The boundary of the chronology violating set

Abstract

A sufficiently general definition for the future and past boundaries of the chronology violating region is given. In comparison to previous studies, this work does not assume that the complement of the chronology violating set is globally hyperbolic. The boundary of the chronology violating set is studied and several propositions are obtained which confirm the reasonability of the definition. Some singularity theorems related to chronology violation are considered. Among the other results we prove that compactly generated horizons are compactly constructed.

A new singularity theorem for black holes which allows chronology violation in the interior

“…We shall now recall some recent results of Minguzzi, though our account merely includes what is necessary. The interested reader is encouraged to consult the comprehensive description proposed in the original papers [11], [12]. Another ingredient we shall use, also due to Minguzzi, is the recent proposal [12] for the definition of the boundary of a chronology violating region.…”

“…The interested reader is encouraged to consult the comprehensive description proposed in the original papers [11], [12]. Another ingredient we shall use, also due to Minguzzi, is the recent proposal [12] for the definition of the boundary of a chronology violating region. 1 The chronology violating region {C := x ≪ x} is defined as the set of of points through which there passes a closed timelike curve.…”

“…The set B p(f ) ([r]) is closed, achronal, and generated by past (future) null rays. Proposition 2.6 (Minguzzi [12]). The following identity holds…”

“…The first is the notion of the boundary of the chronology violating region. We express the permitted chronology violation using Minguzzi's [12] recently offered definition of the boundary of a chronology violating set. This has the advantage of leading to a statement which relies on clear geometric conditions.…”

“…We have chosen to include such conditions, in view of the chronology violating and singular interior of Kerr. These conditions use the recently offered definitions and theorems of Minguzzi [11], [12], which are described in more detail below.…”