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Related Experiment Videos

Positive mass from holographic causality.

Don N Page1, Sumati Surya, Eric Woolgar

  • 1Theoretical Physics Institute, University of Alberta, Edmonton, Alberta, Canada T6G 2J1. don@phys.ualberta.ca

Physical Review Letters
|September 13, 2002
PubMed
Summary
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Causality in boundary theories proves spacetime mass positivity for asymptotically anti-de Sitter (AdS) spacetimes (n≥3). This bypasses local energy conditions, utilizing a bulk-to-boundary time-delay formula.

Area of Science:

  • Theoretical physics
  • General relativity
  • Quantum field theory

Background:

  • Asymptotically anti-de Sitter (AdS) spacetimes are crucial in theoretical physics, particularly in the context of the holographic principle.
  • Establishing energy conditions, such as positivity of mass, is fundamental for the consistency of gravitational theories.
  • Previous work often relied on local energy conditions, limiting the generality of mass positivity proofs.

Purpose of the Study:

  • To demonstrate that causality in the boundary conformal field theory (CFT) is sufficient to prove mass positivity for (n+1)-dimensional AdS spacetimes.
  • To investigate the implications of holographic causality for specific solutions like the negative mass AdS soliton.
  • To connect these findings to the broader positive energy conjecture in quantum gravity.

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Main Methods:

  • Utilizing the holographic principle to relate properties of bulk AdS spacetimes to their boundary CFTs.
  • Developing and applying a time-delay formula that links the Ashtekar-Magnon mass of the spacetime to the time delay between bulk null curves and boundary null geodesics.
  • Analyzing causality constraints imposed by the boundary theory on the bulk spacetime.

Main Results:

  • Proof of mass positivity for (n+1)-dimensional AdS spacetimes (n≥3) solely based on boundary causality, without assuming local energy conditions.
  • A precise relationship established between spacetime mass and boundary causal structure via the time-delay formula.
  • Insights into the holographic causality of negative mass AdS solitons and their relevance to energy positivity conjectures.

Conclusions:

  • Boundary causality is a powerful tool for proving fundamental properties of gravitational spacetimes in holographic settings.
  • The time-delay formula provides a novel and effective method for connecting bulk and boundary physics.
  • The results support and refine conjectures regarding positive energy in quantum gravity theories.