SURFACE GRAVITY IN DYNAMICAL SPHERICALLY SYMMETRICAL SPACETIMES

A definition of surface gravity at the apparent horizon of dynamical s pherically symmetric spacetimes is proposed. It is based on a unique f oliation by ingoing null hypersurfaces. The function parametrizing the hypersurfaces can be interpreted as the phase of a light wave uniform ly emitted by some far-away static observer. The definition gives back the accepted value of surface gravity in the static case by virtue of its nonlocal character. Although the definition is motivated by the b ehavior of outgoing null rays, it turns out that there is a simple con nection between the surface gravity, the acceleration of any radially moving observer, and the observed frequency change of the infalling li ght signal. In particular, this gives a practical and simple method of how any geodesic observer can determine surface gravity by measuring only the redshift of the infalling Light wave. The surface gravity can be expressed as an integral of matter field quantities along an ingoi ng null line, which shows that it is a continuous function along the a pparent horizon. A formula for the area change of the apparent horizon is presented, and the possibility of thermodynamical interpretation i s discussed. Finally, concrete expressions of surface gravity are give n for a number of four-dimensional and two-dimensional dynamical black hole solutions.