*Valeri P. Frolov and Andrei Zelnikov*

- Published in print:
- 2011
- Published Online:
- January 2012
- ISBN:
- 9780199692293
- eISBN:
- 9780191731860
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199692293.003.0009
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology

This Chapter contains brief review of the theory of classical and quantum fields propagating in the black hole geometry. It includes such subjects as quasinormal modes and ringing radiation, ...
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This Chapter contains brief review of the theory of classical and quantum fields propagating in the black hole geometry. It includes such subjects as quasinormal modes and ringing radiation, separation of variables in the Kerr spacetime and hidden symmetries, Hawking effect and quantum evaporation of black holes, quantum fields in the Rindler frame and the Unruh effect. We formulate and discuss four laws of the black hole thermodynamics. At the end of the Chapter we briefly discuss higher dimension generalizations.Less

This Chapter contains brief review of the theory of classical and quantum fields propagating in the black hole geometry. It includes such subjects as quasinormal modes and ringing radiation, separation of variables in the Kerr spacetime and hidden symmetries, Hawking effect and quantum evaporation of black holes, quantum fields in the Rindler frame and the Unruh effect. We formulate and discuss four laws of the black hole thermodynamics. At the end of the Chapter we briefly discuss higher dimension generalizations.

*John W. Moffat*

- Published in print:
- 2020
- Published Online:
- June 2020
- ISBN:
- 9780190650728
- eISBN:
- 9780197517383
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780190650728.003.0002
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology

A major question confronting physicists studying black holes was whether thermodynamics applied to them—that is, whether the black holes radiated heat and lost energy. Bekenstein considered heat and ...
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A major question confronting physicists studying black holes was whether thermodynamics applied to them—that is, whether the black holes radiated heat and lost energy. Bekenstein considered heat and thermodynamics important for the interior of black holes. Based on the second law of thermodynamics, Hawking proposed that black holes evaporate over a very long time through what we now call Hawking radiation. This concept contradicts the notion that nothing can escape a black hole event horizon. Quantum physics enters into Hawking’s calculations, and he discovered the conundrum that the radiation would violate quantum mechanics, leading to what is called the information loss problem. These ideas are still controversial, and many physicists have attempted to resolve them, including Russian theorists Zel’dovich and Starobinsky. Alternative quantum physics interpretations of black holes have been proposed that address the thermodynamics problems, including so-called gravastars.Less

A major question confronting physicists studying black holes was whether thermodynamics applied to them—that is, whether the black holes radiated heat and lost energy. Bekenstein considered heat and thermodynamics important for the interior of black holes. Based on the second law of thermodynamics, Hawking proposed that black holes evaporate over a very long time through what we now call *Hawking radiation*. This concept contradicts the notion that nothing can escape a black hole event horizon. Quantum physics enters into Hawking’s calculations, and he discovered the conundrum that the radiation would violate quantum mechanics, leading to what is called the *information loss problem*. These ideas are still controversial, and many physicists have attempted to resolve them, including Russian theorists Zel’dovich and Starobinsky. Alternative quantum physics interpretations of black holes have been proposed that address the thermodynamics problems, including so-called *gravastars*.

*Rodolfo Gambini and Jorge Pullin*

- Published in print:
- 2011
- Published Online:
- December 2013
- ISBN:
- 9780199590759
- eISBN:
- 9780191774980
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199590759.003.0010
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology

This chapter discusses several topics in which loop quantum gravity techniques have been applied. These include black hole entropy in the context of black hole thermodynamics and how loop quantum ...
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This chapter discusses several topics in which loop quantum gravity techniques have been applied. These include black hole entropy in the context of black hole thermodynamics and how loop quantum gravity accounts for the entropy; the master constraint technique and the closely related uniform discretizations as a means of dealing with some of the problems of the Hamiltonian constraint; the spin foam techniques to treat the covariant quantization of gravity via path integral techniques; the possibility that observational effects could arise in the dispersion of the light that arrives from gamma ray bursts; possible limitations in the measurement of times and distances; and the problem of time in quantum gravity and recent proposals to deal with it.Less

This chapter discusses several topics in which loop quantum gravity techniques have been applied. These include black hole entropy in the context of black hole thermodynamics and how loop quantum gravity accounts for the entropy; the master constraint technique and the closely related uniform discretizations as a means of dealing with some of the problems of the Hamiltonian constraint; the spin foam techniques to treat the covariant quantization of gravity via path integral techniques; the possibility that observational effects could arise in the dispersion of the light that arrives from gamma ray bursts; possible limitations in the measurement of times and distances; and the problem of time in quantum gravity and recent proposals to deal with it.

*George Jaroszkiewicz*

- Published in print:
- 2016
- Published Online:
- January 2016
- ISBN:
- 9780198718062
- eISBN:
- 9780191787553
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198718062.003.0021
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology

This chapter discusses the role of imaginary time in physics. It emphasizes the difference between imaginary (or complex path) time and complex time. Starting with Minkowski’s famous 1908 lecture, ...
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This chapter discusses the role of imaginary time in physics. It emphasizes the difference between imaginary (or complex path) time and complex time. Starting with Minkowski’s famous 1908 lecture, the chapter considers the effect of replacing real time with imaginary time in relativity, Schrodinger wave mechanics, particle propagators, and Green’s functions in quantum field theory. The chapter reviews the use of imaginary time in Feynman path integrals, quantum gravity, quantum thermodynamics, and black hole thermodynamics.Less

This chapter discusses the role of imaginary time in physics. It emphasizes the difference between imaginary (or complex path) time and complex time. Starting with Minkowski’s famous 1908 lecture, the chapter considers the effect of replacing real time with imaginary time in relativity, Schrodinger wave mechanics, particle propagators, and Green’s functions in quantum field theory. The chapter reviews the use of imaginary time in Feynman path integrals, quantum gravity, quantum thermodynamics, and black hole thermodynamics.