We derive master equations for linear perturbations in Einstein-Maxwell scalar theory, for any spacetime dimension D and any background with a maximally symmetric n = (D − 2)-dimensional spatial component. This is done by expressing all fluctuations analytically in terms of several master scalars. The resulting master equations are Klein-Gordon equations, with non-derivative couplings given by a potential matrix of size 3, 2 and 1 for the scalar, vector and tensor sectors respectively. Furthermore, these potential matrices turn out to be symmetric, and positivity of the eigenvalues is sufficient (though not necessary) for linear stability of the background under consideration. In general these equations cannot be fully decoupled, only in specific cases such as Reissner-Nordström, where we reproduce the Kodama-Ishibashi master equations. Finally we use this to prove stability in the vector sector of the GMGHS black hole and of Einstein-scalar theories in general.
We have developed a quasi-analytical model for the production of radiation in strong-line blazars, assuming a spine-sheath jet structure. The model allows us to study how the spine and sheath spectral components depend on parameters describing the geometrical and physical structure of "the blazar zone". We show that typical broad-band spectra of strong-line blazars can be reproduced by assuming the magnetization parameter to be of order unity and reconnection to be the dominant dissipation mechanism. Furthermore, we demonstrate that the spine-sheath model can explain why gamma-ray variations are often observed to have much larger amplitudes than the corresponding optical variations. The model is also less demanding of jet power than one-zone models, and can reproduce the basic features of extreme γ-ray events.
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