Brown–York energy and radial geodesics

Abstract

We compare the Brown–York (BY) and the standard Misner–Sharp (MS) quasilocal energies for round spheres in spherically symmetric spacetimes from the point of view of radial geodesics. In particular, we show that the relation between the BY and MS energies is precisely analogous to that between the (relativistic) energy E of a geodesic and the effective (Newtonian) energy Eeff appearing in the geodesic equation, thus shedding some light on the relation between the two. Moreover, for Schwarzschild-like metrics we establish a general relationship between the BY energy and the geodesic effective potential which explains and generalizes the recently observed connection between negative BY energy and the repulsive behaviour of geodesics in the Reissner–Nordström metric. We also comment on the extension of this connection between geodesics and the quasilocal BY energy to regions inside a horizon.