On Finsler spacetimes with a timelike Killing vector field

Abstract

We study Finsler spacetimes and Killing vector fields taking care of the fact that the generalised metric tensor associated to the Lorentz–Finsler function L is in general well defined only on a subset of the slit tangent bundle. We then introduce a new class of Finsler spacetimes endowed with a timelike Killing vector field that we call stationary splitting Finsler spacetimes. We characterize when a Finsler spacetime with a timelike Killing vector field is locally a stationary splitting. Finally, we show that the causal structure of a stationary splitting is the same of one of two Finslerian static spacetimes naturally associated to the stationary splitting.

Finsler gravity action from variational completion

“…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 .…”

On the Analyticity of Static Solutions of a Field Equation in Finsler Gravity

“…In some cases, smoothness or at least C 1 -regularity of weak extremals hold; for example, this is true for some stationary splitting Finsler spacetimes and for standard static Finsler spacetimes in next section, see, respectively, [32] bundle which is usual in Finsler geometry (compare with [39]). A vector field K onM is a Killing vector field for (M, L, B) if K c | B (L) = 0, where K c denotes the complete lift of K to TM (restricted to the open subset B).…”

“…Recently, a definition of a Finsler spacetime has been proposed [29] that encompasses definitions which generalize Beem's one as those in [18][19][20]30]. The authors declare in [29] that their definition does not include some classes of Finsler spacetimes studied in [31,32] which can be seen as generalizations of standard static and stationary Lorentzian spacetimes and that have already appeared in other papers [33][34][35][36]. Thus, it is worth to relax slightly the definition in [29] in order to include them.…”

“…Let us recall the notion of a Killing vector field for a Finsler metric. We refer to [32] for details. Since L is C 1 on the open cone sub-bundle B, we take B ⊂ TM \ 0 as the base space instead of the slit tangent 1…”

Charged anisotropic strange stars in Finslerian geometry

“…Smoothness of the line element is discussed elaborately for the standard static spacetime in [49,50].…”