![]() Is the Lorentz factor see equation (7.16) in. Is the rest mass, c is the velocity of light, Where F is the force, p is the relativistic momentum, m is the relativistic mass, Newton’s second law in special relativity is: ![]() In the following, we will consider only positive and decreasing velocities. We assume a one dimensional motion with a resistive force of Newtonian type, The CMB is not related with the model that is presented here. ![]() Section 3 applies the relativistic results to the motion of SN 1993J, to the light curve of GRB 130427A and GRB 060729. Section 2 derives a relativistic equation of motion in the presence of viscosity proportional to the square of the velocity. This paper is a highly idealized attempt to model SN light curves by assuming that the resistivity of the ambient interstellar medium is quadratic to the velocity of the SN envelope. The Lagrangian and a Hamiltonian for a relativistic particle moving in a dissipative medium characterized by a force that depends on the square of the velocity of the particle have been derived. Relativistic viscosity has the following applications: change in the mean particle momentum and spreading around the mean for the cosmic rays (CR) acceleration of CR in shear flows, such as active galactic nuclei (AGN), gamma ray burst (GRB) and jets interaction of a neutral particle with the microwave background radiation (CMB) and generation of the CMB in the expanding universe.
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