Thermodynamic topological classes of the rotating, accelerating black holes

In this paper, we investigate the topological numbers for the rotating, accelerating neutral black hole and its AdS extension, as well as the rotating, accelerating charged black hole and its AdS extension. We find that the topological number of an asymptotically flat accelerating black hole consistently differs by one from that of its non-accelerating counterpart. Furthermore, we show that for an asymptotically AdS accelerating black hole, the topological number is reduced by one compared to its non-accelerating AdS counterpart. In addition, we demonstrate that within the framework of general relativity, the acceleration parameter and the negative cosmological constant each independently add one to the topological number. However, when both factors are present, their effects neutralize each other, resulting in no overall change to the topological number.