  The phase velocity of light is co-parallel to the direction of energy flow in
classical vacuum. However, in certain uncommon materials, these two vectors can
be oppositely directed, in which case the phase velocity is termed `negative'.
This negative phase velocity (NPV) gives rise to many exotic phenomenons, such
as negative refraction, inverse Doppler shift and inverse Cerenkov radiation,
and has technological allure. According to quantum electrodynamics, the
presence of a magnetostatic field makes vacuum an anisotropic medium for the
passage of light. Under the influence of a sufficiently strong magnetostatic
field, vacuum supports NPV. Such ultrastrong magnetic fields are believed to
arise due to dynamo action in newborn neutron stars and in binary neutron star
mergers, for examples. In view of the possible occurrence of negative
refraction, the influence of ultrastrong magnetostatic fields must be carefully
taken into account in astronomical observations relating to neutron stars and
associated gamma-ray bursts.
