标题： 静态多电荷AdS黑洞在规范超引力中的热力学拓扑类 显示英文标题

标题： Topological classes of thermodynamics of the static multi-charge AdS black holes in gauged supergravities

摘要： 我们在拓扑方法框架下，使用广义的非平衡Helmholtz自由能，研究了四维和五维规范超引力理论中的静态多电荷AdS黑洞的拓扑数。 我们发现，在规范超引力理论中，静态带电AdS黑洞的拓扑数显著受到电荷参数数量的影响。 我们还表明，从热力学拓扑的角度来看，四维规范超引力中的单电荷AdS黑洞和四维Reissner-Nordström-AdS（RN-AdS）黑洞属于不同的类别，尽管它们都是四维静态单电荷AdS黑洞。 此外，对于四维静态双电荷AdS黑洞和规范超引力理论中的五维静态单电荷AdS黑洞，我们发现了一个新的特性，即不同的电荷参数值可以影响它们的拓扑数。 此外，我们证明在规范超引力理论中，当四维双电荷静态AdS黑洞的两个电荷参数都取较小值，以及五维单电荷静态AdS黑洞的电荷参数取较小值时，在不同的固定温度下，它们具有两个不同的拓扑数，这构成了对“黑洞只能有一个确定的拓扑数”这一猜想的前两个反例。 显示英文摘要

摘要： We investigate, in the framework of the topological approach to black hole thermodynamics, using the generalized off-shell Helmholtz free energy, the topological numbers of the static multi-charge AdS black holes in the four- and five-dimensional gauged supergravities. We find that the topological number of static charged AdS black holes in gauged supergravity theories are significantly affected by the number of the electric charge parameters. We also show that, from the perspective of the thermodynamic topology, the single-charge AdS black hole in four-dimensional gauged supergravity and the four-dimensional Reissner-Nordstr\"om-AdS (RN-AdS) black hole belong to different classes, even though they are both four-dimensional static single-charge AdS black holes. Moreover, for the four-dimensional static two-charge AdS black hole and the five-dimensional static single-charge AdS black hole in gauged supergravity theory, we find a new property unique to them, namely that different values of the electric charge parameters can influence their topological number. In addition, we demonstrate that, in gauged supergravity theory, for the four-dimensional two-charge static AdS black hole when both two electric charge parameters take smaller values and the five-dimensional single-charge static AdS black hole when the electric charge parameter takes a smaller value, have two different topological numbers at different fixed temperatures, which constitute the first two counterexamples to the conjecture that a black hole can only have one definite topological number.