Relativistic kinetic gases as direct sources of gravity

Abstract

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. The most natural mathematical framework for this task is Finsler spacetime geometry. Following this line of argumentation, we construct a coupling between the kinetic gas and a recently proposed Finsler geometric extension of general relativity. Additionally, we explicitly show how the coordinate invariance of the action of the kinetic gas leads to a novel formulation of conservation of the energy-momentum distribution of the gas on the tangent bundle.

The kinetic gas universe

“…The Finsler extension of the Einstein equations coupled to the kinetic gas can be derived from a generally covariant action principle on the observer space, see [7],…”

“…More technically, theẋ derivative of the Finsler metric, usually called the Cartan tensor, measures the departure of a given Finsler geometry from (pseudo)-Riemannian geometry; the Landsberg tensor then is given by the so-called dynamical covariant derivative of this quantity P a bc = 1 2 g Lad ∇ ∂ ∂ẋ b g L cd . For further mathematical details about the Finsler geometric objects appearing we refer to the articles [6,7] and the books [8,9] as well as references therein.…”

Broken Scale Invariance, Gravity Mass, and Dark Energy inModified Einstein Gravity with Two Measure Finsler like Variables

“…This is a good opportunity for authors, which allows them to explain their approach, geometric methods, and new results for the construction of new classes of generic, offdiagonal cosmological solutions in more detail, as well as elaborating on applications in non-standard particle physics and modified gravity. To comment on key ideas and constructions in the authors' works, and compare them to similar ones from the mentioned alternative geometric and cosmological theories, we have to additionally cite [75][76][77][78][79], and references therein. We note that readers should pay attention to reference [24], with respective Introduction and Conclusion sections, and Appendix B (in that work), containing historical remarks and a review of 20 directions on modern generalized Finsler geometry and applications in modern particle physics, modified gravity, and cosmology, mechanics and thermodynamics, information theory, etc.…”

“…For instance, certain constructions with cosmological kinetic/statistical Finsler spacetime in [73,75] are subjected to very complex type conservation laws and nonlinear kinetic/diffusion equations. Those authors have not cited and or applied earlier, locally anisotropic, generalized Finsler kinetic/diffusion/statistical constructions performed for the metric compatible connections studied in [77][78][79] (N. Voicu was at S. Vacaru's seminars in Brashov in 2012, on Finsler kinetics, diffusion and applications in modern physics and information theory; see also [33], but, together with her co-authors, do not cite, discuss, or apply such locally anisotropic, metric, compatible and solvable geometric flow, kinetic and geometric thermodynamic theories); • Various variational principles and certain versions of Finsler modified Einstein equations were proposed and developed in [72,73,75], but such theories have been not elaborated on total bundle spaces, for certain metric compatible Finsler connections. Usually, metric non-compatible Finsler connections were used, when it is not possible to elaborate on certain general methods for the construction of exact and parametric solutions to nonlinear systems of PDEs; for instance, describing locally anisortopic interactions of modified Finsler-Einstein-Dirac-Yang-Mills-Higgs systems.…”

Schwarzschild-like solutions in Finsler–Randers gravity

“…Generalized Einstein field equations have been studied in the Finsler, Lagrange, generalized Finsler and Finsler-like spaces, for an osculating gravitational approach in which the second variable y(x) is a tangent/vector field [1][2][3] and in Finsler cosmology [4][5][6][7][8]. Different sets of generalized Einstein field equations were derived for the aforementioned spaces in the framework of a tangent bundle [9][10][11][12][13][14][15][16][17] and for the momentum space on the cotangent bundle [18][19][20][21][22][23]. Additionally, Lorentz invariance violation in Finsler/Finslerlike spacetime and in Finsler cosmology in very special relativity has also been studied in a large series of papers [5,[24][25][26][27].…”