Entanglement Entropy of Black Holes

By S. Solodukhin. Living Reviews in Relativity, 2011

635 citations recorded by the source corpus.

The entanglement entropy is a fundamental quantity, which characterizes the correlations between sub-systems in a larger quantum-mechanical system. For two sub-systems separated by a surface the entanglement entropy is proportional to the area of the surface and depends on the UV cutoff, which regulates the short-distance correlations. The geometrical nature of entanglement-entropy calculation is particularly intriguing when applied to black holes when the entangling surface is the black-hole horizon. I review a variety of aspects of this calculation: the useful mathematical tools such as the geometry of spaces with conical singularities and the heat kernel method, the UV divergences in the entropy and their renormalization, the logarithmic terms in the entanglement entropy in four and six dimensions and their relation to the conformal anomalies. The focus in the review is on the systematic use of the conical singularity method. The relations to other known approaches such as ’t Hooft’s brick-wall model and the Euclidean path integral in the optical metric are discussed in detail. The puzzling behavior of the entanglement entropy due to fields, which non-minimally couple to gravity, is emphasized. The holographic description of the entanglement entropy of the blackhole horizon is illustrated on the two- and four-dimensional examples. Finally, I examine the possibility to interpret the Bekenstein-Hawking entropy entirely as the entanglement entropy.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/232df42c97c8a52eb09b85320ae66a71d5ccfba4

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The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Astronomy and Astrophysics

1. T. Takayanagi
2. R. Myers
3. D. Harlow
4. T. Nishioka
5. T. Faulkner
6. V. Hubeny
7. M. Rangamani
8. William Donnelly

In Nuclear and High Energy Physics

1. R. Myers
2. D. Harlow
3. T. Takayanagi
4. T. Nishioka
5. Aitor Lewkowycz
6. T. Faulkner
7. M. Rangamani
8. J. Maldacena

In Statistical and Nonlinear Physics

1. D. Harlow
2. R. Myers
3. T. Nishioka
4. T. Takayanagi
5. T. Faulkner
6. Aitor Lewkowycz
7. Aron C. Wall
8. J. Maldacena

Citations in the corpus

• Thermodynamics, gravitational anomalies and cones (2012, background): “This object has been studied in the literature on entanglement entropy (see [57] for a review).”
• Entanglement entropy and nonabelian gauge symmetry (2014, background): “Perhaps the most significant role of entanglement entropy is in black hole thermodynamics [4].”
• Entanglement entropy from a holographic viewpoint (2012, background): “Historically, the entanglement entropy has originally been introduced to quantum field theories in the attempt to understand the microscopic origin of black hole entropy [12, 13, 14, 10, 15, 16, 17, 18].”
• Geometric entropy and edge modes of the electromagnetic field (2015, background): “Understanding these contact terms has been identified as one of the major open problems in the entanglement entropy of black holes [4].”
• Quantum corrections to holographic entanglement entropy (2013, methodology): “2 Quantum argument This is a generalization of the black hole discussion in [14, 15] to situations without the U(1) symmetry.”
• Logarithmic corrections to Schwarzschild and other non-extremal black hole entropy in different dimensions (2012, methodology): “The main difference between our approach and those reviewed in [27] is threefold: (i) we take into account possible contribution to the conformal anomaly due to the presence of background fields other than the gravitational field, (ii) we give special treatment to integration over the zero modes and”
• Logarithmic corrections to $${\mathcal{N} = 2}$$ black hole entropy: an infrared window into the microstates (2011, methodology): “This is due to the fact that the constant term comes from fluctuations of the metric and the gauge field under which the black hole is charged, and for these fields the analysis of [41, 53, 54] would be insufficient on two counts: first it does not take into account correctly the mixing between thes”
• TASI Lectures on the Emergence of Bulk Physics in AdS/CFT (2017, background): “This is a coding analogue of the standard observation that entropy can be passed between the bulk and the area terms by changing the UV cutoff [83].”
• The Ryu–Takayanagi Formula from Quantum Error Correction (2016, background): “This is the ultimate realization of the standard observation that the separation of the righthand-side of the RT formula into two terms is cutoff-dependent [49], or in our language”
• On the architecture of spacetime geometry (2012, background): “While there was a great deal of work done to confirm this idea in explicit examples [13, 14], unfortunately, there were cases where it appeared that the desired matching was not achieved.”
• Local subsystems in gauge theory and gravity (2016, background): “It has long been recognized that the entanglement naturally present in the vacuum could account for the Bekenstein-Hawking entropy of black holes [1–3] (see [4] for a review).”
• Entanglement entropy: Holography and renormalization group (2018, methodology): “The UV divergent structures of entanglement entropy is discussed for lattice models in (Eisert et al., 2010) and for QFT on a curved space by employing the heat kernel method in (Solodukhin, 2011).”
• Logarithmic corrections to rotating extremal black hole entropy in four and five dimensions (2011, methodology): “11) This coincides with the results in [47, 58, 59].”
• Relative entropy and holography (2013, background): “Of course, entanglement entropy has long been proposed as the origin of black hole entropy [8–10].”
• Exact results for the entanglement entropy and the energy radiated by a quark (2013, background): “Essentially the same issue is discussed in [22, 23, 24, 21].”