Observable form of pulses emitted from relativistic collapsing objects

In this work, we discuss observable characteristics of the radiation emitted from a surface of a collapsing object. We study a simplified model in which a radiation of massless particles has a sharp in time profile and it happens at the surface at the same moment of comoving time. Since the radiating surface has finite size the observed radiation will occur during some finite time. Its redshift and bending angle are affected by the strong gravitational field. We obtain a simple expression for the observed flux of the radiation as a function of time. To find an explicit expression for the flux we develop an analytical approximation for the bending angle and time delay for null rays emitted by a collapsing surface. In the case of the bending angle this approximation is an improved version of the earlier proposed Beloborodov-Leahy-approximation. For rays emitted at $R > 2R_g$ the accuracy of the proposed improved approximations for the bending angle and time delay is of order (or less) than 2-3%. By using this approximation we obtain an approximate analytical expression for the observed flux and study its properties.Comment: 13 pages, 10 figures;Typos in equations and refrences are corrected. No change in the results and discussion

General Relativistic Electromagnetic Fields of a Slowly Rotating Magnetized Neutron Star. II. Solution of the Induction Equations

We have solved numerically the general relativistic induction equations in the interior background spacetime of a slowly rotating magnetized neutron star. The analytic form of these equations was discussed in a recent paper (Rezzolla et al 2001a), where corrections due both to the spacetime curvature and to the dragging of reference frames were shown to be present. Through a number of calculations we have investigated the evolution of the magnetic field with different rates of stellar rotation, different inclination angles between the magnetic moment and the rotation axis, as well as different values of the electrical conductivity. All of these calculations have been performed for a constant temperature relativistic polytropic star and make use of a consistent solution of the initial value problem which avoids the use of artificial analytic functions. Our results show that there exist general relativistic effects introduced by the rotation of the spacetime which tend to decrease the decay rate of the magnetic field. The rotation-induced corrections are however generally hidden by the high electrical conductivity of the neutron star matter and when realistic values for the electrical conductivity are considered, these corrections become negligible even for the fastest known pulsar.Comment: 13 pages, 5 figures. Accepted for publication by MNRAS. Replaces previous version without unnecessary mn.st

General Relativistic Electromagnetic Fields of a Slowly Rotating Magnetized Neutron Star. I. Formulation of the equations

We present analytic solutions of Maxwell equations in the internal and external background spacetime of a slowly rotating magnetized neutron star. The star is considered isolated and in vacuum, with a dipolar magnetic field not aligned with the axis of rotation. With respect to a flat spacetime solution, general relativity introduces corrections related both to the monopolar and the dipolar parts of the gravitational field. In particular, we show that in the case of infinite electrical conductivity general relativistic corrections due to the dragging of reference frames are present, but only in the expression for the electric field. In the case of finite electrical conductivity, however, corrections due both to the spacetime curvature and to the dragging of reference frames are shown to be present in the induction equation. These corrections could be relevant for the evolution of the magnetic fields of pulsars and magnetars. The solutions found, while obtained through some simplifying assumption, reflect a rather general physical configuration and could therefore be used in a variety of astrophysical situations.Comment: A few typos corrected; matches the versions in MNRA