The logic of space represents a current branch of research in modal logic. In this paper, the authors first report the known results for modal logics where the accessibility relations are induced by the Minkowski metrics in \(\mathbb{R}^n\), \(n\geq 2\) (chronological and causal accessibility). The arising systems then are identified as logics of balls and spatial analogues to intervals in \(\mathbb{R}^n\), respectively. An irreflexive version of causal accessibility (called the `after' relation) is studied as well. In the next part of the paper the authors give examples of non-finitely axiomatizable and undecidable relativistic modal logics. Finally, the intermediate logics of some of the frames considered in this paper are determined. The paper is concluded with several precisely formulated open problems.