Brown-York Energy and Radial Geodesics

Details Brown-York Energy and Radial Geodesics Brown-York Energy and Radial Geodesics

2007-08-02

arxiv.org/abs/0708.0321v3

Class.Quant.Grav.25:105004,2008

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

v3: 7 pages, shortened and revised version to appear in CQG

Scientific paper

10.1088/0264-9381/25/10/105004

We compare the Brown-York (BY) and the standard Misner-Sharp (MS) quasilocal energies for round spheres in spherically symmetric space-times 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 E_{eff} 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 generalises the recently observed connection between negative BY energy and the repulsive behaviour of geodesics in the Reissner-Nordstrom metric. We also comment on the extension of this connection between geodesics and the quasilocal BY energy to regions inside a horizon.

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