RELATIVISTIC HYDRODYNAMICS AND ITS APPLICATIONS

Abstract

Relativistic fluids are used to model a complicated Physical systems which consists of many interacting particles. The equations which describe the dynamic of relativistic system have a special symmetry called Lorentz symmetry. However, equations of relativistic hydrodynamics are completely different from the equations of ordinary hydrodynamic whose equations do not have Lorentz symmetry. In this thesis we start by giving a quick background in Lorentz sym- metry and mathematical objects such as 4-vectors and tensors that are needed to understand relativistic hydrodynamics.Then introduce the equation of relativistic hydrodynamics which obey an entropy condition, study how to derive them.Also, we describe how they are related to the hydrodynamic variable(4-velocity, temperature and chemical potential). Following this, we solve the equations of relativistic hydrodynamics within a linear response regime to get hydrodynamic modes, which demonstrate how fluid at rest react to small perturbati