A local Generalized second law in crossed product constructions

Understand

In this paper, we show a local generalized second law (the generalized entropy is nondecreasing) in crossed product constructions for maximally extended static and Kerr black holes using modular theory.

• The new ingredient is the use of results from a recent paper discussing the entropy of the algebra of operators in subregions of arbitrary spacetimes.
• These results rely on an assumption which we show is true in our setting.
• However, we do assume as in that paper, that the gravitational constraints are implemented on each partial Cauchy slice.