  The failure of frictional interfaces and the spatiotemporal structures that
accompany it are central to a wide range of geophysical, physical and
engineering systems. Recent geophysical and laboratory observations indicated
that interfacial failure can be mediated by slow slip rupture phenomena which
are distinct from ordinary, earthquake-like, fast rupture. These discoveries
have influenced the way we think about frictional motion, yet the nature and
properties of slow rupture are not completely understood. We show that slow
rupture is an intrinsic and robust property of simple non-monotonic
rate-and-state friction laws. It is associated with a new velocity scale
$c_{min}$, determined by the friction law, below which steady state rupture
cannot propagate. We further show that rupture can occur in a continuum of
states, spanning a wide range of velocities from $c_{min}$ to elastic
wave-speeds, and predict different properties for slow rupture and ordinary
fast rupture. Our results are qualitatively consistent with recent
high-resolution laboratory experiments and may provide a theoretical framework
for understanding slow rupture phenomena along frictional interfaces.
