### 2.2 SRHD as a hyperbolic system of conservation laws

An important property of system (5) is that it is hyperbolic for causal EOS [8]. For hyperbolic systems
of conservation laws, the Jacobians have real eigenvalues and a complete set of eigenvectors
(see Section 9.3). Information about the solution propagates at finite velocities given by the eigenvalues of
the Jacobians. Hence, if the solution is known (in some spatial domain) at some given time, this fact can be
used to advance the solution to some later time (initial value problem). However, in general, it is not
possible to derive the exact solution for this problem. Instead one has to rely on numerical
methods which provide an approximation to the solution. Moreover, these numerical methods
must be able to handle discontinuous solutions, which are inherent to nonlinear hyperbolic
systems.
The simplest initial value problem with discontinuous data is called a Riemann problem, where the
one-dimensional initial state consists of two constant states separated by a discontinuity. The
majority of modern numerical methods, the so-called Godunov-type methods, are based on
exact or approximate solutions of Riemann problems. Because of its theoretical and numerical
importance, we discuss the solution of the special relativistic Riemann problem in the next
Section 2.3.