Black holes and black hole thermodynamics without event horizons
  We investigate whether black holes can be defined without using event horizons. In particular we focus on the thermodynamic properties of event horizons and the alternative, locally defined horizons. We discuss the assumptions and limitations of the proofs of the zeroth, first and second laws of black hole mechanics for both event horizons and trapping horizons. This leads to the possibility that black holes may be more usefully defined in terms of trapping horizons. We also show how Hawking radiation can also be seen to arise from trapping horizons and discuss which horizon area should be associated with the gravitational entropy. 
Alex B. Nielsen