An application of Lorentz-invariance violation in black hole thermodynamics

Abstract

In this paper, we have applied the Lorentzinvariance violation (LIV) class of dispersion relations (DRs) with the dimensionless parameter n = 2 and the "sign of LIV" η + = 1, to a phenomenological study of the effect of quantum gravity in a strong gravitational field. Specifically, we have studied the effect of the LIV-DR induced quantum gravity on the Schwarzschild black hole thermodynamics. The result shows that the effect of the LIV-DR induced quantum gravity speeds up the black hole evaporation, and its corresponding black hole entropy undergoes a leading logarithmic correction to the "reduced Bekenstein-Hawking entropy", and the ill-defined situations (i.e. the singularity problem and the critical problem) are naturally bypassed when the LIV-DR effect is present. Also, to put our results in a proper perspective, we have compared results with the earlier findings by another quantum-gravity candidate, i.e. the generalized uncertainty principle (GUP). Finally, we conclude from the inert remnants at the final stage of the black hole evaporation that, the GUP as a candidate for describing quantum gravity can always do as well as the LIV-DR by adjusting the model-dependent parameters, but in the same model-dependent parameters the LIV-DR acts as a more suitable candidate.

Black Hole Thermodynamics and Generalized Uncertainty Principle with Higher Order Terms in Momentum Uncertainty

“…Interestingly the correction to the Schwarzschild black hole temperature due to quadratic and linear-quadratic GUP has also been compared with the corrections from the quantum Raychaudhuri equation [47]. Very recently the Lorentz-invariance-violating class of dispersion relations has been applied to study the thermodynamics of black holes [48]. It would therefore be interesting to compare these results with those coming from the GUP.…”

Lorentz violation, quantum tunneling, and information conservation *

“…In the context of the LIV-DR, the observation of synchrotron radiation from the Crab nebula serves as an important constraint on theories related to quantum gravity [19]. Moreover, there are many other similar and interesting techniques that are designed to experimentally investigate the violation of Lorentz invariance [20][21][22][23][24][25][26][27][28][29][30][31][32], i.e., testing Lorentz-symmetry violation using atomic systems [31,32]. These observations indicate that the concept of the LIV as a candidate for describing the effect of quantum gravity has been one of the most interesting and popular research topics in recent years.…”

“…From expression (32), it can easily be determined that the original result, i.e., can be recovered by setting . For a closed physical system, based on information theory, we know that the uncertainty of an event (an emission with an energy E) or the information we gain from this event [110] is on average.…”

Noncommutative correction to the entropy of Schwarzschild black hole with GUP

“…In recent years, the effect of GUP on the thermodynamics of various types of black holes has been extensively analyzed [4][5][6][7][8][9][10][11][12][13][14]. Consequently, it has been found in many cases that the GUP has an important role in black hole physics, which is the emergence of black hole remnants [15][16][17][18][19][20][21][22][23]. In addition, in determining the entropy of black holes it has been found due to the effect of quantum gravity logarithmic corrections to the law of the area [24][25][26][27][28][29].…”