Observable form of pulses emitted from relativistic collapsing objects

TL;DR

This paper models the observable radiation from a collapsing relativistic object, deriving analytical expressions for flux, redshift, and bending effects, with high-accuracy approximations for null ray trajectories.

Contribution

It introduces an improved analytical approximation for bending angles and time delays of null rays emitted during collapse, enhancing the modeling of observable radiation.

Findings

Derived a simple flux expression as a function of time.

Developed an improved approximation for bending angles with 2-3% accuracy.

Provided analytical insights into radiation characteristics during collapse.

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 $R > 2R_g$ 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.