The Hawking Effect for Massive Particles
Bernard R. Durney
Route de Carcés, Lorgues, France.
DOI: 10.4236/ijaa.2014.41002   PDF   HTML   XML   5,367 Downloads   7,148 Views  

Abstract

This paper describes a particularly transparent derivation of the Hawking effect for massive particles in black holes. The calculations are performed with the help of Painlevé-Gullstrand’s coordinates which are associated with a radially free-falling observer that starts at rest from infinity. It is shown that if the energy per unit rest mass, e, is assumed to be related to the Killing constant, k, by k2 = 2e 1 then e, must be greater than ?. For particles that are confined below the event horizon (EH), k is negative. In the quantum creation of particle pairs at the EH with k = 1, the time component of the particle’s four velocity that lies below the EH is compatible only with the time component of an outgoing particle above the EH, i.e, the outside particle cannot fall back on the black hole. Energy conservation requires that the particles inside, and outside the EH has the same value of e, and is created at equal distances from the EH, (1 – rin = rout – 1). Global energy conservations force then the mass of the particle below the EH to be negative, and equal to minus the mass the particle above the EH, i.e., the black hole looses energy as a consequence of pair production.

Keywords

Hawking Effect

Share and Cite:

Durney, B. (2014) The Hawking Effect for Massive Particles. International Journal of Astronomy and Astrophysics, 4, 11-15. doi: 10.4236/ijaa.2014.41002.

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1] Hartle, J.B. (2003) Gravity. Addison Wesley, Boston, 291.
[2] Schutz, B. (2007) A First Course in General Relativity. Cambridge University Press, Cambridge.
[3] Carlip, S. (2004) Re: Hawking Radiation and Vacuum Fluctuation. http://sci.techarchive.net/sci. physcsresearch/2004-10
[4] Wald, R.M. (2001) The Thermodynamics of Black Holes. Living Reviews Relativity, 4, 6.
[5] Parker, L. (1969) Quantized Fields and Particle Creation in expanding Universes. Physical Review, 183, 1057.

Copyright © 2021 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.