Black Holes and Complexity via Constructible Universe

Abstract

The relation of randomness and classical algorithmic computational complexity is a vast and deep subject by itself. However, already, 1-randomness sequences call for quantum mechanics in their realization. Thus, we propose to approach black hole’s quantum computational complexity by classical computational classes and randomness classes. The model of a general black hole is proposed based on formal tools from Zermelo–Fraenkel set theory like random forcing or minimal countable constructible model Lα. The Bekenstein–Hawking proportionality rule is shown to hold up to a multiplicative constant. Higher degrees of randomness and algorithmic computational complexity are derived in the model. Directions for further studies are also formulated. The model is designed for exploring deep quantum regime of spacetime.

Keywords

• black holes
• computational complexity
• forcing
• model theory
• ZFC