity, describing the gravitational field generated by a kinetic gas, must also be modeled on the tangent bundle.

Built on

C. Pfeifer, “Finsler spacetime geometry in Physics,” arXiv:1903.10185 [gr-qc]
Original
1903
Earlier work this paper cites.
M. Bartelmann, E. Kozlikin, R. Lilow, C. Littek, F. Fabis, I. Kostyuk, C. Viermann, L. Heisenberg, S. Konrad, and D. Geiss, “Cosmic Structure Formation with Kinetic Field Theory,” arXiv:1905.01179 [astro-ph.CO]
Original
1910
Earlier work this paper cites.
PhD thesis, Georg-August Universität zu Göttingen, 1918
P. Finsler, Über Kurven und Flächen in allgemeinen Räumen · 1918
Earlier work this paper cites.
W. Israel, “Relativistic kinetic theory of a simple gas,” Journal of Mathematical Physics
1963
Earlier work this paper cites.
J. K. Beem, “Indefinite Finsler spaces and timelike spaces,” Can. J. Math
1970
Earlier work this paper cites.
D. Reidel Publishing Company, 1985
G. S. Asanov, Finsler Geometry, Relativity and Gauge Theories · 1985
Earlier work this paper cites.
Amer. Math. Soc., Providence, RI, 1992
M. J. Gotay and J. E. Marsden, “Stress-energy-momentum tensors and the Belinfante-Rosenfeld formula,” in Mathematical aspects of classical field theory (Seattle, WA, 1991) · 1992
Earlier work this paper cites.
S. Rutz, “A Finsler generalisation of Einstein’s vacuum field equations,” General Relativity and Gravitation
1993
Earlier work this paper cites.
Springer, 2000
D. Bao, S. S. Chern, and Z. Shen, An Introduction to Riemann-Finsler geometry · 2000
Earlier work this paper cites.
Editura Academiei Romane, 2007
R. Miron and I. Bucataru, Finsler Lagrange geometry · 2007
Earlier work this paper cites.
H. F. Goenner, “On the History of Geometrization of Space-time: From Minkowski to Finsler Geometry,” 414 Heraeus-Seminar
Original
2008
Earlier work this paper cites.