Light Cone Thermodynamics

Abstract

We show that null surfaces defined by the outgoing and infalling wave fronts emanating from and arriving at a sphere in Minkowski spacetime have thermodynamical properties that are in strict formal correspondence with those of black hole horizons in curved spacetimes. Such null surfaces, made of pieces of light cones, are bifurcate conformal Killing horizons for suitable conformally stationary observers. They can be extremal and non-extremal depending on the radius of the shining sphere. Such conformal Killing horizons have a constant light cone (conformal) temperature, given by the standard expression in terms of the generalisation of surface gravity for conformal Killing horizons. Exchanges of conformally invariant energy across the horizon are described by a first law where entropy changes are given by $1/(4{\ell }_p^2)$ of the changes of a geometric quantity with the meaning of horizon area in a suitable conformal frame. These conformal horizons satisfy the zeroth to the third laws of thermodynamics in an appropriate way. In the extremal case they become light cones associated with a single event; these have vanishing temperature as well as vanishing entropy.

arXiv comment30 pages, 5 pictures; V_2: a problem in the proof of the first law has been corrected. Results remain unchanged. Geometric interpretation and presentation improved; V_3: matches published version

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Cited by in corpus (19)

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• Null infinity as an open Hamiltonian system
• Einstein's Equations from the Stretched Future Light Cone
• Conformal quantum mechanics of causal diamonds
• Generating multi-partite entanglement from the quantum vacuum with a finite-lifetime mirror
• Thermal effect in a causal diamond: open quantum systems approach
• Entanglement Degradation in Causal Diamonds
• Thermodynamics of Regular Black Holes in Anti-de Sitter Space
• Light Cone Black Holes
• Spectral Properties of the Symmetry Generators of Conformal Quantum Mechanics: A Path-Integral Approach
• Emergent Gravity in a Holographic Universe
• Spacetime Thermodynamics with Contorsion
• A Local First Law of Gravity
• Vacuum thermal effects in flat space-time from conformal quantum mechanics
• Conformal quantum mechanics of causal diamonds: Time evolution, thermality, and instability via path integral functionals
• Abbott-Deser-Tekin like conserved quantities in Lanczos-Lovelock gravity: beyond Killing diffeomorphisms
• Path integral derivation of the thermofield double state in causal diamonds
• On the existence of conformal Killing horizons in LRS spacetimes