arXiv:1412.6893v3 [astro-ph.HE] 9 Oct 2015 The Particle Production at the Event Horizon of a Black Hole as Gravitational Fowler-Nordheim Emission in Uniformly Accelerated Frame, in The Non-Relativistic Scenario Sanchari De a • Sutapa Ghosh b • Somenath Chakrabarty a† Abstract In the conventional scenario, the Hawking radiation is believed to be a tunneling process at the event horizon of the black hole. In the quantum field theoretic approach the Schwinger’s mechanism is gen- erally used to give an explanation of this tunneling pro- cess. It is the decay of quantum vacuum into particle anti-particle pairs near the black hole surface. However, in a reference frame undergoing a uniform accelerated motion in an otherwise flat Minkowski space-time ge- ometry, in the non-relativistic approximation, the par- ticle production near the event horizon of a black hole may be treated as a kind of Fowler-Nordheim field emis- sion, which is the typical electron emission process from a metal surface under the action of an external elec- trostatic field. This type of emission from metal sur- face is allowed even at extremely low temperature. It has been noticed that in one-dimensional scenario, the Schr¨ odinger equation satisfied by the created particle (anti-particle) near the event horizon, can be reduced to a differential form which is exactly identical with that obeyed by an electron immediately after the emission from the metal surface under the action of a strong elec- trostatic field. The mechanism of particle production near the event horizon of a black hole is therefore identi- fied with Schwinger process in relativistic quantum field theory, whereas in the non-relativistic scenario it may be interpreted as Fowler-Nordheim emission process, when observed from a uniformly accelerated frame. Sanchari De a Sutapa Ghosh b Somenath Chakrabarty a† a Department of Physics, Visva-Bharati, Santiniketan-731235, India b Department of Physics, Barasat Govt. College, Barasat 700124, India † E-mail: somenath.chakrabarty@visva-bharati.ac.in 1 Introduction During the last few decades a lot of work have been re- ported on the identical nature of Schwinger mechanism of pair production in presence of strong electric field Schwinger (1951) (see also Crispino et al (2007); Kim (2007) and references therein) and the Hawking radia- tion Hawking (1974, 1975) (see also Birrell and Davies (1982)) at the event horizon of a black hole. The strong electric field which separates two oppositely charged particles beyond their Compton wavelength in the Schwinger process is replaced by the event horizon in the case of Hawking radiation. Further, the Hawk- ing radiation was also explained as an outcome of the so called Unruh effect in the relativistic picture (see Birrell and Davies (1982)). The argument of Unruh for such emission process is that an observer in an accel- erated frame will see radiation in the vacuum of iner- tial observer (known as Unruh effect) Unruh (1976a,b). Whereas from inertial frame, there will be no radiation in the vacuum states. Which therefore indicates that the vacuum is a relative concept. The Unruh effect pre- dicts that an accelerating observer will see black-body radiation in a true vacuum of an inertial observer. The temperature of the inertial vacuum as measured by the accelerated observer increases with the magnitude of ac- celeration and is given by T = T U = α/(2πck), known as the Unruh temperature. In other words, the back- ground appears to be warm from an accelerating refer- ence frame. The ground state for an inertial observer is seen as in thermodynamic equilibrium with a non-zero temperature by the uniformly accelerated observer. In presence of strong black hole gravitational field near the event horizon, which is equivalent to an accelerated frame without gravity, the temperature of the vacuum will be large enough to create particle and anti-particle pairs if kT U > 2m 0 c 2 , with m 0 the rest mass of the par- ticle (anti-particle). However, all such explanations are