Bi-metric pseudo-Finslerian spacetimes

JOURNAL OF GEOMETRY AND PHYSICS

卷:61

Article

Skakala, Jozef¹  Visser, Matt¹ 

[1] Victoria Univ Wellington, Sch Math Stat & Operat Res, Wellington 6140, New Zealand

关键词: Finsler norm;    Finsler metric;    Pseudo-Finsler norms;    Bimetric theories;   

DOI  :  10.1016/j.geomphys.2011.03.003

来源: Elsevier

【 摘 要 】

Finsler spacetimes have become increasingly popular within the theoretical physics community over the last two decades. However, because physicists need to use pseudo-Finsler structures to describe propagation of signals, there will be nonzero null vectors in both the tangent and cotangent spaces - this causes significant problems in that many of the mathematical results normally obtained for usual (Euclidean signature) Finsler structures either do not apply, or require significant modifications to their formulation and/or proof. We shall first provide a few basic definitions, explicitly demonstrating the interpretation of bi-metric theories in terms of pseudo-Finsler norms. We shall then discuss the tricky issues that arise when trying to construct an appropriate pseudo-Finsler metric appropriate to bi-metric spacetimes. Whereas in Euclidian signature the construction of the Finsler metric typically fails only at the zero vector, in Lorentzian signature the Finsler metric is typically ill-defined on the entire null cone. Consequently it is not a good idea to try to encode bi-metricity into pseudo-Finsler geometry. One has to be very careful when applying the concept of pseudo-Finsler geometry in physics. (C) 2011 Elsevier B.V. All rights reserved.

【 授权许可】

Free