Abstract
Recently the modified Dirac equation with Lorentz invariance violation has been proposed, which would be helpful to resolve some issues in quantum gravity theory and high energy physics. In this paper, the modified Dirac equation has been generalized in curved spacetime, and then fermion tunneling of black holes is researched under this correctional Dirac field theory. We also use semiclassical approximation method to get correctional Hamilton-Jacobi equation, so that the correctional Hawking temperature and correctional black hole’s entropy are derived.
Highlights
In 1974, Hawking proved black holes could radiate Hawking radiation once considering the quantum effect near the horizons of black holes [1, 2]. This theory indicates that black hole would be viewed as thermodynamic system, so that black hole physics can be connected closely with gravity, quantum theory, and thermodynamics physics
Our work in 2009 showed that the Hamilton-Jacobi equation can be derived from Dirac equation via semiclassical approximation, so we proved that the Hamilton-Jacobi equation can be used to study the fermions tunneling directly [33–35]
The fermions tunneling radiation of black strings is researched, and we find that the modified Dirac equation could lead to Hawking temperature’s correction, which depends on the correction parameter σ and particle mass m in the modified Dirac equation
Summary
In 1974, Hawking proved black holes could radiate Hawking radiation once considering the quantum effect near the horizons of black holes [1, 2]. Wilczek et al proposed a semiclassical method to study the quantum tunneling from the horizon of black hole [3– 21] Along with this method, the Hamilton-Jacobi method was applied to calculate the Hawking tunneling radiation. Kerner and Mann studied fermions tunneling of black hole by a new method [22–32], which assumes the wave function of Dirac equation Ψ as spin-up and spin-down and calculates the fermions tunneling, respectively. This method is still impossible to apply in arbitrary dimensional spacetime. We apply the modified HamiltonJacobi equation to the fermions tunneling radiation of 2 + 1-dimensional black string and higher dimensional BTZlike black strings in Sections 3 and 4, respectively, and Section 5 includes some conclusion and the discussion about the correction of black hole’s entropy
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