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{{Quantum book backlink|Advanced and frontier topics}}
'''Black hole thermodynamics''' is the study of the thermodynamic properties of black holes, combining concepts from general relativity, quantum mechanics, and statistical physics. It establishes deep connections between gravity, entropy, and quantum theory.<ref>{{cite book |last=Wald |first=Robert M. |title=Quantum Field Theory in Curved Spacetime and Black Hole Thermodynamics |publisher=University of Chicago Press |year=1994}}</ref>

[[File:Black_hole_thermodynamics yellow.jpg|thumb|400px|Black hole thermodynamics: event horizon, entropy, Hawking radiation, and temperature.]]
=Quantum Black hole thermodynamics=
=== Laws of black hole thermodynamics ===

Black holes obey laws analogous to the laws of thermodynamics:

* '''Zeroth law''' — the surface gravity is constant on the event horizon.
* '''First law''' — relates changes in mass, area, and angular momentum:

<math>
dM = \frac{\kappa}{8\pi G} dA + \cdots
</math>

* '''Second law''' — the horizon area never decreases.
* '''Third law''' — it is impossible to reach zero surface gravity.

These laws suggest that black holes have well-defined thermodynamic properties.
=== Bekenstein–Hawking entropy ===

Black holes possess entropy proportional to the area of their event horizon:

<math>
S = \frac{k c^3 A}{4 G \hbar}.
</math>

This result, discovered by [[Wikipedia:Jacob Bekenstein|Bekenstein]] and [[Wikipedia:Stephen Hawking|Hawking]], shows that entropy scales with area rather than volume.

This relation suggests a deep connection between gravity and information.
=== Hawking radiation ===

Quantum effects near the event horizon cause black holes to emit radiation, known as '''Hawking radiation'''.<ref>{{cite journal |last=Hawking |first=Stephen W. |title=Particle Creation by Black Holes |journal=Communications in Mathematical Physics |volume=43 |year=1975}}</ref>

The temperature of a black hole is given by

<math>
T = \frac{\hbar c^3}{8\pi G M k}.
</math>

This implies that black holes are not completely black but slowly evaporate over time.
=== Information paradox ===

The evaporation of black holes leads to the '''information paradox''': if a black hole completely evaporates, it appears that information about the initial state is lost.

This conflicts with the principles of quantum mechanics, which require unitary evolution.

The resolution of this paradox is an active area of research involving:

* '''holographic principle'''
* '''quantum gravity'''
* '''black hole complementarity'''

=== Physical significance ===

Black hole thermodynamics:

* connects gravity with quantum theory,
* suggests a fundamental link between geometry and information,
* plays a key role in modern theories such as string theory and holography.

=See also=
{{#invoke:PhysicsQC|tocHeadingAndList|Physics:Quantum basics/See also}}

=References=
{{reflist|3}}

{{Author|Harold Foppele}}

{{Sourceattribution|Quantum Black hole thermodynamics|1}}

Physics:Quantum Black hole thermodynamics - Revision history

imported>WikiHarold: Repair Quantum Collection B backlink template

imported>WikiHarold: Repair Quantum Collection B backlink template