  We investigate the phenomenon of gravity-induced entanglement in
optomechanical systems. Assuming photon number conservation and the Newtonian
potential expanded up to the quadratic order of the oscillator positions, we
exactly solve the dynamics of the optomehcanical systems. Then, we find that
the phase difference due to the Newtonian gravity leads to the large
entanglement of photons in separated cavities. We clarify the generating
mechanism of large gravity-induced entanglements in optomechanical systems in
an exact manner. We also determine the characteristic time to generate the
maximal entanglement of photons. Finally, by comparing the characteristic time
with the decoherence time due to photon leakage, we evaluate the range of the
dissipation rate required for testing the gravity-induced entanglement.
