  Magnetospheres of many astrophysical objects can be accurately described by
the low-inertia (or "force-free") limit of MHD. We present a new numerical
method for solution of equations of force-free relativistic MHD based on the
finite-difference time-domain (FDTD) approach with a prescription for handling
spontaneous formation of current sheets. We use this method to study the
time-dependent evolution of pulsar magnetospheres in both aligned and oblique
magnetic geometries. For the aligned rotator we confirm the general properties
of the time-independent solution of Contopoulos et al. (1999). For the oblique
rotator we present the 3D structure of the magnetosphere and compute, for the
first time, the spindown power of pulsars as a function of inclination of the
magnetic axis. We find the pulsar spindown luminosity to be L = (mu^2
Omega^4/c^3) (1+ sin^2(alpha)) for a star with the dipole moment "mu", rotation
frequency "Omega", and magnetic inclination angle "alpha". We also discuss the
effects of current sheet resistivity and reconnection on the structure and
evolution of the magnetosphere.
