  We study the low energy states of the t-J model with two holes on a 32-site
lattice with periodic boundary conditions. In contrary to common belief, we
find that the state with d_{x^2-y^2} symmetry is not always the ground state in
the realistic parameter range 0.2\le J/t\le 0.4. There exist low-lying
finite-momentum p-states whose energies are lower than the d_{x^2-y^2} state
when J/t is small enough. We compare various properties of these low energy
states at J/t=0.3 where they are almost degenerate, and find that those
properties associated with the holes (such as the hole-hole correlation and the
electron momentum distribution function) are very different between the
d_{x^2-y^2} and p states, while their spin properties are very similar.
Finally, we demonstrate that by adding ``realistic'' terms to the t-J model
Hamiltonian, we can easily destroy the d_{x^2-y^2} ground state. This casts
doubt on the robustness of the d_{x^2-y^2} state as the ground state in a
microscopic model for the high temperature superconductors.
