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Every Coxeter group admits a geometric representation as a group generated byreflections in a real vector space. In the projective representation space,limit directions are limits of injective sequences in the orbit of some basepoint. Limit roots are limit directions that can be obtained starting fromsimple roots. In this article, we study the limit directions arising from anypoint when the representation space is a Lorentz space. In particular, wecharacterize the light-like limit directions using eigenvectors ofinfinite-order elements. This provides a spectral perspective on limit roots,allowing for efficient computations. Moreover, we describe the space-like limitdirections in terms of the projective Coxeter arrangement.

Limit Directions for Lorentzian Coxeter Systems