Topological signatures in Kerr-Sen AdS black hole thermodynamics

TL;DR

This paper employs topological methods to analyze the phase structure of Kerr-Sen AdS black holes, revealing invariant topological charges and multiple thermodynamic phases, with novel complex residue techniques providing deeper insights into black hole thermodynamics.

Contribution

It introduces a topological framework using Duan's theory and a complex residue method to classify black hole phases and analyze their topological invariants in Kerr-Sen AdS spacetime.

Findings

Identifies three thermodynamic phases with distinct winding numbers.

Shows the topological charge remains invariant under dilaton charge variations.

Develops a complex continuation method linking residues to topological invariants.

Abstract

Black hole thermodynamics and topology have emerged as a strong foundation for a coordinate-independent understanding of phase transitions. Using both Duan's topological current theory and a novel complex residue method, we perform a topological study of the Kerr-Sen AdS black hole arising in heterotic string theory. In turn, we find the zero points corresponding to on-shell black hole states and calculate their winding numbers to find the global topological charge by building the generalized off-shell free energy and examining the corresponding vector field in a parametric space. Our analysis reveals that the Kerr-Sen AdS black hole exhibits three distinct thermodynamic phases -- small, intermediate, and large black hole branches -- characterized by critical points with winding numbers $+1$, $-1$, and $+1$ respectively, culminating in a total topological charge $W = +1$. Significantly, this topological number remains invariant under variations of the dilaton charge parameter, indicating that the dilaton field does not alter the fundamental topological class established for Kerr-AdS and RN-AdS black holes. However, the rotation parameter proves crucial in determining the phase structure and the emergence of multiple critical points. We systematically examine three limiting configurations: the full Kerr-Sen AdS spacetime, the GMGHS AdS limit ($a = 0$), and the asymptotically flat Kerr-Sen case ($\Lambda = 0$). In addition, we propose a novel approach that analytically continues the thermodynamic characterisation into the complex plane. The characterized complex function, derived from the off-shell Gibbs free energy, possesses isolated singular points whose residues directly encode the winding numbers. Our results indicate that topology offers deep insights into black hole phase transitions, with potential implications to holographic dualities.