In this article, we calculate the classical vortex solution of a spontaneously broken gauge theory interacting with gravity in (2+1)-dimension. We also calculate the conditions for the formation of a (2+1)-dimensional black hole due to magnetic vortex (a Nielsen-Olesen vortex). The semiclassical Hawking temperature for this black hole is calculated, where we see that the temperature of a BTZ black hole increases or decreases without changing the size of the horizon if we insert the magnetic vortex fields in the black hole. Finally, the first law of black hole thermodynamics is described for this particular solution, which shows that the additional work terms from the scalar and gauge fields compensate the change in the temperature relative to its usual value for the BTZ solution.

在本文中，我们计算了在 (2+1) 维中与重力相互作用的自发破缺规范理论的经典涡旋解。我们还计算了由于磁涡流（Nielsen-Olesen 涡流）而形成（2+1）维黑洞的条件。计算了这个黑洞的半经典霍金温度，我们看到如果我们在黑洞中插入磁涡旋场，BTZ 黑洞的温度会增加或减少而不会改变视界的大小。最后，针对此特定解描述了黑洞热力学第一定律，这表明来自标量场和规范场的附加功项补偿了温度相对于 BTZ 解的通常值的变化。