  This paper studies high-order accurate entropy stable nodal discontinuous
Galerkin (DG) schemes for the ideal special relativistic magnetohydrodynamics
(RMHD). It is built on the modified RMHD equations with a particular source
term, which is analogous to the Powell's eight-wave formulation and can be
symmetrized so that an entropy pair is obtained. We design an affordable fully
consistent two-point entropy conservative flux, which is not only consistent
with the physical flux, but also maintains the zero parallel magnetic
component, and then construct high-order accurate semi-discrete entropy stable
DG schemes based on the quadrature rules and the entropy conservative and
stable fluxes. They satisfy the semidiscrete entropy inequality for the given
entropy pair and are integrated in time by using the high-order explicit strong
stability preserving Runge-Kutta schemes to get further the fully-discrete
nodal DG schemes. Extensive numerical tests are conducted to validate the
accuracy and the ability to capture discontinuities of our schemes. Moreover,
our entropy conservative flux is compared to an existing flux through some
numerical tests. The results show that the zero parallel magnetic component in
the numerical flux can help to decrease the error in the parallel magnetic
component in one-dimensional tests, but two entropy conservative fluxes give
similar results since the error in the magnetic field divergence seems
dominated in the two-dimensional tests.
