Version 1
: Received: 25 September 2023 / Approved: 26 September 2023 / Online: 26 September 2023 (10:17:56 CEST)
Version 2
: Received: 19 February 2024 / Approved: 19 February 2024 / Online: 19 February 2024 (14:44:34 CET)
Version 3
: Received: 4 March 2024 / Approved: 5 March 2024 / Online: 5 March 2024 (10:56:30 CET)
How to cite:
Denur, J. Firewalls, Hawking (Tolman) Radiation, and a Tentative Resolution of the Firewall-Mass Problem. Preprints2023, 2023091751. https://doi.org/10.20944/preprints202309.1751.v3
Denur, J. Firewalls, Hawking (Tolman) Radiation, and a Tentative Resolution of the Firewall-Mass Problem. Preprints 2023, 2023091751. https://doi.org/10.20944/preprints202309.1751.v3
Denur, J. Firewalls, Hawking (Tolman) Radiation, and a Tentative Resolution of the Firewall-Mass Problem. Preprints2023, 2023091751. https://doi.org/10.20944/preprints202309.1751.v3
APA Style
Denur, J. (2024). Firewalls, Hawking (Tolman) Radiation, and a Tentative Resolution of the Firewall-Mass Problem. Preprints. https://doi.org/10.20944/preprints202309.1751.v3
Chicago/Turabian Style
Denur, J. 2024 "Firewalls, Hawking (Tolman) Radiation, and a Tentative Resolution of the Firewall-Mass Problem" Preprints. https://doi.org/10.20944/preprints202309.1751.v3
Abstract
It has been theorized that black holes are surrounded by firewalls, although there is not universal agreement concerning this. We first review basic concepts pertaining to Schwarzschild black holes and Hawking radiation. Then we discuss the anticipation of Hawking radiation—albeit from non-black holes—initially by R. C. Tolman and shortly thereafter with P. Ehrenfest. We compare evaporation into a vacuum at absolute zero (0 K) of black holes with that of non-black holes, and show that not only black holes but also non-black holes evaporate within a finite time. The times required for evaporation of black holes and non-black holes are compared. Next, we show that (i) if firewalls exist, they can originate via Hawking radiation at the minimum possible ruler distance (the Planck length) beyond the Schwarzschild horizon, where it has not suffered any gravitational redshift, or, alternatively, suffered maximal gravitational blueshift and (ii) the firewall temperature is on the order of the Planck temperature, independently of the mass and hence also of the Schwarzschild radius of a Schwarzschild black hole. We then explain the exponential nature of the gravitational frequency shift as a function of the gravitational potential. Next, we consider the firewall-mass problem, and provide an at least prima facie tentative resolution thereto based on: (i) the mass of a firewall being canceled by the negative gravitational mass = (negative gravitational energy)/c2 accompanying its formation, (ii) the unchanged observations of a distant observer upon formation of a firewall, and (iii) Birkhoff's Theorem (actually first discovered by Jørg Tofte Jebsen). We then consider one aspect of thermodynamics in gravitational fields, showing that equilibrium relativistic gravitational temperature gradients cannot be exploited to violate the Second Law of Thermodynamics.
Keywords
Schwarzschild black holes; Schwarzschild non-black holes; Ruler distance; Planck units; Hawking radiation; Tolman radiation; Gravitational frequency shift; Firewall mass; Negative gravitational mass-energy; Birkhoff's Theorem; Thermodynamic equilibrium; First Law of Thermodynamics; Second Law of Thermodynamics
Subject
Physical Sciences, Astronomy and Astrophysics
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
