Recent X-ray observations have shown broad, skewed iron line emission from Seyfert 1 galaxies which is explained by the emission being fluorescence on a disk close to a black hole. During one interval, the line in MCG-6-30-15 was so broad and redshifted that a Kerr black hole is implied. We are therefore studying the effects of the Kerr metric on the line profile, and extending the work by Laor and Kojima which dealt only with extreme values of the spin parameter. Here we report that the spin parameter of the black hole in MCG-6-30-15 is high (a/M > 0.94), and invert the line profile to obtain the disk emissivity profile, which approximates a power-law. Continuum radiation returning to the disk because of the Kerr metric does not enhance the equivalent width of the line seen above 3 keV by more than about 20 per cent if the continuum source corotates with the disk.

In this paper we present a fully relativistic approach to modelling both the continuum emission and the reflected fluorescent iron line from a primary X‐ray source near a Kerr black hole. The X‐ray source is located above an accretion disc orbiting around the black hole. The source is assumed to be a static point source located on an arbitrary position above the disc, on or off the axis of rotation. We carry out Monte Carlo simulations in order to estimate the iron line spectrum as well as its equivalent width. Because of the gravitational lensing effect, an enhancement of the iron line is expected when the primary source is located close to the central black hole. We find that for a source located on the axis of rotation the enhancement is relatively modest. An observer at inclination 30° would measure an equivalent width of ∼300 eV in the extreme case of a maximally rotating black hole and a source located at height 1.5 gravitational radii from the centre. This corresponds to an equivalent width enhancement factor of about 2 compared with the classical value where no lensing effect comes into play. However, when allowing the source to be located off the axis of rotation, much stronger enhancement can be obtained. In the extreme case of a maximally rotating black hole and a source located just above the approaching side of the disc, an observer at inclination 30° could measure an equivalent width as high as ∼1.5 keV (i.e., ∼10 times the classical value). We also find that observers located at high inclination angles observe a stronger line than observers at low inclination angles.

A new method is proposed for modelling spherically symmetric inhomogeneities in the Universe. The inhomogeneities have finite size and are compensated, so they do not exert any measurable gravitational force beyond their boundary. The region exterior to the perturbation is represented by a Friedmann‐‐Robertson‐‐Walker (FRW) universe, which we use to study the anisotropy in the cosmic microwave background (CMB) induced by the cluster. All calculations are performed in a single, global coordinate system, with non‐linear gravitational effects fully incorporated. An advantage of the gauge choices employed here is that the resultant equations are essentially Newtonian in form. Examination of the problem of specifying initial data shows that the new model presented here has many advantages over `Swiss cheese' and other models. Numerical implementation of the equations derived here is described in a subsequent paper.

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A new method for modelling spherically symmetric inhomogeneities is applied to the formation of clusters in an expanding Universe. We impose simple initial velocity and density perturbations of finite extent, and we investigate the subsequent evolution of the density field. Photon paths are also calculated, allowing a detailed consideration of gravitational lensing effects and microwave background anisotropies induced by the cluster. We apply the method to modelling high‐redshift clusters and, in particular, we consider the reported microwave decrement observed towards the quasar pair PC 1643+4631 A&B. We also consider the effect on the primordial microwave background power spectrum due to gravitational lensing by a population of massive high‐redshift clusters.