I am reading a lot of papers that derive the Hawking temperature solving either the Klein Gordon equation for scalar fields or the Dirac equation for spin $\tfrac12$ particles via tunnelling probability or direct computation of the solution. But I was unable to find a paper that solves the Maxwell equation in a Kerr or Schwarzschild space-time. Does anyone know if such calculation has been made?
$\begingroup$
$\endgroup$
5
-
1$\begingroup$ AFAIK Maxwell's equations are not modeling photons but classical electromagnetism. Photons are quantum elementary particles and quantum mechanics theories have to be used, if you google there are a number of papers treating the classical Maxwell fields in gravitational metrics, but those are not photons.4 $\endgroup$– anna vCommented Jan 14 at 13:02
-
$\begingroup$ My first guess would be that there is no closed form solution for that problem even in the classical case. The main problem is that we are introducing another time scale and a second spatial scale given by the frequency and wavelength of the electromagnetic waves. The phenomenological behavior of waves much longer than the scale of the black hole is very different from that of waves that are much shorter. We can't solve that problem in closed form for all wavelengths even for a classical scattering body. $\endgroup$– FlatterMannCommented Jan 14 at 13:49
-
1$\begingroup$ @annav But the derivation of Hawking radiation, does require solving the classical field equations. $\endgroup$– TimRiasCommented Jan 14 at 14:42
-
1$\begingroup$ The original source is a series of papers by D. Page Particle emission rates from a black hole from 1975-1977. $\endgroup$– A.V.S.Commented Jan 14 at 18:20
-
$\begingroup$ This is the paper A.V.S. referred to: journals.aps.org/prd/pdf/10.1103/PhysRevD.14.3260 $\endgroup$– TimRiasCommented Jan 15 at 18:40
Add a comment
|