[Paper Review] Classical Black Holes Are Hot

Erik Curiel|PhilSci-Archive (University of Pittsburgh)|Aug 16, 2014

Cosmology and Gravitation Theories44 references3 citations

TL;DR

This paper argues that classical black holes in general relativity can be treated as thermodynamic systems without invoking quantum mechanics, by showing that surface gravity and horizon area play the roles of temperature and entropy in a classical Carnot-like cycle. The key contribution is demonstrating that the analogy between black-hole mechanics and thermodynamics is physically meaningful and self-contained within classical general relativity.

ABSTRACT

In the early 1970s it is was realized that there is a striking formal analogy between the Laws of black-hole mechanics and the Laws of classical thermodynamics. Before the discovery of Hawking radiation, however, it was generally thought that the analogy was only formal, and did not reflect a deep connection between gravitational and thermodynamical phenomena. It is still commonly held that the surface gravity of a stationary black hole can be construed as a true physical temperature and its area as a true entropy only when quantum effects are taken into account; in the context of classical general relativity alone, one cannot cogently construe them so. Does the use of quantum field theory in curved spacetime offer the only hope for taking the analogy seriously? I think the answer is `no'. To attempt to justify that answer, I shall begin by arguing that the standard argument to the contrary is not physically well founded, and in any event begs the question. Looking at the various ways that the ideas of "temperature" and "entropy" enter classical thermodynamics then will suggest arguments that, I claim, show the analogy between classical black-hole mechanics and classical thermodynamics should be taken more seriously, without the need to rely on or invoke quantum mechanics. In particular, I construct an analogue of a Carnot cycle in which a black hole "couples" with an ordinary thermodynamical system in such a way that its surface gravity plays the role of temperature and its area that of entropy. Thus, the connection between classical general relativity and classical thermodynamics on their own is already deep and physically significant, independent of quantum mechanics.

Motivation & Objective

• To challenge the widespread view that the thermodynamic analogy for black holes only holds when quantum effects like Hawking radiation are included.
• To argue that classical general relativity alone provides a sufficient foundation for treating black holes as thermodynamic systems.
• To resolve the apparent paradox of how a perfect absorber (classical black hole) can have a non-zero temperature by reinterpreting thermodynamic concepts in a classical framework.
• To show that the laws of black-hole mechanics and classical thermodynamics are not merely formal analogies but reflect a deep physical connection.
• To address foundational concerns about energy non-locality and heat transfer in gravitational systems by drawing parallels with classical thermodynamics.

Proposed method

• Constructs a classical analogue of the Carnot cycle involving a Schwarzschild black hole and a conventional thermodynamic system.
• Uses the black hole's surface gravity as a proxy for temperature and its horizon area as a proxy for entropy.
• Applies the formal structure of thermodynamic cycles to black holes, showing energy exchange and work extraction are conceptually coherent.
• Relies on quasi-local mass-energy definitions in stationary, axisymmetric spacetimes to avoid issues with non-local gravitational energy.
• Draws parallels between the non-local nature of gravitational energy and the non-local nature of heat in classical thermodynamics.
• Reinterprets entropy not as a statistical measure but as a measure of extractable work, explaining the discontinuous entropy jump at horizon formation.

Experimental results

Research questions

• RQ1 Can classical black holes be treated as thermodynamic systems without invoking quantum field theory in curved spacetime?
• RQ2 Is the analogy between black-hole mechanics and thermodynamics merely formal, or does it reflect a deeper physical connection in classical general relativity?
• RQ3 How can a black hole with zero temperature as a perfect absorber still be assigned a non-zero temperature via surface gravity?
• RQ4 What is the physical meaning of entropy in black holes if not derived from statistical mechanics?
• RQ5 How can energy exchange occur between a global quantity like ADM mass and localized stress-energy in a thermodynamically consistent way?

Key findings

• The standard argument that classical black holes cannot have temperature or entropy is not physically well founded and begs the question.
• A classical Carnot-Geroch cycle can be constructed where the black hole's surface gravity acts as temperature and its area as entropy, demonstrating thermodynamic behavior without quantum input.
• The non-local nature of gravitational energy does not preclude thermodynamic reasoning, as heat in classical thermodynamics is also non-local and lacks a local density.
• Entropy in black holes can be understood as a measure of free energy and extractable work, explaining the discontinuous jump in entropy at horizon formation.
• The laws of black-hole mechanics are theorems of differential geometry and do not require the Einstein field equation for their derivation, unlike the laws of thermodynamics, which are empirical.
• The deep physical significance of the analogy between black-hole mechanics and thermodynamics is established independently of quantum mechanics, suggesting a classical foundation for black hole thermodynamics.