Black hole thermodynamics

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A Geroch "gravitational thermodynamic engine”, conceived by Robert Geroch (c.1975), drawn by Louis Fulgoni, which, using a black hole as a heat sink, in theory, converts heat into work, via the so-called "Geroch process" (or Geroch cycle).[1]

In thermodynamics, Black-hole thermodynamics is the topic of thermodynamics, the second law in particular, applied to black holes, stars that collapse into black holes, the radiation of black holes, or heat engines operating near black holes.


In 1916, Karl Schwarzschild solved the gravitational field equations of Einstein’s general relativity, to outline the basics of what a black hole was.

In 1939, Robert Oppenheimer, with Harlan Snyder, published a paper which showed that Schwarzschild solution describes the final state of a spherically collapsing massive star, as diagrammed below, which shows spherical collapse to a black hole:[1]

Oppenheimer-Snyder black hole formation (Beckenstein).jpg

This diagram, show the spacetime histories of the collapsing body's surface (illustrated as one-dimensional), of the resulting singularity and of the horizon expanding to engulf the body. The tilting of the light cone by gravitation explains why the region interior to the horizon is invisible from outside. The spacelike hypersurtaces labeled Σ supplant, in relativity, the concept of space at a given time. This was the first-time "black holes" became a central phenomenon of astrophysics.[1]

In 1971, John Wheeler, the person who coined the term “black hole” (1967), in conversation with Jacob Bekenstein, his graduate student at Princeton, argued that the “black holes have no hair” conjecture, aka “no-hair theorem” (Israel, 1967)[2], allows for a wicked creature, which Bekenstein dubs “Wheeler’s demon”, to commit a crime against the second law, by dropping a package containing some entropy into a stationary black hole, thus decreasing the entropy in the part of the universe visible from the exterior.

In 1974, Stephen Hawking showed that black holes must radiate spontaneously with a thermal spectrum.

Geroch cycle | Process

In c.1960s (or 1970s), Robert Geroch, during a Q&A session of a colloquium he gave at Princeton, conceived of the so-called “Geroch process” (or Geroch cycle), which is diagrammed adjacent, which shows a “gravitational thermodynamic engine”, which, using a black hole as a heat sink, converts heat into work.[3]

The box is filled with thermal radiation and lowered in the hole’s filed to its event horizon. The gravitational field, supposedly, does work on the box in this process. The radiation is then allowed to escape into the hole, and the box is hauled back up at expense of less work than was obtained in the first stage. The box, which is not allowed to touch the horizon, can then be refilled with thermal radiation, from the reservoir, which is said to yield an efficiency of conversion of less than 1 percent.

End matter


  1. 1.0 1.1 1.2 Bekenstein, Jacob D. (1980). “Black-hole Thermodynamics” (pdf), Physics Today (pgs. 24-31), Jan.
  2. No-hair theorem – Wikipedia.
  3. Dougherty, John; Callender, Craig. (2016). “Black Hole Thermodynamics: More Than and Analogy? (pdf) (pg. 8),

External links

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