In this paper, first by using the generalized Klein-Gordon and Proca equations, we investigate the scalar/vector particles tunneling from a BBH and recover the corresponding Bekenstein-Hawking temperatures.
In Section 3, we study the Proca equation to find a massive boson in this geometry.
To calculate the BHR of the tunneling vector particles from the BBH, the Proca equation is used on the BBH geometry.
Then we solve the Proca equation on the background of the BBH,
It has been known for quite long time that the electrodynamics of Maxwell equations can be extended and generalized further into Proca equations. The implications of introducing Proca equations include an alternative description of superconductivity, via extending London equations.
The background argument of Proca equations can be summarized as follows .
In this regards, it has been shown by Sternberg , that the classical London equations for superconductors can be written in differential form notation and in relativistic form, where they yield the Proca equations. In particular, the field itself acts as its own charge carrier .
Similarly in this regards, in a recent paper Tajmar has shown that superconductor equations can be rewritten in terms of Proca equations .
With a nonzero photon mass, the usual Maxwell equations transform into the so-called Proca equations which will form the basis for our assessment in superconductors and are only valid for the superconducting electrons."