Singularities can be found at black holes, where the density is infinite. Time cannot exist there. Also, if you travel at the speed of light, you yourself will not feel time (means time will not exist for you). Thus, your one second will be equal to infinite seconds in the universe.

Does time exist in space?

Einstein showed that time and space are intimately linked and that the progression of time is relative, not absolute. Although there is nothing in physics that says time must flow in a certain direction, scientists generally agree that time is a very real property of the Universe.

What is a place without time?

An anachronism is something that is out of place in terms of time or chronology.