Black Holes Like Boiling Water ✛

Original: "Van der Waals Black Holes: Universality, Quantum Corrections, and Topological Classifications"

arXiv:2507.21663 · 2025-07-29 · CC BY 4.0 · 1 min

Some black holes behave like boiling water: they can evaporate and condense.

Some black holes behave like water: they can boil and condense. Their entropy (disorder) was once measured by the horizon area — a discovery by Jacob Bekenstein and Stephen Hawking. But quantum effects made entropy more complex; yet the link between extreme states endures — like a water droplet that boils and evaporates but still obeys the general laws of liquids.

Scientists have built a topological map of states marked by charges. Different quantum corrections draw different maps. In one case, charges are stable; in another, they break into groups, but the total sum of their weights remains unchanged. These charges are like bubbles in a boiling droplet: their arrangement shifts, but the collective 'importance' stays the same. The most surprising part: the more massive a black hole, the colder it gets. The record-holders are colder than the cosmic background — their temperature is near absolute zero.

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The most massive black hole can be colder than the space around it — its temperature is near absolute zero.

\frac{\partial M_{\text{ext}}}{\partial \epsilon} = \lim_{M \to M_{\text{ext}}} \left( -T \frac{\partial S}{\partial \epsilon} \right) \cdot \frac{\partial S_{\text{BH}}}{\partial S}

The derivative of the extremal mass with respect to the correction parameter equals the limit of the product of temperature and the derivative of entropy, multiplied by the correction factor, which is the derivative of the horizon area with respect to the modified entropy.

S = \pi r_h^2 - \frac{\alpha \pi}{4} \ln\left(\frac{4r_h^2 + \alpha}{\alpha}\right)

The entropy receives a negative logarithmic correction that reduces it compared to the horizon area.

Scientists

Jacob Bekenstein Stephen Hawking John Archibald Wheeler Fritz Zwicky Karl Schwarzschild Subrahmanyan Chandrasekhar

Concepts

wald entropy black hole thermodynamics hawking area law logarithmic correction quantum corrections topological protection modified gravity singularities extremal black hole schwarzschild metric topological charge general relativity tidal charge Bekenstein-Hawking entropy Hawking area theorem classical gravity topology Wien's displacement law generalized uncertainty principle homotopy event horizon stability

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Black Holes Like Boiling Water ✛