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The properties of symmetric nuclear matter are investigated in the nonlinear relativistic mean field theory of nuclear matter. We consider the constraints imposed by four nuclear ground state properties on the coupling constants and on the equation of state at zero and at finite temperature. We find that the compression constant K(${\ensuremath{\rho}}_{0}$) as well as the temperature is irrelevant for the stiffness of the equation of state for ${m}^{\mathrm{*}}$(${\ensuremath{\rho}}_{0}$)\ensuremath{\le}0.7. The main point is that the relativistic mean field theory exhibits acausal and unphysical behavior for compressibilities below K(${\ensuremath{\rho}}_{0}$)=200 MeV. Every set of coupling constants with a negative quartic coupling constant c is unstable against small quantum fluctuations.

Nuclear equation of state from the nonlinear relativistic mean field theory