False vacuum decay catalyzed by black hole in a heat bath

Abstract

We study false vacuum decay catalyzed by black holes. We consider a scalar field model with unstable potential in the background of a dilaton black hole in two dimensions. The model reproduces many features of the Schwarzschild black hole background in four dimensions, including the centrifugal barrier for linearized field perturbations. We study decays from the non-equilibrium state describing the evaporating black hole immersed in the thermal bath with a different temperature. We analytically construct the tunneling solution relevant at small field excitations and evaluate the decay suppression. We show how they reduce to those for the Hartle-Hawking (equilibrium) and Unruh states in the corresponding limits. For large field excitations the decay proceeds via stochastic activation; we find the relevant non-thermal sphaleron configuration in a certain region of parameters of the model and construct the semiclassical solution describing tunneling onto this sphaleron. Our results provide insights into the vacuum decay induced by small primordial black holes in the radiation-dominated era of the universe.

Figures (13)

• Figure 1: The scalar field potential.
• Figure 2: Effective potential for linear field modes in the background of the dilaton BH and with the dilaton barrier $q\gtrsim m^2/(2\lambda^2)$.
• Figure 3: Contour $\mathscr{C}$ in the complex time plane for the calculation of the vacuum decay probability. We show the case when the branch-cuts of the bounce (shown with thick black lines) lie on the real axis. This corresponds to a theory with the scalar potential unbounded from below.
• Figure 4: Bounce solution (\ref{['Core_far']}) describing tunneling from the non-equilibrium vacuum (\ref{['state']}) far away from the BH. Solid black line is the bounce profile $\varphi_{\mathrm{b}}$, the red dashed line is its time-derivative $\dot{\varphi_{\mathrm{b}}}/m$, both are shown at the nucleation time $t=0$. The gray dashed line marks the field value $\varphi_{\rm max}$ at the maximum of the potential barrier, see \ref{['Phimax']}. We take $\ln(m/\sqrt{\kappa})=25$, the BH temperature $\lambda/m=10$, the dilaton barrier $q\lambda/m=1$ and the temperature of the environment $\lambda'/m=5$(left), $\lambda'/m=10$(middle), $\lambda'/m=15$(right).
• Figure 5: Critical line $b_{\rm far}(\lambda,\lambda')=1$. The dashed straight line is $\lambda=\lambda'$.