Quantum Gravity and String Theory

   

On Thermal Relativity, Modified Hawking Radiation, and the Generalized Uncertainty Principle

Authors: Carlos Castro

After a brief review of the thermal relativistic $corrections$ to the Schwarzschild black hole entropy, it is shown how the Stefan-Boltzman law furnishes large modifications to the evaporation times of Planck-size mini-black holes, and which might furnish important clues to the nature of dark matter and dark energy since one of the novel consequences of thermal relativity is that black holes do $not$ completely evaporate but leave a Planck size remnant. Equating the expression for the modified entropy (due to thermal relativity corrections) with Wald's entropy should in principle determine the functional form of the modified gravitational Lagrangian $ {\cal L } (R_{abcd}) $. We proceed to derive the generalized uncertainty relation which corresponds to the effective temperature $ T_{eff} = T_H ( 1 - { T^2_H \over T^2_P } )^{ - 1/2} $ associated with thermal relativity and given in terms of the Hawking ($T_H$) and Planck ($T_P$) temperature, respectively. Such modified uncertainty relation agrees with the one provided by string theory up to first order in the expansion in powers of $ { (\delta p)^2 \over M^2_P} $. Both lead to a minimal length (Planck size) uncertainty. Finally, an explicit analytical expression is found for the modifications to the purely thermal spectrum of Hawking radiation which could cast some light into the resolution of the black hole information paradox.

Comments: 11 Pages. Submitted to Phys. Letts. B

Download: PDF

Submission history

[v1] 2019-03-22 05:15:19
[v2] 2019-03-25 22:39:31

Unique-IP document downloads: 28 times

Vixra.org is a pre-print repository rather than a journal. Articles hosted may not yet have been verified by peer-review and should be treated as preliminary. In particular, anything that appears to include financial or legal advice or proposed medical treatments should be treated with due caution. Vixra.org will not be responsible for any consequences of actions that result from any form of use of any documents on this website.

Add your own feedback and questions here:
You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.

comments powered by Disqus