Book contents
- Frontmatter
- Contents
- Preface
- 1 Foundations of quantum statistical mechanics
- 2 Elementary examples
- 3 Quantum statistical master equation
- 4 Quantum kinetic equations
- 5 Quantum irreversibility
- 6 Entropy and dissipation: the microscopic theory
- 7 Global equilibrium: thermostatics and the microcanonical ensemble
- 8 Bose–Einstein ideal gas condensation
- 9 Scaling, renormalization and the Ising model
- 10 Relativistic covariant statistical mechanics of many particles
- 11 Quantum optics and damping
- 12 Entanglements
- 13 Quantum measurement and irreversibility
- 14 Quantum Langevin equation and quantum Brownian motion
- 15 Linear response: fluctuation and dissipation theorems
- 16 Time-dependent quantum Green's functions
- 17 Decay scattering
- 18 Quantum statistical mechanics, extended
- 19 Quantum transport with tunneling and reservoir ballistic transport
- 20 Black hole thermodynamics
- A Problems
- Index
- References
20 - Black hole thermodynamics
Published online by Cambridge University Press: 05 August 2015
- Frontmatter
- Contents
- Preface
- 1 Foundations of quantum statistical mechanics
- 2 Elementary examples
- 3 Quantum statistical master equation
- 4 Quantum kinetic equations
- 5 Quantum irreversibility
- 6 Entropy and dissipation: the microscopic theory
- 7 Global equilibrium: thermostatics and the microcanonical ensemble
- 8 Bose–Einstein ideal gas condensation
- 9 Scaling, renormalization and the Ising model
- 10 Relativistic covariant statistical mechanics of many particles
- 11 Quantum optics and damping
- 12 Entanglements
- 13 Quantum measurement and irreversibility
- 14 Quantum Langevin equation and quantum Brownian motion
- 15 Linear response: fluctuation and dissipation theorems
- 16 Time-dependent quantum Green's functions
- 17 Decay scattering
- 18 Quantum statistical mechanics, extended
- 19 Quantum transport with tunneling and reservoir ballistic transport
- 20 Black hole thermodynamics
- A Problems
- Index
- References
Summary
Introduction to black holes
In 1783 John Mitchell wrote, “If the semi-diameter of a sphere of the same density as the sun were to exceed that of the sun in the proportion of five hundred to one, and supposing light to be attracted by the same force in proportion to its vis-inertia with other bodies, all light emitted from such a body would be made to return towards it, by its own gravity” (Mitchell, 1783). Much later, in a prophetic paper, Oppenheimer and Snyder (1939) described the nature of “continued gravitational contraction” of a neutron star. With the nuclear heat gone, the core of the dead star becomes incapable of supporting itself under its own gravitational pull. The final phase is that the high density of the remaining core prevents the escape of the last light. The star disappears from view. Wheeler, later, coined the term black hole for such an object in the cosmos (Misner et al., 1973).
What is most remarkable is that today astronomers/astrophysicists have identified, with modern technical skills, numbers (uncountable) of these black holes. There seems no empirical doubt as to their existence. See the incredible visual treat in the volume The Universe, edited by Martin Rees (2005). Frolov and Novikov (1998) have given a condensed list of objects, eleven in number, which are binary systems that contain black holes. This comes from X-ray studies of binaries. As pointed out by them, the central arguments for the existence of black holes are: (a) the emission has a compact nature, and (b) the emission makes possible the analysis of the orbital motion, and one obtains the mass of the compact partner. If it is of the order of three solar masses, it is a black hole. See the resultant discussion of Cherepaschuk (1996). The strongest black hole candidates are three in number: GS2023+338, GS2000+25 and XN oph 1997. The first has a period of 6.5 days, a mass of the compact companion is of the order of 10 solar masses, and its luminosity is 6 × 1038 erg/sec.
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- Information
- Quantum Statistical Mechanics , pp. 390 - 403Publisher: Cambridge University PressPrint publication year: 2009