TITLE:
Classical and Relativistic Models for Time Duration of Gamma-Ray Bursts
AUTHORS:
Lorenzo Zaninetti
KEYWORDS:
Cosmology, Observational Cosmology, Distances, Redshifts, Radial Velocities, Spatial Distribution of Galaxies
JOURNAL NAME:
Journal of High Energy Physics, Gravitation and Cosmology,
Vol.3 No.4,
October
31,
2017
ABSTRACT: A classical model based on a power law assumption for the radius-time relationship in the expansion of a supernova (SN) allows to derive an analytical expression for the flow of mechanical kinetic energy and the time duration of gamma-ray burst (GRB). A random process based on the ratio of two truncated lognormal distributions for luminosity and luminosity distance allows to derive the statistical distribution for time duration of GRBs. The high velocities involved in the first phase of expansion of a SN require a relativistic treatment. The circumstellar medium is assumed to follow a density profile of Plummer type with eta = 6. A series solution for the relativistic flow of kinetic energy allows to derive in a numerical way the duration time for GRBs. Here we analyze two cosmologies: the standard cosmology and the plasma cosmology.