Black Holes without Event Horizons
  We discuss some of the drawbacks of using event horizons to define black holes. The reasons are both practical, physical and theoretical. We argue that locally defined trapping horizons can remedy many of these drawbacks. We examine of the question of whether black hole thermodynamics should be associated with event horizons or trapping horizons. To this end we discuss what role trapping horizons may play in black hole thermodynamics. In addition, we show how trapping horizons may give rise to Hawking radiation and discuss the issue of gravitational entropy. 
Alex B. Nielsen