### Abstract

We establish a quantum measure of classicality in the form of the occupation number, N, of gravitons in a gravitational field. This allows us to view classical background geometries as quantum Bose-condensates with large occupation numbers of soft gravitons. We show that among all possible sources of a given physical length, N is maximized by the black hole and coincides with its entropy. The emerging quantum mechanical picture of a black hole is surprisingly simple and fully parameterized by N. The black hole is a leaky bound-state in form of a cold Bose-condensate of N weakly-interacting soft gravitons of wave-length √N times the Planck length and of quantum interaction strength 1/N. Such a bound-state exists for an arbitrary N. This picture provides a simple quantum description of the phenomena of Hawking radiation, Bekenstein entropy as well as of non-Wilsonian UV-self-completion of Einstein gravity. We show that Hawking radiation is nothing but a quantum depletion of the graviton Bose-condensate, which despite the zero temperature of the condensate produces a thermal spectrum of temperature T = 1/(√N). The Bekenstein entropy originates from the exponentially growing with N number of quantum states. Finally, our quantum picture allows to understand classicalization of deep-UV gravitational scattering as 2 → N transition. We point out some fundamental similarities between the black holes and solitons, such as a t'Hooft-Polyakov monopole. Both objects represent Bose-condensates of N soft bosons of wavelength √N and interaction strength 1/N. In short, the semi-classical black hole physics is 1/N-coupled large-N quantum physics.

Original language | English (US) |
---|---|

Pages (from-to) | 742-767 |

Number of pages | 26 |

Journal | Fortschritte der Physik |

Volume | 61 |

Issue number | 7-8 |

DOIs | |

State | Published - 2013 |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*Fortschritte der Physik*,

*61*(7-8), 742-767. https://doi.org/10.1002/prop.201300001

**Black hole's quantum N-portrait.** / Dvali, G.; Gomez, C.

Research output: Contribution to journal › Article

*Fortschritte der Physik*, vol. 61, no. 7-8, pp. 742-767. https://doi.org/10.1002/prop.201300001

}

TY - JOUR

T1 - Black hole's quantum N-portrait

AU - Dvali, G.

AU - Gomez, C.

PY - 2013

Y1 - 2013

N2 - We establish a quantum measure of classicality in the form of the occupation number, N, of gravitons in a gravitational field. This allows us to view classical background geometries as quantum Bose-condensates with large occupation numbers of soft gravitons. We show that among all possible sources of a given physical length, N is maximized by the black hole and coincides with its entropy. The emerging quantum mechanical picture of a black hole is surprisingly simple and fully parameterized by N. The black hole is a leaky bound-state in form of a cold Bose-condensate of N weakly-interacting soft gravitons of wave-length √N times the Planck length and of quantum interaction strength 1/N. Such a bound-state exists for an arbitrary N. This picture provides a simple quantum description of the phenomena of Hawking radiation, Bekenstein entropy as well as of non-Wilsonian UV-self-completion of Einstein gravity. We show that Hawking radiation is nothing but a quantum depletion of the graviton Bose-condensate, which despite the zero temperature of the condensate produces a thermal spectrum of temperature T = 1/(√N). The Bekenstein entropy originates from the exponentially growing with N number of quantum states. Finally, our quantum picture allows to understand classicalization of deep-UV gravitational scattering as 2 → N transition. We point out some fundamental similarities between the black holes and solitons, such as a t'Hooft-Polyakov monopole. Both objects represent Bose-condensates of N soft bosons of wavelength √N and interaction strength 1/N. In short, the semi-classical black hole physics is 1/N-coupled large-N quantum physics.

AB - We establish a quantum measure of classicality in the form of the occupation number, N, of gravitons in a gravitational field. This allows us to view classical background geometries as quantum Bose-condensates with large occupation numbers of soft gravitons. We show that among all possible sources of a given physical length, N is maximized by the black hole and coincides with its entropy. The emerging quantum mechanical picture of a black hole is surprisingly simple and fully parameterized by N. The black hole is a leaky bound-state in form of a cold Bose-condensate of N weakly-interacting soft gravitons of wave-length √N times the Planck length and of quantum interaction strength 1/N. Such a bound-state exists for an arbitrary N. This picture provides a simple quantum description of the phenomena of Hawking radiation, Bekenstein entropy as well as of non-Wilsonian UV-self-completion of Einstein gravity. We show that Hawking radiation is nothing but a quantum depletion of the graviton Bose-condensate, which despite the zero temperature of the condensate produces a thermal spectrum of temperature T = 1/(√N). The Bekenstein entropy originates from the exponentially growing with N number of quantum states. Finally, our quantum picture allows to understand classicalization of deep-UV gravitational scattering as 2 → N transition. We point out some fundamental similarities between the black holes and solitons, such as a t'Hooft-Polyakov monopole. Both objects represent Bose-condensates of N soft bosons of wavelength √N and interaction strength 1/N. In short, the semi-classical black hole physics is 1/N-coupled large-N quantum physics.

UR - http://www.scopus.com/inward/record.url?scp=84879820682&partnerID=8YFLogxK

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U2 - 10.1002/prop.201300001

DO - 10.1002/prop.201300001

M3 - Article

VL - 61

SP - 742

EP - 767

JO - Fortschritte der Physik

JF - Fortschritte der Physik

SN - 0015-8208

IS - 7-8

ER -