标题： 中性黑洞和带电黑洞附近的量子场自发破缺对称性恢复 显示英文标题

标题： Spontaneously broken symmetry restoration of quantum fields in the vicinity of neutral and electrically charged black holes

摘要： 我们研究了围绕中性（即史瓦西）和带电（即雷斯勒-诺斯特伦）黑洞的相互作用量子标量场自发破缺对称性的恢复问题。 这是通过一种半经典的自洽程序实现的，通过求解描述背景场和真空极化动力学的非线性耦合方程组完成。 黑洞在其自身的视界处产生一个无限高的温度，该温度随距离增加而下降至霍金温度。 由于视界附近的高温，在黑洞周围会形成一个气泡，其中标量场只能取值为零，这是能量的最小值。 因此，在此区域内能量和场的对称性得以保持。 在气泡半径处，由于自发对称破缺机制，标量场的值发生了相变。 实际上，在气泡半径之外，温度足够低，标量场会在新的能量极小值处稳定下来，显示出该外区域的对称性被破坏。 相反地，在接近视界的内气泡附近，存在从外区域到内气泡的对称性恢复。 不同黑洞电荷所导致的不同特性同样值得注意。 研究发现，温度较低（即更带电）的黑洞具有较小的对称性恢复气泡长度。 在极端情况下，气泡长度为零，即不存在气泡。 此外，对于温度较低的黑洞，激发量子场模式变得更加困难，因此真空极化值较小。 在极端情况下，黑洞温度为零，真空极化从未被激发。 显示英文摘要

摘要： We consider the restoration of a spontaneously broken symmetry of an interacting quantum scalar field around neutral, i.e., Schwarzschild, and electrically charged, i.e., Reissner-Nordstr\"om, black holes in four dimensions. This is done through a semiclassical self-consistent procedure, by solving the system of non-linear coupled equations describing the dynamics of the background field and the vacuum polarization. The black hole at its own horizon generates an indefinitely high temperature which decreases to the Hawking temperature at infinity. Due to the high temperature in its vicinity, there forms a bubble around the black hole in which the scalar field can only assume a value equal to zero, a minimum of energy. Thus, in this region the symmetry of the energy and the field is preserved. At the bubble radius, there is a phase transition in the value of the scalar field due to a spontaneous symmetry breaking mechanism. Indeed, outside the bubble radius the temperature is low enough such that the scalar field settles with a nonzero value in a new energy minimum, indicating a breaking of the symmetry in this outer region. Conversely, there is symmetry restoration from the outer region to the inner bubble close to the horizon. Specific properties that emerge from different black hole electric charges are also noteworthy. It is found that colder black holes, i.e., more charged ones, have a smaller bubble length of restored symmetry. In the extremal case the bubble has zero length, i.e., there is no bubble. Additionally, for colder black holes, it becomes harder to excite the quantum field modes, so the vacuum polarization has smaller values. In the extremal case, the black hole temperature is zero and the vacuum polarization is never excited.