On Abraham-Lorentz force, Unruh and Hawking radiations

Abstract: Assuming the radiation emitted by an accelerating charge follows the Unruh radiation, we obtained the characteristics of the de Broglie wave associated with the accelerating charge. The de Broglie wavelength of the accelerating charged particle is found to be inversely proportional to the temperature of the emitted radiation. Merging the Abraham-Lorentz and Unruh formulae shows that the particle de Broglie wavelength is found to vary inversely with its acceleration. It is found to have the same structure as that of the Wien's displacement law relating the maximum wavelength of the Black Body radiation to its temperature. A maximum acceleration that a charged particle can attain is derived that sets a limit to the the maximum electric field. The Abraham-Lorentz force for a black hole radiation is found to be proportional to its evaporation rate. The final mass of the black hole left-over is found to be $\sqrt{\frac{\alpha\hbar c}{24 \pi G} }$, where $G$ is the gravitational constant, $c$ the speed of light, $h=2\pi\hbar$ is the Planck constant, and $\alpha$ is the fine structure constant. The minimum entropy and spin of the black hole emitting Hawking radiation are, respectively, found to be $(\alpha/6) k_B$ and $(\alpha/6)\hbar$. The presently observed universal acceleration is a manifestation of the Unruh black body temperature of $10^{-29}K$. This agrees with the black body radiation temperature ($T$) relating $TR=const.$ prevailing since the time of the big bang, where $R$ is the universe radius.