Thermodynamic Phase Transitions in Einstein-Maxwell-Scalar-Gauss-Bonnet Gravity

TL;DR

This paper explores thermodynamic phase transitions in scalarized charged black holes within Einstein-Maxwell-Scalar-Gauss-Bonnet gravity, revealing complex behaviors including multiple phase transitions and stability regimes.

Contribution

It demonstrates that curvature-induced scalarization leads to rich thermodynamic phenomena without external confinement or extended formalism.

Findings

Identifies coexistence of stable scalarized and Reissner-Nordström states.

Discovers second-order and zeroth-order phase transitions depending on coupling strength.

Shows the scalarized branch shrinks and the Reissner-Nordström phase becomes dominant at strong coupling.

Abstract

Although asymptotically flat black holes generically lack thermodynamic phase transitions, we show that curvature-induced scalarization of electrically charged black holes in Einstein-Maxwell- Scalar-Gauss-Bonnet theory provides a natural setting for nontrivial thermodynamic behavior, without invoking external confining mechanisms or an extended thermodynamic formalism. Working within the canonical ensemble and employing the Euclidean approach, we identify the coexistence of locally stable scalarized and small Reissner-Nordstr\"om thermal states, which promotes free-energy crossings to bona fide phase transitions between equilibrium phases. For weak coupling, a second-order phase transition coincides with the second bifurcation point, at which the scalarized branch reconnects with the Reissner-Nordstr\"om branch and scalar hair is spontaneously shed. As the coupling strength increases, this transition becomes zeroth order, the scalarized branch shrinks, and a fish-like structure develops in its Helmholtz free energy, rendering locally stable thermal states partially metastable, and yielding up to three phase transitions. In the strong-coupling limit, the scalarized branch reduces to a Schwarzschild-like solution, and the Reissner-Nordstr\"om phase ultimately emerges as the sole thermodynamically preferred configuration