Horizons and non-local time evolution of quantum mechanical systems

Abstract

According to general relativity, trapping surfaces and horizons are classical causal structures that arise in systems with sharply defined energy and corresponding gravitational radius. The latter concept can be extended to a quantum mechanical state simply by means of the spectral decomposition, which allows one to define an associated "horizon wave-function". Since this auxiliary wave-function contains crucial information about the causal structure of space-time, a new proposal is formulated for the time-evolution of quantum states in order to account for the fundamental classical property that outer observers cannot receive signals from inside a horizon. The simple case of a single massive free particle at rest is used throughout the paper as a toy model to illustrate the main ideas.

13 pages, LaTeX with 6 pdf plots in 4 figures. Added comments

References in corpus (2)

• Black holes as self-sustained quantum states, and Hawking radiation
• Quantum Black Hole Wave Packet: Average Area Entropy and Temperature Dependent Width

Cited by in corpus (2)

• Thermal corpuscular black holes
• A quantum peek inside the black hole event horizon