npsm 새물리 New Physics : Sae Mulli

pISSN 0374-4914 eISSN 2289-0041


Research Paper

New Phys.: Sae Mulli 2019; 69: 573-577

Published online May 31, 2019

Copyright © New Physics: Sae Mulli.

Effects of the Temperature of the Universe on Black-Hole Evaporations

Won Sik L'Yi*

Department of Physics, Chungbuk National University, Cheongju 28644, Korea


Received: March 27, 2019; Revised: April 26, 2019; Accepted: May 1, 2019

This is an open-access article distributed under the terms of the Creative Commons Attribution Non-Commercial License ( which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.


Assuming that black holes are in thermal equilibrium with the Universe, which is considered a heat bath, we investigated the finite-temperature effect of the Universe on black-hole evaporation. We found that if a black hole receives cosmic background radiation from the Universe, it steadily acquires mass if its initial mass is greater than the critical mass $M_c = (8\pi T_U/T_P)^{-1} M_P,$ where $T_U$ is the temperature of the Universe, $T_P$ and $M_P$ are the Planck temperature and the mass respectively. If the initial mass of the black hole is less than $M_c,$ it evaporates at a finite time $t_e.$

For $T_U \approx 2.725 \ \textrm{K},$ the average temperature of microwave background radiation, the critical mass is approximately equal to $ 4.5 \times 10^{19} \,\textrm{kg},$ or $ 2.26\times 10^{-13} M_\odot.$

Keywords: Black hole, Evaporation

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