Black hole induced false vacuum decay from first principles

We provide a method to calculate the rate of false vacuum decay induced by a black hole. The method uses complex tunneling solutions and consistently takes into account the structure of different quantum vacua in the black hole metric via boundary conditions. The latter are connected to the asymptotic behavior of the time-ordered Green’s function in the corresponding vacua. We illustrate the technique on a two-dimensional toy model of a scalar field with inverted Liouville potential in an external background of a dilaton black hole. We analytically derive the exponential suppression of tunneling from the Boulware, Hartle-Hawking and Unruh vacua and show that they are parametrically different. The Unruh vacuum decay rate is exponentially smaller than the decay rate of the Hartle-Hawking state, though both rates become unsuppressed at high enough black hole temperature. We interpret the vanishing suppression of the Unruh vacuum decay at high temperature as an artifact of the two-dimensional model and discuss why this result can be modified in the realistic case of black holes in four dimensions.

Analytical Solution and Quasi-Periodic Behavior of a Charged Dilaton Black Hole

With the vast breakthrough brought by the Event Horizon Telescope, the theoretical analysis of various black holes has become more critical than ever. In this paper, the second-order asymptotic analytical solution of the charged dilaton black hole flow in the spinodal region is constructed from the perspective of dynamics by using the two-timing scale method. Through a numerical comparison with the original charged dilaton black hole system, it is found that the constructed analytical solution is highly consistent with the numerical solution. In addition, several quasi-periodic motions of the charged dilaton black hole flow are numerically obtained under different groups of irrational frequency ratios, and the phase portraits of the black hole flow with sufficiently small thermal parameter perturbation display good stability. Finally, the final evolution state of black hole flow over time is studied according to the obtained analytical solution. The results show that the smaller the integral constant of the system, the greater the periodicity of the black hole flow.

Quantum gravity effect on the Hawking radiation of spinning dilaton black hole

The quantum gravity correction to the Hawking temperature of the 2+1 dimensional spinning dilaton black hole is studied by using the Hamilton-Jacobi approach in the context of the Generalized Uncertainty Principle (GUP). It is observed that the modified Hawking temperature of the black hole depends on both black hole and the tunnelling particle properties. Moreover, it is observed that the mass and the angular momentum of the scalar particle have the same effect on the Hawking temperature of the black hole, while the mass and total angular momentum (orbital+spin) of Dirac particle have different effect. Furthermore, the mass and total angular momentum (orbital+spin) of vector boson particle have a similar effect that of Dirac particle. Also, thermodynamical stability and phase transition of the black hole are discussed for scalar, Dirac and vector boson in the context of GUP, respectively. And, it is observed that the scalar particle probes the black hole as stable whereas, as for Dirac and vector boson particles, it might undergoes second-type phase transition to become stable while in the absence of the quantum gravity effect all of these particle probes the black hole as stable.