By Ahmad S.A.B.
The necessity to build a fermion quantum box concept in black-hole spacetimes is an acute one. The learn of gravitational cave in necessitates the necessity of such. during this dissertation, we build the speculation of unfastened fermions dwelling at the static Schwarzschild black-hole and the rotating Kerr black-hole. the development capitalises upon the truth that either black-holes are desk bound axisymmetric strategies to Einstein's equation. A factorisability ansatz is constructed wherein uncomplicated quantum modes are available, for such desk bound spacetimes with azimuthal symmetry. those modes are then hired for the needs of a canonical quantisation of the corresponding fermionic concept. even as, we advise that it can be most unlikely to increase a quantum box conception always throughout an occasion horizon. This cut up of a quantum box idea guarantees the thermal personality of the Hawking radiation. In our case, we compute and end up that the spectrum of neutrinos emitted from a black-hole through the Hawking method is certainly thermal. We additionally examine fermion scattering amplitudes off the Schwarzschild black-hole.
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Extra resources for Fermion QFT in black hole spacetimes
Example text
The simplest way to proceed, is by matching the interior metric of the star to the exterior metric, across the surface of the star. And because we are dealing with a spherically symmetric situation, the matching problem essentially reduces to a two-dimensional problem involving only the radial and temporal coordinates. Therefore, we shall use the notation and terminology of the two-dimensional physics and follow closely the method as outlined in [2]. Let the two-dimensional, radial and temporal metric outside the star be ds2 = C(r)dudv where u = t − r ∗ − R0∗ , v = t + r ∗ − R0∗ , r ∗ = C −1 dr and R0∗ = some constant.
This should not be surprising. There are other indications that also hints at this. In the next chapter, we shall discuss the famous result of Hawking - thermal emission from black-holes. There we shall present arguments that also support this conclusion. 50 CHAPTER 5 : THERMAL NEUTRINO EMISSION FROM THE SCHWARZSCHILD BLACK-HOLE In the previous chapter, we have suggested that it may be impossible to extend the quantum field theory into the event horizon in a continuous manner linking the exterior of the horizon to its interior.
In support of this hypothesis, we present in this chapter, the famous thermal Hawking radiation from black-holes [2,5]. However, instead of scalar fields, we shall use the machinery of the previous chapter to show that neutrino emission from black-holes is thermal. And we shall follow closely the calculations and discussions in [2,5]. 6). 6) may be approximated by e±iωr . 1) jmj κj where v = t + r∗ and where, uωjmj κj = 2M 2 ω 1− π r vωjmj κj = 2M 2 ω 1− π r 1/4 1/4 r sin1/2 θ 1 − γ 5 (+) Φmj κj 2 r sin1/2 θ 1 − γ 5 (−) Φmj κj 2 are the left handed neutrino wave functions.
Fermion QFT in black hole spacetimes by Ahmad S.A.B.
by Daniel
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