Finsler spacetime geometry in physics

Pfeifer, Christian

doi:10.1142/s0219887819410044

Cited by 81 publications

(79 citation statements)

References 65 publications

(79 reference statements)

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“…Observe that the first term gives a boundary term which we can neglect. This is so since ∇L = 0 and thus ∇( A i i L ) is a divergence of a 0-homogeneous vector field according to (26). It remains to write L −1 A i |i = div(L −1 A i δ i ) + L −1 A i P i , see (24), to find…”

Section: The Integral I2mentioning

confidence: 99%

“…The appearance of Finsler geometry in physics, see [26] for a review, raised two questions: the one about a suitable general mathematical definition of Finsler spacetimes, which covers the interesting instances appearing in the literature and the one whether it is possible to find dynamical equations which determine the Finslerian spacetime geometry in the same way as the Einstein equations determine the pseudo-Riemannian geometry of spacetime.…”

Section: Introductionmentioning

confidence: 99%

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Finsler gravity action from variational completion

2019

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In the attempts to apply Finsler geometry to construct an extension of general relativity, the question about a suitable generalization of the Einstein equations is still under debate. Since Finsler geometry is based on a scalar function on the tangent bundle, the field equation which determines this function should also be a scalar equation. In the literature two such equations have been suggested: the one by Rutz and the one by one of the authors. Here we employ the method of canonical variational completion to show that Rutz equation can not be obtained from a variation of an action and that its variational completion yields the latter field equations. Moreover, to improve the mathematical rigor in the derivation of the Finsler gravity field equation, we formulate the Finsler gravity action on the positive projective tangent bundle. This has the advantage of allowing us to apply the classical variational principle, by choosing the domains of integration to be compact and independent of the dynamical variable. In particular in the pseudo-Riemannian case, the vacuum field equation becomes equivalent to the vanishing of the Ricci tensor. * manuel.hohmann@ut.ee † christian.pfeifer@ut.ee ‡ nico.voicu@unitbv.ro arXiv:1812.11161v3 [gr-qc] 1 Oct 2019 3 The ones considered in [44,45] do not fit in our definition. We do not consider these Finsler spacetimes since for them the curvature tensor, which defines the dynamics of Finsler spacetimes, is not necessarily defined for all physical observer directions, which in our definition is given by the conic subbundle T . The definition could be relaxed so as to include the possibility of having an observer direction where curvature is not defined, but in this case, a thorough analysis of whether the evolution of spacetime is causal, as seen by the respective observer, is needed. This is the subject for future work.

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Section: The Integral I2mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Finsler gravity action from variational completion

2019

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“…To describe the kinetic gas and its coupling to gravity geometrically on the tangent bundle, we employ Finsler spacetime geometry and the Finsler spacetime geometric description of the gravitational dynamics [13,17,20,24].…”

Section: A Finsler Spacetimesmentioning

confidence: 99%

“…since ∇ẋ a = 0, ∇L = 0, ∇g L ab = 0, by construction of the Chern-Rund covariant derivative, see (17), and the fact that the 1PDF of a collisonless gas satisfies the Liouville equation r(φ) = 0, see (24). Thus the Liouville equation can be interpreted as covariant energy-momentum distribution tensor conservation equation.…”

Section: B the Action Of A Kinetic Gasmentioning

confidence: 99%

Relativistic kinetic gases as direct sources of gravity

2020

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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.

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“…is integrable then its integral manifold can be used to define the rest spaces of the observer field U (see the question posed in the final paragraph of [41]). From [32], Theorem 4.8, if K := σU is also a Killing vector field, for some positive function σ onM, B = TM and L satisfies L…”

Section: About the Notion Of Stationary And Static Finsler Spacetimesmentioning

confidence: 99%