  The energy of a particle in the Rainbow Rindler metric is derived using
Hamilton's variational principle. Saha Ionization equation and Pair production
in Rainbow Rindler metric have been investigated. Saha ionization equation and
Pair production in Rainbow Rindler metric depend on corrected acceleration
which is energy-dependent. This means energy ($E$) and metric tensor ($g_{\mu
\nu}(E)$) depends on the inertial observer.
  The physical implications of energy-dependent acceleration,
observer-dependent(inertial) energy and metric tensor are discussed. On
comparing the above results with that of Rindler metric we get the result
obtained by Sanchari De and Somenath Chakarabarthy by applying the
correspondence principle.
