标题： 极端致密天体的普遍热力学性质 显示英文标题

标题： The universal thermodynamic properties of Extremely Compact Objects

摘要： 一个极端紧凑天体（ECO）被定义为没有视界的量子物体，其半径仅比其施瓦茨希尔德半径外一小段距离$s$。 我们证明，任何质量为$M$的 ECO，在$d+1$维度中具有$s\ll (M/m_p)^{2/(d-2)(d+1)}l_p$，必须（在领先阶）具有与相应半经典黑洞质量为$M$相同的热力学性质——温度、熵和辐射速率。 论证的一个关键方面是表明，在 ECO 表面之外的区域，托尔曼-奥本海默-沃尔科夫方程没有一致的解，除非该区域充满以（适当蓝移后的）霍金温度的辐射。 在弦理论中已经发现，黑洞微观状态是模糊球——没有视界的物体——它们预期的半径仅比视界半径稍大。 因此，本文的论证为模糊球范式提供了一个很好的闭合：视界的存在缺失消除了信息悖论，并且半经典黑洞的热力学性质仍可以极好地近似恢复。 显示英文摘要

摘要： 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 $s\ll (M/m_p)^{2/(d-2)(d+1)}l_p$ 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.