Surfaces away from horizons are not thermodynamic.

Area of Science:

• Thermodynamics
• General Relativity
• Black Hole Physics

Background:

• Black hole horizons exhibit thermodynamic properties, a concept known since the 1970s.
• Conjectures suggest that other surfaces, beyond horizons, may also possess thermodynamic behavior.
• These conjectures extend to stretched horizons and surfaces within the emergent gravity framework.

Purpose of the Study:

• To investigate whether non-horizon surfaces satisfy a first law of thermodynamics, analogous to horizons.
• To test the thermodynamic conjectures for stretched horizons and surfaces in emergent gravity.
• To determine the validity of the first law of thermodynamics for various surface types in general relativity.

Main Methods:

• Analysis of static asymptotically flat spacetimes.
• Mathematical derivation to test the first law of thermodynamics on different surfaces.
• Comparison of results for horizons, stretched horizons, and emergent gravity surfaces.

Main Results:

• The first law of thermodynamics is confirmed for black hole horizons in static asymptotically flat spacetimes.
• The first law is an excellent approximation for stretched horizons, but its approximate nature highlights limitations of black hole mechanics alone.
• The first law fails for surfaces away from horizons in the emergent gravity program, except in spherically symmetric cases.

Conclusions:

• The thermodynamic behavior of stretched horizons is well-approximated by the first law, but this does not fully imply true thermodynamic properties.
• The failure of the first law for general surfaces in emergent gravity undermines a core assumption of this theoretical program.
• This research clarifies the conditions under which thermodynamic laws apply to different types of surfaces in gravitational contexts.