  Time metamaterials exhibit a great potential for wave manipulation, drawing
increasing attention in recent years. Here, we explore the exotic wave dynamics
in an anisotropic photonic time crystal (APTC), formed by an anisotropic medium
whose optical properties are uniformly and periodically changed in time. Based
on a temporal transfer matrix formalism, we show that a stationary charge
embedded in an APTC can emit radiation, in contrast to the case of an isotropic
photonic time crystal, and its distribution in momentum space is controlled by
the APTC band structure. Our approach extends the functionalities of time
metamaterials, offering new opportunities for simultaneous radiation generation
and control, with implications for both classical and quantum applications.
