Relativistic mechanics of continuous media

In this work we study the relativistic mechanics of continuous media oil a fundamental level using a manifestly covariant proper time procedure. We formulate equations of motion and continuity (and constitutive equations) that are the Starting Point for any calculations regarding continuous media. In the force free limit, the Standard relativistic equations are regained, so that these equations can he regarded as a generalization of the standard procedure. In the case of all inviscid fluid ive derive all analogue of the Bernoulli equation. For irrotational flow ive prove that the velocity field can be derived from a potential. If in addition, the fluid is incompressible, the potential must obey the d'Alembert equation, and thus the problem is reduced to solving the d'Alembert equation with specific boundary conditions (in both space and Mile), The solutions indicate the existence of light velocity sound wares in an incompressible fluid (a result known in previous literature(19)). Relaxing the constraints and allowing the fluid to become linearly compressible one call derive a wave equation, from which the sound velocity call again be computed. For a stationary background flow, it has been demonstrated that the sound velocity attains its correct values for the incompressible and non-relativistic limits. Finally viscosity is introduced, bulk and shear viscosity constants are defined, and we formulate equations for the motion of a viscous fluid.