  We investigate the unequal mass relativistic bound state system, the $B_c$
mesons, in a light-front Hamiltonian formalism. We adopt an effective
Hamiltonian based on soft-wall light-front holography, together with a
longitudinal confinement that was first introduced for heavy quarkonium. We
also include the one gluon-exchange interaction with a running coupling, which
produces the spin structure. We present the mass spectrum and light-front wave
functions. We also use the light-front wave functions to calculate decay
constants, charge and momentum densities, as well as distribution amplitudes.
The results are compared with experiments and other theoretical approaches, all
of which are in reasonable agreement.
