Thermodynamic geometry of charged AdS black holes with a string cloud in Lorentz-violating Einstein-Kalb-Ramond gravity

TL;DR

This paper explores the thermodynamic microstructure of charged AdS black holes within a Lorentz-violating gravity framework, revealing how parameters influence phase transitions and microscopic interactions.

Contribution

It introduces a novel analysis of black hole thermodynamics incorporating Lorentz violation and string clouds, highlighting their effects on phase behavior and critical phenomena.

Findings

Curvature singularities align with phase boundaries and critical points.

Sign of Ruppeiner curvature indicates microscopic interaction types.

Lorentz-violating and string cloud parameters shift critical scales but preserve universality.

Abstract

We investigate the thermodynamic microstructure of electrically charged AdS black holes in Einstein-Kalb-Ramond bumblebee gravity in the presence of a spherically symmetric cloud of strings. Employing Weinhold and Ruppeiner thermodynamic geometries in complementary thermodynamic representations, we show that curvature singularities consistently track the spinodal boundaries and the second-order critical point associated with a Van der Waals-like small/large black-hole phase transition. Moreover, the sign structure of the Ruppeiner curvature provides a transparent characterization of the competing microscopic interactions across the coexisting phases. We find that the Lorentz-violating parameter $\ell$ and the string-cloud parameter $\alpha$ shift the critical scales and rescale correlation measures while preserving the universality class of the critical behavior. We further comment on dynamical and holographic implications and contrast the thermodynamic sensitivity to $(\ell,\alpha)$ with thin-disk optical signatures.