Abstract
The effect of Lorentz symmetry breaking (LSB) on the Hawking radiation of Schwarzschild-like black hole found in the bumblebee gravity model (SBHBGM) is studied in the framework of quantum gravity. To this end, we consider Hawking radiation spin-0 (bosons) and spin-12 particles (fermions), which go in and out through the event horizon of the SBHBGM. We use the modified Klein-Gordon and Dirac equations, which are obtained from the generalized uncertainty principle (GUP) to show how Hawking radiation is affected by the GUP and LSB. In particular, we reveal that, independent of the spin of the emitted particle, GUP causes a change in the Hawking temperature of the SBHBGM. Furthermore, we compute the semi-analytic greybody factors (for both bosons and fermions) of the SBHBGM. Thus, we reveal that LSB is effective on the greybody factor of the SBHBGM such that its redundancy decreases the value of the greybody factor. Our findings are graphically depicted.
Highlights
1 2 particles, which go in and out through the event horizon of the SBHBGM
Klein-Gordon and Dirac equations, which are obtained from the generalized uncertainty principle (GUP) to show how Hawking radiation is affected by the GUP and Lorentz symmetry breaking (LSB)
We reveal that LSB is effective on the greybody factor of the SBHBGM such that its redundancy decreases the value of the greybody factor
Summary
The Lagrangian density of the BGM [143, 144] yields the following extended vacuum. where Gμν and TμBν are the Einstein and bumblebee energy-momentum tensors, respectively. Where Gμν and TμBν are the Einstein and bumblebee energy-momentum tensors, respectively. V ≡ V (א) provides a non-vanishing VEV for Bμ As it was stated above (see [145, 146]), the VEV of the bumblebee field is determined when V = V = 0. One can immediately see that when the bumblebee field Bμ vanishes, we recover the ordinary Einstein equations. The solution is obtained when the bumblebee field Bμremains frozen in its VEV bμ [147, 148]. Which is different than the Kretschmann scalar of the Schwarzschild BH It means that none of the coordinate transformations link the metric (12) to the usual Schwarzschild BH. One can see from Eq (15) that the non-zero LSB parameter has the effect of reducing the Hawking temperature of a Schwarzschild BH
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