Black hole echos reflect the phase transition and fluctuations in Hawking radiation

Abstract

Black holes are thermal objects. They can form thermodynamic phases and exhibit phase transitions. Furthermore, black holes can also radiate, termed as Hawking radiation. However, the signatures of these behaviors are challenging to observe. In this work,we consider Hawking radiation in black hole phase transitions. We uncovered that an echo can emerge from the correlations between individual single event and joint two events. This provides possible signature of black hole phase transition and fluctuations in Hawking radiation.

Figures (5)

• Figure 1: Schematic of the reaction model and corresponding free energy landscape. (a) Full-reaction network. (b,c) Half-reactions A and B. (d,e) Landscapes with two basins. Stochastic trajectories within a basin represent local transitions, governed by the half-reaction dynamics and quantified by the Green's function.
• Figure 2: Mean first-passage time (MFPT), calculated from the distribution $f_{ba}(t,t)$, as a function of temperature. Curves correspond to dissipation coefficients $\eta = 100$ (red), $10^4$ (blue), and $10^5$ (purple), at fixed $Q=0.1$, $P=0.003/(8\pi)$, and $b_a=b_b=50$.
• Figure 3: (a) Same-time difference function $\delta(t)$ versus $\log(t)$ for temperatures $T = 0.0312$ (blue), $0.0313$ (red), and $0.0314$ (green), with fixed $Q=0.1$, $P=0.003/(8\pi)$, $\eta=100$, and $b_a=b_b=50$. The echo time is defined as the location of the maximum following an initial rapid decrease. (b) Relative Hawking radiation rate $|\alpha_b|$ for the large black hole (state B) as a function of temperature.
• Figure 4: Variation of the echo peak height with parameters. (a,b) The peak increases with $Q \sim 0.1\text{--}0.15$ and $P \sim \frac{3}{8 \pi}0.01\text{--}\frac{3}{8 \pi}0.0101$, while showing a rise-and-fall behavior with $T$, for fixed $\eta=100$ and $b_a=b_b=50$.
• Figure 5: The difference function $\delta(t_1, t_2/k)$ at fixed parameters: $T = 0.0312$, $Q = 0.1$, $P = 3/(8\pi) \times 0.01$,$\eta=100$ and $b_a=b_b=50$.