  In this thesis, the connections between thermodynamics and general relativity
are explored. We review the concept of gravitationally induced temperature
gradients in equilibrium states, first introduced by Richard Tolman. We explore
these Tolman-like temperature gradients, understanding their physical origin
and whether they can be generated by other forces or not. We then generalize
this concept for fluids following generic four-velocities, which are not
necessarily generated by Killing vectors, in general stationary space-times.
  We then move to a more fundamental question: can we still define thermal
equilibrium for non-Killing flows? To answer this we review two of the main
theories of relativistic non-perfect fluids: Classical Irreversible
Thermodynamics and Extended Irreversible Thermodynamics. We also take a tour
through the interesting concept of Born-rigid motion, showing some explicit
examples of non-Killing rigid flows for Bianchi Type I space-times. These
results are important since they show that the Herglotz--Noether theorem cannot
be extended for general curved space-times. We then connect the Born-rigid
concept with the results obtained by the relativistic fluid's equilibrium
conditions and show that the exact thermodynamic equilibrium can only be
achieved along a Killing flow. We do, however, introduce some interesting
possibilities which are allowed for non-Killing flows.
  Following, we launch into black hole thermodynamics, specifically studying
the trans-Planckian problem for Hawking radiation. We construct a kinematical
model consisting of matching two Vaidya spacetimes along a thin shell and show
that, as long as the Hawking radiation is emitted only a few Planck lengths (in
proper distance) away from the horizon, the trans-Plackian problem can be
avoided.
