# Relativistic Fluids and Magneto-fluids: With Applications in by A. M. Anile

By A. M. Anile

A unified and systematic remedy of the most effects and methods of relativistic fluid dynamics with an emphasis on waves and surprise waves. the 1st 4 chapters offer an advent to the basic ideas of relativistic fluid dynamics and magneto-fluids. the rest chapters current particular issues, together with non-linear electromagnetic waves in relativistic chilly plasmas, relativistic asymptotic waves, and relativistic surprise waves. Examples of the purposes of the speculation to plasma physics, nuclear physics and astrophysics are awarded.

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**Example text**

2. 102). It is of great interest to investigate the form taken by the when expressed in terms of the main field U'. One has proposition (Ruggeri and Strumia, 1981a). 8. A convex covariant density system is a conservative hyperbolic symmetric system in the field U'. PROPOSITION Proof. Let us consider the following Legendre transformation h'* = U'AFaA - h\ with h'a = h'\UfB). Then dU'B because dF«A T L tB du - 1 dh* B eu' ' It follows that A'xA dF«A 8U'B d2h" dU'A8U>B> which is a symmetric matrix.

36) assumed to be sufficiently differentiable. All the influence of the background gravitational field is included in the covariant derivatives. 39) where 0a and 0" indicate the null vector and matrix, respectively, and Pe,pfs are the partial derivatives of p(e,S). Now we shall assume the following restriction on the state equation 0

We have the following proposition. 1. 1. PROPOSITION Proof. 1) hold. Let £a be the timelike vector field of M which defines time-orientation. A simple calculation gives det (A*U = (e + p) V « 4 ( ( " a S « ) 2 ~ p y ^ v ) # 0 because £a is timelike and p'e