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Observable form of pulses emitted from relativistic collapsing objects

Valeri P. Frolov^1,* and Hyun Kyu Lee^1,2,3,†

¹Theoretical Physics Institute, Department of Physics, University of Alberta, Edmonton, AB, Canada, T6G 2J1
²KIPAC, 2575 Sand Hill Road, Menlo Park, CA 94025, USA
³Department of Physics, Hanyang University, Seoul 133-791, Korea

^*E-mail: frolov@phys.ualberta.ca
^†E-mail: hyunkyu@hanyang.ac.kr

Phys. Rev. D 71, 044002 – Published 8 February, 2005

DOI: https://doi.org/10.1103/PhysRevD.71.044002

Abstract

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 $R > 2 R_{g}$ 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.

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Observable form of pulses emitted from relativistic collapsing objects

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