Science › Black holes & quantum gravity
Black-hole entropy: information on the surface
1972· Theory
Well supportedStrong evidence or math, but not fully tested.
A black hole's hidden disorder, set by its horizon's surface area rather than its volume.
See it on the Science map →How it works
Entropy counts how many hidden internal arrangements fit the same outward appearance. Bekenstein (1972) and Hawking (1974) found a black hole's entropy equals the number of tiny Planck-sized patches on its horizon, divided by four: roughly one bit for every few patches. That makes black holes the most entropy-dense objects possible. Strangely, the count scales with surface area, not volume, as if everything inside were recorded on the boundary.
Why it matters
It inspired the holographic principle, the idea that a region's full contents may be encoded on its boundary, now central to quantum-gravity research.
Think of it like
Like valuing a building by its facade area instead of its floor area, and finding that works every time.
How we know
Strongly supported by consistent theory: Hawking's temperature calculation, string theory's 1996 microstate count, and LIGO tests (2021, 2025) confirming horizon area grows in mergers. Not directly measured.
Still a mystery
What the microscopic states actually are for a real, spinning black hole is still unknown.
Connections (6)
▸Event horizon: the point of no return measures by its area Black-hole entropy: information on the surfaceWell supported
The relationship
Hawking proved in 1971 that a horizon's area never shrinks, even when black holes merge, much like entropy never decreases. Bekenstein proposed the match was real, and Hawking's 1974 result made it exact: a black hole's entropy equals its horizon area measured in units of tiny Planck-sized patches, divided by four. So the horizon's surface, not the volume inside, sets how much information a black hole holds.
How the link was found
Hawking's area theorem (1971), Bekenstein's entropy proposal (1972), and Hawking's 1974 calculation fixing the exact factor of one quarter.
Is it proven?
Strongly supported by theory and string theory's 1996 microstate count. LIGO measured horizon area before and after mergers in 2021 and 2025: it grew, as required.
Open questions and mysteries
Why surface area rather than volume? This led to the holographic principle, still unproven for our universe.
▸Stephen Hawking pinned down the exact value of Black-hole entropy: information on the surfaceWell supported
The relationship
Bekenstein argued a black hole's entropy is proportional to its horizon area, but could not fix the exact number. Hawking's 1974 temperature result settled it. In thermodynamics, temperature and entropy are tied together, so knowing the temperature pins down the entropy exactly: one quarter of the horizon area, measured in Planck units. This is the Bekenstein–Hawking formula.
How the link was found
Stephen Hawking, 1974–75, as a direct consequence of his radiation calculation.
Is it proven?
The quarter factor has been rederived by several methods, and string theory reproduced it exactly for special black holes in 1996.
Open questions and mysteries
What microscopic states the entropy counts for ordinary, spinning black holes is unknown.
▸Jacob Bekenstein proposed Black-hole entropy: information on the surfaceWell supported
The relationship
John Wheeler posed a puzzle: drop a cup of hot tea into a black hole and its entropy seems to vanish, breaking the second law of thermodynamics. Bekenstein proposed that the black hole gains entropy as it grows, proportional to its horizon area. Then total entropy, ordinary plus black hole, never decreases. He called this the generalized second law.
How the link was found
Jacob Bekenstein, Princeton PhD student of Wheeler, in 1972, with a fuller paper in 1973. Hawking and others initially rejected it.
Is it proven?
Hawking's 1974 discovery that black holes have a temperature made the idea consistent. String theory's 1996 count of black-hole states matched it for special cases.
Open questions and mysteries
Whether the generalized second law holds in all situations, including quantum ones, is mostly but not completely proven.
▸Black-hole entropy: information on the surface is the black-hole version of Entropy: disorder always growsWell supported
The relationship
Ordinary entropy counts how many internal arrangements match what we see. Black-hole entropy applies the same accounting to black holes and folds them into the second law: ordinary entropy plus black-hole entropy never goes down. Black holes turn out to be enormous entropy stores. The Milky Way's central black hole holds far more entropy than all its stars combined.
How the link was found
Bekenstein (1972) proposed it; Bardeen, Carter and Hawking (1973) set out the four "laws of black hole mechanics" that mirror thermodynamics; Hawking's 1974 result made the match exact.
Is it proven?
The mathematics is consistent, and the 1996 string-theory count matched it. LIGO's horizon-area tests (2021, 2025) support the black-hole second law.
Open questions and mysteries
Ordinary entropy counts atoms. What are the "atoms" of a black hole?
▸Black-hole entropy: information on the surface inspired The holographic principleSpeculative
The relationship
A black hole is the most information-dense object possible, and its entropy grows with the area of its horizon, not its volume. So the most information any region can hold is set by its surface area. 't Hooft and Susskind took this limit literally: the region's full contents might be encoded on its boundary.
How the link was found
Jacob Bekenstein proposed black-hole entropy in 1972; Stephen Hawking fixed its exact value in 1974. Gerard 't Hooft drew the holographic conclusion in 1993, and Leonard Susskind extended it in 1995.
Is it proven?
Hawking's calculation and the 1996 Strominger-Vafa count of black-hole microstates in string theory agree on the area law. The leap from black holes to every region of space remains untested.
Open questions and mysteries
Hawking radiation has never been observed. And whether an area limit means the world is literally encoded on a boundary, or only bounded by one, is debated.
▸String theory counted the microstates behind Black-hole entropy: information on the surfaceWell supported
The relationship
Black-hole entropy implies a black hole has a huge number of hidden internal states. Andrew Strominger and Cumrun Vafa built a special black hole in string theory out of string-theory objects called D-branes, then counted the ways they could be arranged. The count exactly matched Bekenstein and Hawking's one quarter of the horizon area.
How the link was found
Andrew Strominger and Cumrun Vafa, 1996, using the D-branes discovered by Joseph Polchinski in 1995.
Is it proven?
The match is exact and has been repeated for many related cases, a strong sign of consistency. It works only for idealized, perfectly balanced black holes, not the spinning ones astronomers observe.
Open questions and mysteries
Can the count be done for real astrophysical black holes, and what do these microstates look like from outside?