Black hole's quantum N‐portrait
Black hole's quantum N‐portrait
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DOI：
10.1002/prop.201300001
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发表时间：
2011-12
期刊：
影响因子：
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通讯作者：
G. Dvali;César Gómez
中科院分区：
文献类型：
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作者：
G. Dvali;César Gómez
我们以重子在引力场中的占据数N的形式建立了经典性的量子度量。这使我们能够将经典背景几何看作具有大量软引力子的量子玻色凝聚体。我们表明，在给定物理长度的所有可能源中，黑洞的N最大，并且与它的熵一致。新出现的黑洞量子力学图像出奇地简单，并且完全由N参数化。黑洞是一个泄漏束缚态，其形式是N个弱相互作用软引力子的冷玻色凝聚体，其波长为√N倍普朗克长度，量子相互作用强度为1/N。这种束缚态对于任意n都存在。这幅图提供了霍金辐射、贝肯斯坦熵以及爱因斯坦引力的非威尔逊紫外自完成现象的简单量子描述。我们证明了霍金辐射只不过是引力子玻色凝聚体的量子耗尽，尽管凝聚体的温度为零，但它产生的热谱温度为T = 1/(√N)。贝肯斯坦熵来源于N个量子态的指数增长。最后，我们的量子图像允许理解深紫外引力散射的经典化为2→N跃迁。我们指出了黑洞和孤子之间的一些基本的相似之处，例如t'Hooft - Polyakov单极子。这两个物体都代表了波长为√N、相互作用强度为1/N的N个软玻色子的玻色凝聚体。简而言之，半经典黑洞物理是1/N耦合的大N量子物理。
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.