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The future is not always open.

James D E Grant1, Michael Kunzinger2, Clemens Sämann2

  • 11Department of Mathematics, University of Surrey, Guildford, UK.

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This summary is machine-generated.

Lorentzian causality theory fundamentals break down in low regularity settings. Chronological futures may be non-open and differ from standard definitions, impacting synthetic geometry approaches.

Keywords:
Causal bubblesCausality theoryChronological futureLow regularity

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Area of Science:

  • General Relativity
  • Differential Geometry
  • Mathematical Physics

Background:

  • Lorentzian causality theory is foundational in General Relativity.
  • Standard definitions rely on smooth (C^1) curves.
  • Low regularity spacetimes challenge these assumptions.

Purpose of the Study:

  • Investigate the breakdown of Lorentzian causality in low regularity.
  • Characterize spacetimes exhibiting these phenomena.
  • Relate findings to synthetic approaches in geometry.

Main Methods:

  • Analysis of chronological futures using locally Lipschitz curves.
  • Refinement of the 'causal bubble' concept.
  • Examination of curve deformation ('push-up') possibilities.

Main Results:

  • Chronological futures can be non-open in low regularity.
  • Futures defined by Lipschitz curves may differ from C^1 curves.
  • Characterization of spacetimes allowing these causal anomalies.

Conclusions:

  • Fundamental aspects of Lorentzian causality are not robust in low regularity.
  • Findings are crucial for developing synthetic Lorentzian geometry.
  • The study highlights the need for refined causal definitions in non-smooth settings.