Physics:Quantum Black hole thermodynamics

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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.[1]

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:

dM=κ8πGdA+⋯

  • 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:

S=kc3A4Gℏ.

This result, discovered by Bekenstein and 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.[2]

The temperature of a black hole is given by

T=ℏc38πGMk.

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

Table of contents (185 articles)

Index

Full contents

9. Quantum optics and experiments (5) ↑ Back to index
14. Plasma and fusion physics (8) ↑ Back to index
Conceptual illustration of plasma physics in a fusion context, showing magnetically confined ionized gas in a tokamak and the collective behavior governed by electromagnetic fields and transport processes.
Conceptual illustration of plasma physics in a fusion context, showing magnetically confined ionized gas in a tokamak and the collective behavior governed by electromagnetic fields and transport processes.

References

  1. ↑ Wald, Robert M. (1994). Quantum Field Theory in Curved Spacetime and Black Hole Thermodynamics. University of Chicago Press. 
  2. ↑ Hawking, Stephen W. (1975). "Particle Creation by Black Holes". Communications in Mathematical Physics 43. 
Author: Harold Foppele

Source attribution: Quantum Black hole thermodynamics

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