Topological changes and response singularities in black hole thermodynamic branch structure
Year: 2026
Type: preprint
Abstract: In this paper, we investigate how different diagnostics characterize the thermodynamic branch structure of black holes. In three charged AdS black hole examples, the thermodynamic topological transition point $τ_a$, where the total topological number changes, is separated from the point $τ_b$ where the branch response considered here, evaluated along a path with fixed charge parameters, becomes singular. Using the zero-point curves $τ(r_h)$, we identify the local mechanisms behind this separation. At $τ_a$, a zero point with nonzero winding enters or leaves the positive-radius physical branch set through the boundary of the counted domain, changing $W$ without making the corresponding positive-radius branch singular. At $τ_b$, the zero-point curve develops a finite-radius turning point, where two branches with opposite winding numbers annihilate and the branch response diverges. Thus, in the analyzed examples, a change in the topological number records a change in branch membership, whereas a response singularity records a loss of local invertibility along an admitted branch. The two diagnostics therefore probe different local events of the same zero-point branch geometry.
Source: arXiv (Cornell University)
Author: Wu, Di
Institutions: University of Waterloo, China West Normal University
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
Awards: G4550890110, G7512978759
OpenAlex ID: W7167839583