Standard static Finsler spacetimes

Abstract

We introduce the notion of a standard static Finsler spacetime where the base is a Finsler manifold. We prove some results which connect causality with the Finslerian geometry of the base extending analogous ones for static and stationary Lorentzian spacetimes.Comment: AMS-LaTeX, 22 pages, 1 figure. v2 matches the published versio

Finsler gravity action from variational completion

“…In order to correctly define a Lagrangian on P T M + , we must construct a 4-form of the type ρ = f dV + 0 , with a zero homogeneous f , as discussed in (45). To achieve this the above expression for L must be (−4)-homogeneous and so α must be chosen to be −4, since R is 2-homogeneous and det g L is 0-homogeneous.…”

“…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 .…”

Extended hamiltonian formalism and Lorentz-violating lagrangians

“…Note that the functional form of the lagrangian is independent of the choice of R + (p) or R − (p) in Eq. (13). The conjugate momenta are now…”

Foundations of Finsler Spacetimes from the Observers’ Viewpoint

“…In general, one would need measurements involving magnitudes which are dimensionally independent (in particular, this would be achieved by measuring adimensional constants, as commented above). In principle, this might be achieved by measuring essentially different interactions, as in the case of light and gravity propagation (see below Definition 2.8) 13 . Anyway, as we will see, the Lorentz-Finsler viewpoint will open other possibilities by using infinitesimal anisotropy.…”

“…(b) Product metrics −dt 2 + F 2 or, with more generality, the rough Lorentz-Finsler version of static spacetimes −Λ(x)dt 2 + F 2 (x, y), with natural coordinates (x, y) at T M , are never smooth at ∂ t whenever F is Finsler but not Riemannian. Consequently, some authors have included the possible existence of non-smooth directions as a fundamental ingredient of Lorentz-Finsler metrics (see for example [13,51]). Nevertheless, as explained in Rem.…”