  A large class of quantum theories of gravity show that the Heisenberg's
uncertainty principle is modified to the "Generalised Uncertainty Principle"
(GUP) near the Planckian scale. It has also been shown that the GUP induces
perturbative corrections to all quantum mechanical Hamiltonians, even at low
energies, and thereby introduces Planck scale corrections to the Schr\"odinger
equation and to the relativistic quantum mechanical equations. Some of these
corrections give rise to potentially measurable effects in the low-energy
laboratory. Another prediction of these corrections is that a measured length
must be quantized, as seen by studying the solutions of the GUP modified
Schr\"odinger, Klein-Gordon, and Dirac equations in a one, two, and three
dimensional box. This result was subsequently extended to spacetimes with weak
gravitational fields. In this work, we further extend this length quantization
to spacetimes with strong gravitational fields and show that this result
continues to hold, thereby showing that it is robust.
