On the Definition of Averagely Trapped Surfaces

Abstract

Previously suggested definitions of averagely trapped surfaces are not well-defined properties of 2-surfaces, and can include surfaces in flat space-time. A natural definition of averagely trapped surfaces is that the product of the null expansions be positive on average. A surface is averagely trapped in the latter sense if and only if its area $A$ and Hawking mass $M$ satisfy the isoperimetric inequality $16\pi M^2>A$, with similar inequalities existing for other definitions of quasi-local energy.

4 pages

References in corpus (4)

• General Laws of Black-Hole Dynamics
• Quasi-Local Gravitational Energy
• Trapped surfaces and spherical closed cosmologies
• Condensation of Matter and Trapped Surfaces in Quasi-Polar Gauge

Cited by in corpus (7)

• Loop Quantum Gravity: An Inside View
• Counting a black hole in Lorentzian product triangulations
• Spacetimes foliated by Killing horizons
• Neighbourhoods of Isolated Horizons and their stationarity
• The marginally trapped surfaces in spheroidal spacetimes
• The Hawking Energy on the Past Lightcone in Cosmology
• A note on electrical and thermodynamic properties of Isolated Horizon