The universal extremal relation and thermodynamic topology of Van der Waals-type black holes—solutions to Einstein's equations that behave like real gases—are investigated. In the classical case, entropy obeys the Bekenstein–Hawking area law and the standard universality ratio. When quantum corrections from the generalized uncertainty principle (GUP), extended uncertainty principle (EUP), and rainbow gravity are included, the entropy law is modified, but a generalized form of the extremal relation survives. Topological analysis reveals that varying black hole parameters and models leads to changes in topological classes and winding numbers. In the GUP-corrected case, the distribution of topological charges is stable; for EUP corrections, two classes are found, including configurations with three non-zero charges and zero total charge as the number of individual charges changes; rainbow gravity shows similar consistency in topological behavior.
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.
🎯 The most massive black hole can be colder than the space around it — its temperature is near absolute zero.