Plurisubharmonic geodesics in spaces of non-Archimedean metrics of finite energy

Abstract Given a polarized projective variety ( X , L stretchy="false">) {(X,L)} over any non-Archimedean field, assuming continuity of envelopes, we define metric on the space finite-energy metrics L , related to construction Darvas in complex setting. We show that this makes into geodesic space, where geodesics are given as maximal psh segments. two continuous metrics, segment joining them is furthermore continuous. Our results hold particular all situations relevant study degenerations and K-stability geometry.