An extremely compact object (ECO) is defined as a quantum object without horizon, whose radius is just a small distance s outside its Schwarzschild radius. We show that any ECO of mass M in d + 1 dimensions with s≪(M/mp)2/(d−2)(d+1)lp must have (at leading order) the same thermodynamic properties—temperature, entropy and radiation rates—as the corresponding semiclassical black hole of mass M. An essential aspect of the argument involves showing that the Tolman–Oppenheimer–Volkoff equation has no consistent solution in the region just outside the ECO surface, unless this region is filled with radiation at the (appropriately blueshifted) Hawking temperature. In string theory it has been found that black hole microstates are fuzzballs—objects with no horizon—which are expected to have a radius that is only a little larger than the horizon radius. Thus the arguments of this paper provide a nice closure to the fuzzball paradigm: the absence of a horizon removes the information paradox, and the thermodynamic properties of the semiclassical hole are nonetheless recovered to an excellent approximation.

中文翻译：

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极其紧凑的物体的通用热力学特性


极紧凑天体 （ECO） 被定义为没有视界的量子天体，其半径仅超出其史瓦西半径一小段距离 s。我们表明，任何质量为 M 的 ≪ 在 d + 1 维度上具有 s（M/mp）2/（d-2）（d+1）lp 的 ECO 必须具有与相应的质量为 M 的半经典黑洞相同的热力学性质——温度、熵和辐射率。该论证的一个重要方面包括证明 Tolman-Oppenheimer-Volkoff 方程在 ECO 表面外的区域没有一致的解，除非该区域在（适当地蓝移的）霍金温度下充满辐射。在弦理论中，已经发现黑洞微状态是模糊球——没有水平线的物体——预计其半径仅比水平线半径大一点。因此，本文的论点为模糊球范式提供了一个很好的结论：视界的缺失消除了信息悖论，尽管如此，半经典空穴的热力学特性还是恢复到了一个极好的近似值。