Plummer, H.C. (1911) On the Problem of Distribution in Globular Star Clusters. MNRAS, 71, 460. https://doi.org/10.1093/mnras/71.5.460

has been cited by the following article:

• 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.