Tachyonic γ-ray bursts generated by nonlocal plasma currents
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The dispersion relations of superluminal wave propagation in electron plasmas are derived, and the tachyonic energy flux, the velocity of energy transport, and the relaxation time asymptotics of the conductivity are studied. The formalism is based on Maxwell-type equations for Proca fields with negative mass-square in dispersive and dissipative media. Specifically, superluminal radiation fields generated by the ultra-relativistic electronic source plasma of γ-ray bursts (GRBs) are investigated. The radiation field is coupled to the shock-heated electron gas by a frequency-dependent fine-structure constant. The varying coupling constant generates long-range dispersion in the charge and current densities. At high energy, the coupling strength approaches a finite limit, so that the Proca field becomes minimally coupled to the electron current. The tachyonic fine-structure constant scales with the frequency-dependent superluminal velocity of the radiated modes. This scaling is manifested in the tachyonic flux densities of the GRB plasma, so that the scaling exponent can be extracted from spectral maps in the soft γ-ray band. To this end, tachyonic spectral fits of GRB 930506, GRB 950425, and GRB 910503 are performed. The scaling amplitude of the fine-structure constant is inferred from the burst duration. The transversal and longitudinal tachyonic luminosity of the source plasma is calculated in the high-temperature regime. Estimates of the plasma temperature and the internal energy of the ultra-relativistic electron gas are obtained.
KeywordsDispersion Relation Burst Duration Fourier Amplitude Lorentz Condition Tachyonic Mode
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