^{1}

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^{4}

^{1}

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^{3}.

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.

In 1974, Hawking proved black holes could radiate Hawking radiation once considering the quantum effect near the horizons of black holes [

However, since the Hamilton-Jacobi equation is derived from Klein-Gordon equation, original Hamilton-Jacobi method just can be valid for scalar particles in principle. Therefore, Kerner and Mann studied fermions tunneling of black hole by a new method [

On the other hand, as the basis of general relativity and quantum field theory, Lorentz invariance is proposed to be spontaneously violated at higher energy scales. A possible deformed dispersion relation is given by [

In this paper, we try to generalize the modified Dirac equation in curved spacetime and then study the correction of Hawking tunneling radiation. In Section

As we all know, the gamma matrix and partial derivative should become gamma matrix in curved spacetime

Now let us use the modified Dirac equation to derive the modified Hamilton-Jacobi equation. Firstly, we rewrite the wave function of Dirac equation as [

Therefore, we find that the modified Dirac equation from Lorentz invariance violation could lead to the modified Hamilton-Jacobi equation, and the correction of Hamilton-Jacobi equation depends on the energy and mass of radiation fermions. Using the modified Hamilton-Jacobi equation, we then investigate the fermions Hawking tunneling radiation of

The research of gravity in

Now we research the fermions tunneling of this black hole, so the modified Hamilton-Jacobi equation in this spacetime is given by

As we all know that the linear Maxwell action fails to satisfy the conformal symmetry in higher dimensional spacetime [

In this paper, we consider the deformed dispersion relation with Lorentz invariance violation and generalize the modified Dirac equation in curved spacetime. 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

The first law of black hole thermodynamics requires

On the other hand, from the deformed dispersion relation (

The authors declare that they have no competing interests.

This work was supported by FAPESP no. 2012/08934-0, CNPq, CAPES, and National Natural Science Foundation of China no. 11573022, no. 11205254, no. 11178018, and no. 11375279.