An analysis of the role of general relativistic effects on the decay of neutron star's magnetic field is presented. At first, a generalized induction equation on an arbitrary static background geometry has been derived and, secondly, by a combination of analytical and numerical techniques, a comparison of the time scales for the decay of an initial dipole magnetic field in flat and 1 curved spacetime is discussed. For the case of very simple neutron star models, rotation not accounted for and in the absence of cooling effects, we find that the inclusion of general relativistic effects result, on the average, in an enlargement of the decay time of the field in comparison to the flat spacetime case. Via numerical techniques we show that, the enlargement factor depends upon the dimensionless compactness ratio ǫ = 2GM c 2 R , and for ǫ in the range (0.3 , 0.5), corresponding to compactness ratio of realistic neutron star models, this factor is between 1.2 to 1.3. The present analysis shows that general relativistic effects on the magnetic field decay ought to be examined more carefully than hitherto. A brief discussion of our findings on the impact of neutron stars physics is also presented.

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We analyze the exact general relativistic integrodi †erential equation of radiative transfer describing the interaction of low-energy photons with a Maxwellian distribution of hot electrons in the gravitational Ðeld of a Schwarzschild black hole. We prove that, owing to Comptonization, an initial arbitrary spectrum of low-energy photons unavoidably results in spectra characterized by an extended power-law feature. We examine the spectral index by using both analytical and numerical methods for a variety of physical parameters as such the plasma temperature and the mass accretion rate. The presence of the event horizon as well as the behavior of the null geodesics in its vicinity largely determine the dependence of the spectral index on the Ñow parameters. We come to the conclusion that the bulk motion of a converging Ñow is more efficient in upscattering photons than thermal Comptonization, provided that the electron temperature in the Ñow is of order of a few kiloÈelectron volts or less. In this case, the spectrum observed at inÐnity consists of a soft component, which is produced by those input photons that escape after a few scatterings without any signiÐcant energy change, and a hard component (described by a power law), which is produced by the photons that underwent signiÐcant upscattering. The luminosity of the power-law component is relatively small compared to that of the soft component. For accretion into a black hole, the spectral energy index of the power law is always higher than 1 for plasma temperatures of order of a few kiloÈelectron volts. This result suggests that the bulk motion Comptonization might be responsible for the power-law spectra seen in the black hole X-ray sources.