area theorem

E844098

physical law theorem in general relativity

The area theorem is a principle in black hole physics stating that the total event horizon area of black holes cannot decrease over time in classical general relativity, analogous to the second law of thermodynamics.

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All labels observed (2)

Label	Occurrences
area theorem canonical	1
black hole area theorem	1

How this entity was disambiguated

This entity first appeared as the object of triple T10147862 — 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: area theorem
Context triple: [The four laws of black hole mechanics, keyConcept, area theorem]

A. Bekenstein–Hawking entropy
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.
B. Planck area
The Planck area is the fundamental unit of area in quantum gravity, defined as the square of the Planck length and often considered the smallest meaningful area scale in physics.
C. Bekenstein bound
The Bekenstein bound is a theoretical limit in physics on the maximum amount of information or entropy that can be contained within a finite region of space with a given amount of energy.
D. Schwarzschild radius
The Schwarzschild radius is the critical distance from the center of a non-rotating, spherically symmetric mass at which its escape velocity equals the speed of light, defining the boundary of a black hole.
E. black hole no-hair theorem
The black hole no-hair theorem is a principle in general relativity stating that stationary black holes are completely characterized by only a few macroscopic parameters—mass, electric charge, and angular momentum—regardless of the details of the matter that formed them.
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: area theorem
Target entity description: The area theorem is a principle in black hole physics stating that the total event horizon area of black holes cannot decrease over time in classical general relativity, analogous to the second law of thermodynamics.

A. Bekenstein–Hawking entropy
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.
B. Planck area
The Planck area is the fundamental unit of area in quantum gravity, defined as the square of the Planck length and often considered the smallest meaningful area scale in physics.
C. Bekenstein bound
The Bekenstein bound is a theoretical limit in physics on the maximum amount of information or entropy that can be contained within a finite region of space with a given amount of energy.
D. Schwarzschild radius
The Schwarzschild radius is the critical distance from the center of a non-rotating, spherically symmetric mass at which its escape velocity equals the speed of light, defining the boundary of a black hole.
E. black hole no-hair theorem
The black hole no-hair theorem is a principle in general relativity stating that stationary black holes are completely characterized by only a few macroscopic parameters—mass, electric charge, and angular momentum—regardless of the details of the matter that formed them.
F. None of above. chosen

Statements (47)

Predicate	Object
instanceOf	physical law ⓘ theorem in general relativity ⓘ
alsoKnownAs	Hawking area theorem ⓘ linked to: “The four laws of black hole mechanics” black hole area theorem ⓘ linked to: area theorem
analogy	second law of thermodynamics ⓘ
appliesTo	event horizon of a black hole ⓘ systems of multiple black holes ⓘ
assumes	classical matter obeys positive energy conditions ⓘ event horizon is a null hypersurface ⓘ global hyperbolicity of spacetime ⓘ
condition	Einstein field equations hold ⓘ classical general relativity ⓘ cosmic censorship hypothesis ⓘ no naked singularities ⓘ no quantum effects ⓘ null energy condition ⓘ
consequence	area increase during gravitational collapse ⓘ black holes cannot bifurcate into smaller black holes with smaller total area ⓘ irreversibility of classical black hole dynamics ⓘ
coreStatement	the total area of black hole event horizons cannot decrease with time in classical general relativity ⓘ
domain	classical regime of gravity ⓘ
field	black hole physics ⓘ general relativity ⓘ
implies	black hole horizon area behaves like entropy ⓘ
inspired	Bekenstein’s proposal of black hole entropy ⓘ development of black hole thermodynamics ⓘ
limitation	can be violated by quantum effects such as Hawking radiation ⓘ does not apply when energy conditions are violated ⓘ
mathematicalTool	Raychaudhuri equation ⓘ properties of null geodesic congruences ⓘ
notApplicableIn	full quantum gravity ⓘ semiclassical evaporation phase dominated by Hawking radiation ⓘ
predicts	classical gravitational radiation cannot reduce total horizon area ⓘ merger of two black holes has final horizon area at least as large as the sum of initial areas ⓘ total event horizon area is non-decreasing in any classical process ⓘ
relatedTo	Bekenstein–Hawking entropy ⓘ Penrose process ⓘ linked to: Penrose process for energy extraction black hole thermodynamics ⓘ cosmic censorship conjecture ⓘ generalized second law of thermodynamics ⓘ null energy condition ⓘ
statedBy	Stephen Hawking ⓘ
status	widely accepted within its domain of validity ⓘ
supports	interpretation of black hole area as entropy ⓘ
usedIn	constraints on gravitational wave signals from black hole mergers ⓘ tests of general relativity with LIGO–Virgo observations ⓘ
yearProposed	1971 ⓘ