  Carbon at extreme conditions is the focus of intensive scientific inquiry due
to its importance for applications in inertial confinement fusion experiments
and for understanding the interior structure of carbon-rich exoplanets. The
extreme metastability of diamond at very high pressures has been discovered in
recent dynamic compression experiments. This work addresses an important
question about the existence of other competitive metastable carbon phases that
might be observed in shock experiments. It was found that diamond polytypes,
carbon crystals with mixed cubic and hexagonal diamond stacking planes, are the
only metastable carbon crystal phases energetically competitive with cubic
diamond at pressures between 100 and 1,000 GPa. Above 1 TPa, no metastable
phases are found to be energetically competitive with thermodynamically stable
BC8 and simple cubic phases. The existence of low enthalpy diamond polytypes
suggests that they are likely candidates for metastable phases of carbon to
appear upon shockwave loading of diamond.
