One very interesting feature of his theories on black holes is that the concept of "imaginary time" is introduced to solve what happens at singularities, including black holes and even the big bang. Imaginary time is at right angles to real time, and behaves like a fourth spatial direction. Essentially, the time t is re-defined by turning it into an imaginary variable : t  it'

To the layman (or even some physicists when Hawking proposed this solution), this might sound like a mathematical gimmick, and not a feature of the real world, but many professionals (e.g. seismologists, circuit designers, audio engineers) use imaginary numbers to describe, analyze, and manipulate signals and waves. Hawking cites positivist philosophy to say that nobody actually can determine what is real and what is not. All we can do is find the equations that describe reality best.

Hawking applied imaginary time to the computation of path integrals that were difficult to solve when the time variable was real, due to the oscillating factors. By replacing time t with imaginary time, the equation transforms into something much easier to calculate. After it is solved, the time variable can be transformed back to real time through what is called a "wick rotation".
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