Black Hole Calculator

In 1974, Hawking showed that quantum effects near the event horizon cause black holes to radiate thermally — as if they were a black body at temperature T_H ∝ 1/M. As the hole radiates, it loses mass and shrinks, eventually evaporating entirely. But here lies the paradox: thermal radiation carries no information about what fell in. Quantum mechanics demands that information is never destroyed — yet Hawking's calculation seems to erase it. This is the black hole information paradox. Decades of debate produced no resolution, until recent work involving 'islands' and the Page curve suggested that information may be encoded in subtle quantum correlations in the Hawking radiation itself — entanglement structure invisible to local observers. The paradox is not fully resolved, but the current consensus is that unitarity survives: information escapes, encoded in a way that requires a complete theory of quantum gravity to decode.

A non-rotating black hole is described entirely by its mass. Once you know the Schwarzschild radius r_s = 2GM/c², every other landmark follows as a fixed multiple: the photon sphere at 1.5 r_s, the innermost stable orbit at 3 r_s. Double the mass and all of them double with it. As a black hole, the Sun would span just ~3 km across; Earth, a mere ~9 mm.

Ordinary objects cool as they lose energy; black holes do the reverse. Because T_H ∝ 1/M, radiating mass away makes a hole hotter, not colder — a negative heat capacity. Evaporation therefore runs away: the smaller the hole shrinks, the faster it radiates, ending in a final burst. It also means a black hole can never settle into stable thermal equilibrium with an unlimited heat bath.