Bekenstein–Hawking entropy
E4708
Bekenstein–Hawking entropy is the thermodynamic entropy associated with a black hole, proportional to the area of its event horizon and fundamental in linking gravity, quantum theory, and thermodynamics.
All labels observed (2)
| Label | Occurrences |
|---|---|
| Bekenstein–Hawking entropy canonical | 9 |
| Gibbons–Hawking entropy | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T65797 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Bekenstein–Hawking entropy Context triple: [Schwarzschild black hole, hasEntropyFormula, Bekenstein–Hawking entropy]
-
A.
Schwarzschild black hole
A Schwarzschild black hole is the simplest theoretical black hole solution in general relativity, describing a static, spherically symmetric, non-rotating, uncharged mass with an event horizon defined by the Schwarzschild radius.
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B.
Shannon entropy
Shannon entropy is a fundamental measure in information theory that quantifies the average uncertainty or information content in a random variable or message source.
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C.
Einstein field equations
The Einstein field equations are the core mathematical framework of general relativity, relating the curvature of spacetime to the distribution of matter and energy.
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D.
Oppenheimer–Snyder model
The Oppenheimer–Snyder model is a pioneering theoretical description of gravitational collapse in general relativity, providing one of the first rigorous treatments of how a massive star can form a black hole.
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E.
Feynman–Hellmann theorem
The Feynman–Hellmann theorem is a result in quantum mechanics that relates the derivative of an energy eigenvalue with respect to a parameter in the Hamiltonian to the expectation value of the corresponding derivative of the Hamiltonian.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Bekenstein–Hawking entropy Target entity description: Bekenstein–Hawking entropy is the thermodynamic entropy associated with a black hole, proportional to the area of its event horizon and fundamental in linking gravity, quantum theory, and thermodynamics.
-
A.
Schwarzschild black hole
A Schwarzschild black hole is the simplest theoretical black hole solution in general relativity, describing a static, spherically symmetric, non-rotating, uncharged mass with an event horizon defined by the Schwarzschild radius.
-
B.
Shannon entropy
Shannon entropy is a fundamental measure in information theory that quantifies the average uncertainty or information content in a random variable or message source.
-
C.
Einstein field equations
The Einstein field equations are the core mathematical framework of general relativity, relating the curvature of spacetime to the distribution of matter and energy.
-
D.
Oppenheimer–Snyder model
The Oppenheimer–Snyder model is a pioneering theoretical description of gravitational collapse in general relativity, providing one of the first rigorous treatments of how a massive star can form a black hole.
-
E.
Feynman–Hellmann theorem
The Feynman–Hellmann theorem is a result in quantum mechanics that relates the derivative of an energy eigenvalue with respect to a parameter in the Hamiltonian to the expectation value of the corresponding derivative of the Hamiltonian.
- F. None of above. chosen
Statements (48)
| Predicate | Object |
|---|---|
| instanceOf |
black hole thermodynamics concept
ⓘ
physical quantity ⓘ thermodynamic entropy ⓘ |
| appliesTo | black hole ⓘ |
| contrastsWith | volume-proportional entropy in ordinary thermodynamic systems ⓘ |
| dependsOn | event horizon area ⓘ |
| developedBy | Stephen Hawking ⓘ |
| domain | theoretical physics ⓘ |
| field |
black hole thermodynamics
ⓘ
general relativity ⓘ quantum gravity ⓘ statistical mechanics ⓘ |
| hasFormula | S = k_B c^3 A / (4 G ħ) ⓘ |
| hasLeadingTerm | area divided by 4 in Planck units ⓘ |
| implies | information content of a black hole scales with area not volume ⓘ |
| introducedBy | Jacob Bekenstein ⓘ |
| isAssociatedWith | event horizon ⓘ |
| isCentralTo |
loop quantum gravity black hole entropy calculations
ⓘ
microscopic models of black hole states ⓘ string theory black hole entropy calculations ⓘ |
| isExampleOf | area law for entropy ⓘ |
| isGeometric | true ⓘ |
| isKeyTo |
AdS/CFT correspondence
ⓘ
holographic principle ⓘ |
| isLimitOf | entanglement entropy across a horizon in quantum field theory ⓘ |
| isModifiedBy | quantum gravity corrections ⓘ |
| isNonzeroFor | any black hole with nonzero horizon area ⓘ |
| isProportionalTo |
area of the event horizon
ⓘ
horizon area in Planck units ⓘ |
| isZeroFor | zero-area horizon ⓘ |
| measuredIn | joules per kelvin ⓘ |
| namedAfter |
Jacob Bekenstein
ⓘ
Stephen Hawking ⓘ |
| relatesGeometryTo |
quantum information
ⓘ
thermodynamic entropy ⓘ |
| relatesTo |
Bekenstein bound
ⓘ
Hawking radiation ⓘ black hole temperature ⓘ |
| satisfies | generalized second law of thermodynamics ⓘ |
| supports | view of black holes as thermodynamic systems ⓘ |
| symbol | S ⓘ |
| usedIn |
derivations of holographic entropy bounds
ⓘ
studies of black hole information paradox ⓘ |
| usesConstant |
Boltzmann constant
ⓘ
Newtonian gravitational constant G ⓘ
surface form:
Newtonian gravitational constant
reduced Planck constant ⓘ speed of light ⓘ |
| yearProposed | 1970s ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: Bekenstein–Hawking entropy Description of subject: Bekenstein–Hawking entropy is the thermodynamic entropy associated with a black hole, proportional to the area of its event horizon and fundamental in linking gravity, quantum theory, and thermodynamics.
Referenced by (10)
Full triples — surface form annotated when it differs from this entity's canonical label.
this entity surface form:
Gibbons–Hawking entropy
subject surface form:
The four laws of black hole mechanics