Bose–Einstein condensation in the Rindler space

Based on the Unruh effect, we calculate the critical acceleration of the Bose–Einstein condensation in a free complex scalar field at finite density in the Rindler space. Our model corresponds to an ideal gas performing constantly accelerating motion in a Minkowski space–time at zero-temperature, where the gas is composed of the complex scalar particles and it can be thought to be in a thermal-bath with the Unruh temperature. In the accelerating frame, the model will be in the Bose–Einstein condensation state at low acceleration; on the other hand, there will be no condensation at high acceleration by the thermal excitation brought into by the Unruh effect. Our critical acceleration is the one at which the Bose–Einstein condensation begins to appear in the accelerating frame when we decrease the acceleration gradually. To carry out the calculation, we assume that the critical acceleration is much larger than the mass of the particle.