  In this paper, we consider the Einstein-massive gravity coupled to the
Yang-Mills gauge field in five dimensions. Concentrating on the static
solutions with planar horizon geometry, we explore the thermodynamic behavior
in the extended phase space and examine the validity of the first law of
thermodynamics besides local thermal stability by the Hessian matrix. We
observe that although the topology of boundary is planar, there exists the van
der Waals like phase transition for this kind of solution. We find the critical
quantities and discuss how the massive and Yang-Mills parameters affect them.
Furthermore, some signatures of the first order phase transition such as the
swallow-tail behavior of the Gibbs free energy and divergences of the specific
heat are given in detail. We continue with the calculation of the photon sphere
and the shadow observed by a distant observer. Finally, we use the WKB method
to investigate the quasinormal modes for scalar perturbation under changing the
massive and Yang-Mills parameters.

High Energy Physics - Theory;General Relativity and Quantum Cosmology