A Black Hole as a Heat Engine express

Original: "On the structure of black hole interior in a model of scalar quasi-particles within the GR framework"
· S. Bondarenko
arXiv:2607.03938 · 2026-07-04 · CC BY 4.0 · 1 min
The inside of a black hole may be layered like a cake and work like a heat engine.

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A black hole's interior is layered like an onion. In the new model, instead of an infinite point at the center, there are three regions: a dense core, a transition layer, and a crust just below the horizon. All arise from a single field that interacts with itself.

The core is a region of negative energy, similar to a condensate of particles without motion. It is described by a negative temperature, which in thermodynamics means a state with inverted level populations.

The crust consists of massive thermal excitations with positive energy. Between them is a thin transition layer where matter density is maximal and gravity almost vanishes. The whole structure is held together by Einstein's equations and stitched via Israel's junction conditions.

The formation and evaporation of a black hole becomes a cycle of a nearly adiabatic heat engine. The working substance is the core with negative energy, which exchanges heat with the crust through two different types of temperature.

Original abstract

as written by the authors arXiv:2607.03938

We propose an effective, singularity-free model of the black hole interior described entirely by a scalar field with a non-linear self-interaction potential. The interior consists of three layers -- a core, a transition layer, and a crust -- each fixed by the local quasi-particle density and the corresponding extremum of the potential of the field. The crust is a layer of massive, positive-energy thermal excitations above the zero-potential well, beneath a genuine Schwarzschild horizon at $$r = 2GM_{\rm ADM}$$. The core is an AdS-type region of negative energy density, it simulates a condensate of quasi-particles which carry zero classical kinetic energy and form a negative potential well governed by a negative inverse temperature parameter. The two regions are joined through Israel matching across the transition layer, which sits at an approximately null-gravity hypersurface of maximal regular matter density and where both the sign of the energy density and the type of thermal excitations change. Solving the static Einstein equations, we obtain the metric and mass functions of each layer, the edge equation of state of the crust, the linear stability condition of the null-gravity surface for ordinary and effectively negative mass matter, and the two-temperature thermodynamics linking the kinetic excitations to the negative temperature ground state. The framework unifies core and crust within a single field description and highlights the role of the negative energy AdS core and the associated negative temperature notion in describing black hole interior. In this picture the formation and Hawking evaporation of a black hole appear as a quasi-static cycle of an almost adiabatic thermodynamic engine, with the negative energy core as the working substance.

A negative temperature on the Kelvin scale is hotter than an infinite positive temperature: if you bring a body with negative temperature into contact with one with positive temperature, heat flows from the negative to the positive.

A similar layered world with reversed time flow is described in Greg Egan's novel 'Schild's Ladder'.

Scientists
John Archibald WheelerJacob BekensteinStephen HawkingFritz ZwickyKarl SchwarzschildSubrahmanyan Chandrasekhar
Concepts
schwarzschild black hole non singular black hole inner horizon horizon area surface gravity massless scalar field gravastar schwarzschild metric scalar particle innermost stable circular orbit naked singularity absolute zero torus wald entropy syk model no-hair theorem gravitational atom kerr metric Hawking area theorem hawking radiation mechanism