  In part I we study quantum modified photon trajectories in a Schwarzschild
blackhole spacetime. The photon vacuum polarization effect in curved spacetime
leads to birefringence, i.e. the photon velocity becomes c+/-dc depending on
its polarization. This velocity shift then results in modified photon
trajectories. In this work we give an introduction to this quantum effect in
relativity and we study its effects in Schwarzschild spacetime for critical
orbits. Some key results are that the critical orbits are shifted depending on
polarization and the event horizon remains fixed.
  In Part II we use the 2+1d Nambu-Jona-Lasino NJL model to study the
superfluid behaviour of two-dimensional quark matter. We begin with an
introduction to QCD its symmetries and the NJL model. We then go on to study
the 2+1d NJL model. We show that at high density the 2+1d NJL model represents
a relativistic gapless thin film BCS superfluid.
