Relativistic scaling laws for the light curve in supernovae

In order to explain light curve (LC) for Supernova (SN) we derive a classical formula for the conversion of the flux of kinetic energy into radiation. We then introduce a correction for the absorption adopting an optical depth as function of the time. The developed framework allows to fit the LC of type Ia SN 2005cf ( B and V ) and type IIp SN 2004A (B,V,I and R ). A relativistic formula for the flux of kinetic energy is also derived in terms of a Taylor expansion and the application is done to the LC of GRB 050814. The decay of the radioactive isotopes as a driver the LC for SNs is also reviewed and a new formulation is introduced. The Arnett's formula for bolometric luminosity is corrected for the optical depth and applied to SN 2001ay.