In general relativity, the existence of space-time singularities plays a central role on the notion of black holes and the expanding universe. However, these two speculations have not been firmly verified in spite of the efforts of generations of physicists. The existence of space-time singularities is due to the spacetime singularity theorems of Hawking and Penrose, whose implicit physical assumption is the general validity of E = mc2 that leads to the unique sign for all the couplings. However, recently it is found that such an assumption is not supported by various experiments. In particular, the electromagnetic energy is not equivalent to mass. In fact, the Einstein equation with massive sources has no dynamic solution unless the gravitational energystress tensor with an anti-gravity coupling is added to the source.