Universal scalarization in topological AdS black holes

Abstract

We investigate the universal behavior of black hole scalarization induced by a charged scalar field in the extended phase space of the asymptotic AdS spacetime with three distinct horizon topologies. The results indicate that in all the three cases, the charged black hole spacetime undergoes scalarization at low temperatures. Notably, the spherical topology is unique in that its domain of scalarization theoretically extends to much higher temperatures under low pressure in the extended phase space. Moreover, the scalarization process in the spherical case exhibits complex phase transition behaviors without additional non-linear terms, which are similar to those in the planar and hyperbolic topologies with the assistance of non-linear terms. With increasing pressure in the extended phase space, the condensate of the scalarization in all three cases undergoes a transition from the first-order style to a cave-of-wind style. This study provides deeper insight into the zeroth-order phase transition during black hole scalarization and reveals the complete phase structure of black holes in the extended phase space.

Figures (3)

• Figure 1: The free energy and landscape. Left: The relationship between free energy and temperature for plane topology under different pressure, where the red solid line indicates a first-order phase transition, blue solid lines represent COW phase transitions, magenta solid lines denote second-order phase transitions, and black dashed lines is the normal solution. Right: Landscape analysis corresponding to different pressure on the right-hand side. Different colors represent different pressures. Circles denote stable states, squares represent metastable states, and inverted triangles indicate unstable states. The value of $G_L$ corresponds to that of the conjectured landscape analysis, where only the extremal points satisfy the equations of motion.
• Figure 2: The phase diagrams of planar and hyperbolic topologies. Panel (a): The phase diagram of $b-T$ for planar topology with fixed $L=1$ and $\lambda=-0.35$. Panel (b): The phase diagram of $P-T$ for planar topologies with fixed $b=0.4$ and $\lambda=-0.35$. Panel (c): The phase diagram of $P-T$ for hyperbolic topologies with fixed $b=0.4$ and $\lambda=-0.2$. The red solid and red dashed lines represent the COW and the first-order phase transitions. The blue dashed line delineates the spinodal regions for these phase transitions. The gray area signifies the normal solution, while the yellow and cyan regions correspond to two distinct hairy scalar solutions. The red region denotes the supercritical regime.
• Figure 3: The free energy and phase diagram for sphere topology with $\lambda=0$ and $b=0.4$. Panel (a): The black dashed and solid lines are for the normal and scalaried solutions. Panels (b) and (c): The phase diagram of sphere topology. The red region is the supercritical scalaried black hole region, the yellow and cyan region are the two different scalaried solution regions. Panel (c): The enlarged diagram of panel (b).