arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 1405.4192hep-thgr-qc
收藏

作为自持量子态的黑洞和霍金辐射

Black holes as self-sustained quantum states, and Hawking radiation

Roberto Casadio, Andrea Giugno, Octavian Micu, Alessio Orlandi

摘要:

我们采用最近提出的“视界波函数”的形式来研究引力子的玻色-爱因斯坦凝聚体的黑洞模型中视界的出现。我们从一个无质量标量场(玩具引力子)耦合到静态物质流的克莱因-戈登方程开始。(球对称)经典场再现了物质源产生的牛顿势,相应的量子态由具有连续占据数的标量模的相干叠加给出。假设一个吸引的自相互作用,允许束缚态,人们发现,(大约)只有一个模式是允许的,系统可以被限制在一个区域的大小的史瓦西半径。这个半径然后被证明是对应于一个适当的视界,通过视界波函数的量子系统,与不确定性的大小自然有关的预期典型能量的霍金模式。特别是,这种不确定性降低较大的黑洞质量(与大量的轻标量量子),在协议与半经典的预期,一个结果,不适用于一个单一的非常大质量的粒子。最后,我们推测,一个相变应该发生在恒星的引力坍缩,理想的静态物质流和牛顿势,导致一个黑洞,再次理想的玩具引力子的凝聚表示,并建议一个有效的序参量,可用于调查这种转变。

英文摘要:

We employ the recently proposed formalism of the "horizon wave-function" to investigate the emergence of a horizon in models of black holes as Bose-Einstein condensates of gravitons. We start from the Klein-Gordon equation for a massless scalar (toy graviton) field coupled to a static matter current. The (spherically symmetric) classical field reproduces the Newtonian potential generated by the matter source, and the corresponding quantum state is given by a coherent superposition of scalar modes with continuous occupation number. Assuming an attractive self-interaction that allows for bound states, one finds that (approximately) only one mode is allowed, and the system can be confined in a region of the size of the Schwarzschild radius. This radius is then shown to correspond to a proper horizon, by means of the horizon wave-function of the quantum system, with an uncertainty in size naturally related to the expected typical energy of Hawking modes. In particular, this uncertainty decreases for larger black hole mass (with larger number of light scalar quanta), in agreement with semiclassical expectations, a result which does not hold for a single very massive particle. We finally speculate that a phase transition should occur during the gravitational collapse of a star, ideally represented by a static matter current and Newtonian potential, that leads to a black hole, again ideally represented by the condensate of toy gravitons, and suggest an effective order parameter that could be used to investigate this transition.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

↑