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The first law for slowly evolving horizons.

Ivan Booth1, Stephen Fairhurst

  • 1Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John's, Newfoundland and Labrador, Canada A1C 5S7. ibooth@math.mun.ca

Physical Review Letters
|February 3, 2004
PubMed
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We explore the mechanics of dynamic trapping horizons by treating isolated horizons as equilibrium states. This research establishes a dynamical first law for these horizons using a novel perturbative approach.

Area of Science:

  • Theoretical physics
  • General relativity
  • Black hole thermodynamics

Background:

  • Isolated horizons (IHs) represent equilibrium states in black hole mechanics.
  • Trapping horizons (THs) describe the dynamics of black hole event horizons.
  • Existing formalisms link IHs to the zeroth and second laws of black hole mechanics.

Purpose of the Study:

  • To investigate the mechanics of Hayward's trapping horizons.
  • To establish a dynamical first law for trapping horizons.
  • To develop a new perturbative formulation for dynamic horizons.

Main Methods:

  • Utilizing isolated horizons as equilibrium states for comparison.
  • Applying the trapping horizon formalism to derive laws of mechanics.

Related Experiment Videos

  • Introducing a perturbative formulation for slowly evolving trapping horizons.

    • Main Results:

    • The zeroth law of dynamic horizon mechanics is derived from the isolated horizon formalism.
    • The second law of dynamic horizon mechanics is derived from the trapping horizon formalism.
    • A dynamical first law for trapping horizons is derived via a perturbative approach.

    Conclusions:

    • Slowly evolving trapping horizons can be treated as perturbatively nonisolated.
    • The study provides a unified framework for understanding dynamic horizon mechanics.
    • This work advances the understanding of black hole thermodynamics and dynamics.