Almost isometries of non-reversible metrics with applications to stationary spacetimes

Finsler metrics and relativistic spacetimes

“…So, one will find a correspondence between the conformal properties of the elements in this class of metrics (V, g L ) and the geometric properties of Randers spaces (M, F ). This has been carried out at different levels (see [9,10,11,12,13,18,20,24] or [23] for a review), and we will focus here in three of them, with clear physical applications.…”

Metric structures associated to Finsler metrics

“…Remark 1.1 Remark that in the definition of quasi-metric spaces, it is commonly used d F (x, y) = 0 ⇒ x = y, without assuming that both d F (x, y) and d F (y, x) are zero (Def 2.1 in [JLP13]). This guarantees that the distance is zero only in the diagonal.…”

“…Our definition here is stronger than the usual one. In general, the distance associated to a Finsler metric is a generalized metric, namely, a quasi-metric such that the forward and backward topology coincide, see Remark 2.2 in [JLP13].…”