Electron star birth: A continuous phase transition at nonzero density

TL;DR

It is shown that charged black holes in anti-de Sitter spacetime can undergo a third-order phase transition at a critical temperature in the presence of charged fermions, and the solutions exhibit the low temperature entropy density scaling s~T(2/z).

Abstract

We show that charged black holes in Anti-de Sitter spacetime can undergo a third order phase transition at a critical temperature in the presence of charged fermions. In the low temperature phase, a fraction of the charge is carried by a fermion fluid located a finite distance from the black hole. In the zero temperature limit the black hole is no longer present and all charge is sourced by the fermions. The solutions exhibit the low temperature entropy density scaling s~T^{2/z} anticipated from the emergent IR criticality of recently discussed electron stars.

Figures (5)

• Figure 1: Critical temperature (left plot) and radius (right plot) at which the electron star is born, as a function of the fermion mass. These quantities do not depend on $\hat{\beta}$.
• Figure 2: Radial density profiles of electron stars as a function of temperature. The curves show five temperatures between $0.07 \, T_C$ and $T_C$, with $\hat{\mu}$ held fixed. Both plots have $\hat{\beta} = 10$. The left plots has mass $\hat{m} = 0.7$ while the right plot has $\hat{m} = 0.1$.
• Figure 3: The fraction of charge carried by the fermion fluid as a function of temperature. All curves have $\hat{\beta} = 10$ while from blue to red (solid to dotted) $\hat{m} = \{0.01, 0.07, 0.3, 0.55 ,0.75\}$. In quoting $T/T_c$, the chemical potential is kept fixed.
• Figure 4: Free energy of the Reissner-Nordstrom black hole (top, red) and the free energy of two electron stars (blue) as a function of temperature. The electrons stars have $\hat{\beta} = 10$ and $\hat{m} = 0.2$ (lower) and $\hat{m} =0.3$ (upper). The maximal temperature plotted is the critical temperature of the lower electron star.
• Figure 5: Temperature dependence of the entropy density. Red line (top) is Reissner-Nordstrom. The three blue lines (lower) are electron stars with $\hat{\beta} = 20$ and, from left to right, $\hat{m} = 0.7, 0.36, 0.1$. Fitting to a power law at low temperatures leads to $z \approx 5.4, 2 ,1.5$ respectively.