A black hole is not just a cosmic vacuum cleaner. It is a region with such strong gravity that even light cannot escape it. But place it in a perfect fluid of dark matter and add a cloud of strings, thin filaments stretched across all of space, and the picture gets more complicated. The authors started with the Bekenstein-Hawking entropy (a measure of disorder) and added quantum corrections to it, like ripples on water from random jolts.
These corrections come in two flavors. The first is logarithmic: they arise from weak thermal jitters and alter the black hole's mass, free energy, and heat capacity. Heat capacity is the key to stability: if it is positive, the hole is stable; if negative, it falls apart. With logarithmic corrections, at some point the sign flips, and the black hole goes from unstable to stable. The second flavor is exponential corrections, born from strong quantum leaps. They are nearly invisible for large holes but become dominant when the hole shrinks to Planck scales (about 10⁻³⁵ meters).
The researchers also checked whether such a system has a critical point — a special state where the distinction between liquid and gas disappears (like water at 374°C and 218 atmospheres). To do this, they looked for a place where the first and second derivatives of pressure with respect to volume vanish simultaneously. Alas, no such inflection point exists in the physically allowed region. So the phase transition here is arranged differently.
A black hole's entropy is proportional to the area of its event horizon, not its volume, as if all the information about what fell into the hole is written on its surface, like a hologram.
In Peter Watts's novel Blindsight, black holes are used as computational devices — an idea that echoes attempts to understand their thermodynamics and entropy.