How many futures on Finsler spacetime?

7th International Workshop DICE2014 Spacetime – Matter – Quantum Mechanics

物理学;力学

Minguzzi, E.^1

Dipartimento di Matematica e Informatica U. Dini, Università Degli Studi di Firenze, Via S. Marta 3, Firenze

I-50139, Italy^1

关键词: Conservation law;    Dynamical equation;    General Relativity;    Hyperbolic type;    Indicatrices;    Non-trivial;    Standing problems;    Triangle inequality;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/626/1/012029/pdf
DOI  :  10.1088/1742-6596/626/1/012029

学科分类：力学，机械学

来源: IOP

【 摘 要 】

Some recent results by the author onthe geometry and dynamics of Finsler spacetimes are reviewed. It is shown that in Finslerian generalizations of general relativity the number of predicted lightlike cones is two, one past and one future, as in general relativity. This result is non-trivial as it can fail, for instance, in spacetime dimension two. It is also shown that suitable versions of the reverse Cauchy-Schwarz and reverse triangle inequalities hold on Finsler spacetimes. Finally, a long standing problem of Finslerian gravity concerns the development of dynamical equations which imply a conservation law. We make some progress following a recent proposal by the author according to which physical Finsler spacetimes have affine sphere indicatrices of hyperbolic type.