Tunnelling methods and Hawking's radiation: achievements and prospects

Abstract

The aim of this work is to review the tunnelling method as an alternative description of the quantum radiation from black holes and cosmological horizons. The method is first formulated and discussed for the case of stationary black holes, then a foundation is provided in terms of analytic continuation throughout complex space-time. The two principal implementations of the tunnelling approach, which are the null geodesic method and the Hamilton-Jacobi method, are shown to be equivalent in the stationary case. The Hamilton-Jacobi method is then extended to cover spherically symmetric dynamical black holes, cosmological horizons and naked singularities. Prospects and achievements are discussed in the conclusions. *

Conformally rescaled spacetimes and Hawking radiation

“…There is only a pole in the solution of the Hamilton-Jacobi equation at △ = 0 which is not at χ = 0. For the time dependent conformal transformation of Schwarzschild (6), that contains true future outer trapping horizons not located at △ = 0, once again the Hamilton-Jacobi equation gives a pole for ∂ r I at △ = 0, provided ∂ t I = 0 at those points. This can be seen directly from the Hamilton-Jacobi equation (44) that is manifestly conformally invariant, as it should be.…”

“…This method is very relevant to our current investigation because it forms the basis of the claims in [7] that the tunneling is associated with zero expansion quasi-local horizons of the trapping horizon form. Further details of the method can be found in [6] and references therein.…”

“…Anomaly cancellation has been used by several authors to show the necessity of a Hawking-like flux at the quantum level; in 1+1 dimensions with the trace anomaly of the energy-momentum tensor [3] and in four dimensional spherical symmetry for the gravitational anomaly in the divergence of the energy-momentum tensor [4]. Another popular version is the tunneling calculation [5,6] that obtains the Hawking flux from a path integral across the horizon. The Hawking radiation is usually associated with the existence of an event horizon, but crucial in the tunneling calculation is a pole in the path integral that does not always occur at the location of the causal event horizon.…”

Hawking Radiation of Scalar and Vector Particles from 5D Myers-Perry Black Holes

“…However, this result is debatable and needs more confirmation by other experiments. Furthermore, previously, the Hawking radiation of scalar bosons, spin-1 vector particles, spin-2 particles, spin-3/2 particles of different types of black holes and wormholes are studied [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27].…”

Quantum Corrected Non-Thermal Radiation Spectrum from the Tunnelling Mechanism

“…Considering Hawking radiation [1] in the tunnelling approach, [2][3][4][5][6][7][8][9][10][11] particle creation mechanism caused by the vacuum fluctuations near the BH horizon works as follows. A virtual particle pair is created just inside the horizon and the virtual particle with positive energy can tunnel out the BH horizon as a real particle.…”