No time machines in classical general relativity

Abstract

Irrespective of local conditions imposed on the metric, any extendible spacetime U has a maximal extension containing no closed causal curves outside the chronological past of U. We prove this fact and interpret it as impossibility (in classical general relativity) of the time machines, insofar as the latter are defined to be causality-violating regions created by human beings (as opposed to those appearing spontaneously).

A corrigendum (to be published in CQG) has been added to correct an important mistake in the definition of locality

References in corpus (1)

• The time travel paradox

Cited by in corpus (13)

• The causal hierarchy of spacetimes
• Formation of closed timelike curves in a composite vacuum/dust asymptotically-flat spacetime
• Static Negative Energies Near a Domain Wall
• Chronological spacetimes without lightlike lines are stably causal
• Time machines with the compactly determined Cauchy horizon
• Are Causality Violations Undesirable?
• The boundary of the chronology violating set
• Emergent Time and Time Travel in Quantum Physics
• Augustine of Hippo's philosophy of time meets general relativity
• Evaporation induced traversability of the Einstein--Rosen wormhole
• An Invitation to Lorentzian Geometry
• Quasiregular singularities taken seriously
• An extendible spacetime without closed timelike curves whose every extension contains closed timelike curves