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Black Holes and Thermodynamics: The First Half Century

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Quantum Aspects of Black Holes

Part of the book series: Fundamental Theories of Physics ((FTPH,volume 178))

Abstract

Black hole thermodynamics emerged from the classical general relativistic laws of black hole mechanics, summarized by Bardeen–Carter–Hawking, together with the physical insights by Bekenstein about black hole entropy and the semi-classical derivation by Hawking of black hole evaporation. The black hole entropy law inspired the formulation of the holographic principle by ’t Hooft and Susskind, which is famously realized in the gauge/gravity correspondence by Maldacena, Gubser–Klebanov–Polaykov and Witten within string theory. Moreover, the microscopic derivation of black hole entropy, pioneered by Strominger–Vafa within string theory, often serves as a consistency check for putative theories of quantum gravity. In this book chapter we review these developments over five decades, starting in the 1960s.

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Notes

  1. 1.

    In quantum information language the vacuum quantum state in a black hole space-time for each mode is a two-mode squeezed vacuum, similar to what happens for primordial density fluctuations in cosmology [53].

  2. 2.

    The sum should be regarded as formal since the quantum theory constructions of the two observers are unitarily inequivalent [49].

  3. 3.

    The stretched horizon (or the earlier “brick wall” [119]) is also discussed in these papers and captures the membrane description of a black hole suitable for a distant observer.

  4. 4.

    The derivation in [137] exploits a spherically symmetric ansatz in \(2+\varepsilon \) dimensions, dualizes to a different action for which the limit \(\varepsilon \rightarrow 0\) is well-defined and dualizes back after taking the limit.

  5. 5.

    \(\text {`}\)t Hooft also provided as an example a realization of the holographic principle in terms of some cellular automaton model.

  6. 6.

    Such an encoding results in an entropy that scales like the area, which suggests a local and non-gravitational description on the boundary.

  7. 7.

    The dual field theory at finite temperature is defined on \(S^{3}\times S^{1}\) and therefore has compact volume. Nevertheless, a phase transition is possible because the theory is considered in the large \(N\) limit.

  8. 8.

    We mention in the conclusions that this link is likely to grow stronger in the future. Besides the numerous recent papers on holographic entanglement entropy, some selected papers that also provide such links are [308, 309] and references therein.

  9. 9.

    Loop quantum gravity does provide such a prediction [363, 364], and it disagrees with the semi-classical result.

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Acknowledgments

DG and RM thank their respective collaborators for numerous discussions on black hole thermodynamics in the past 15 years. DG and JS were supported by the START project Y 435-N16 of the Austrian Science Fund (FWF) and the FWF projects I 952-N16 and I 1030-N27.

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  1. Institute for Theoretical Physics, Vienna University of Technology, Wiedner Hauptstrasse 8-10, 1040, Vienna, Austria

    Daniel Grumiller & Jakob Salzer

  2. Department of Physics, Loyola University Chicago, Chicago, IL, 60660, USA

    Robert McNees

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    Xavier Calmet

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Grumiller, D., McNees, R., Salzer, J. (2015). Black Holes and Thermodynamics: The First Half Century. In: Calmet, X. (eds) Quantum Aspects of Black Holes. Fundamental Theories of Physics, vol 178. Springer, Cham. https://doi.org/10.1007/978-3-319-10852-0_2

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