Actually, they have everything to do with it.

Hawking theorizes that prior to what we know as the "Big Bang" there was a period where matter was compressed into an infinitely small space, with such gravitational pull that even photons could not escape it. That being the typical definition of a black hole. He goes on to theorize that this black hole (though on a much larger scale) reached a critical mass and exploded, thus creating the universe.

Quote Hawking:

The Big Bang is like a black hole but on a much larger scale. By finding out how a black hole creates matter we may understand how the Big Bang created all the matter in the Universe.

It is not actually correct to refer to "the big bang theory." In fact, there have been at least five different theories, each of which has run into trouble. The first, as we have seen, was put forward in 1927 by Lemaître. This was soon refuted on a number of different grounds—incorrect conclusions drawn from general relativity and thermodynamics, a false theory of cosmic rays and stellar evolution, etc. After the Second World War, the discredited theory was revived by George Gamow and others in a new form. A number of calculations were advanced by Gamow and others, (incidentally, not without a certain amount of scientific "creative accountancy") to explain the different phenomena which would flow from the big bang—density of matter, temperature, radiation levels, and so on. George Gamow’s brilliant style of writing ensured that the big bang captured the popular imagination. Once again, the theory ran up against serious problems.

A whole number of discrepancies were found which invalidated, not only Gamow’s model, but the "oscillating universe" model subsequently worked out by Robert Dicke and others, in an attempt to get round the problem of what happened before the big bang, by making the universe oscillate in a never-ending cycle. But Gamow had made one important prediction—that such an immense explosion would leave behind evidence in the form of "background radiation," a kind of echo of the big bang in space. This was used to revive the theory some years later.

From the beginning there was opposition to the idea. In 1928 Thomas Gold and Hermann Bondi advanced the "steady state" as an alternative, later popularised by Fred Hoyle. While accepting the expanding universe, it attempted to explain it by the "continuous creation of matter from nothing." This was alleged to be happening all the time, but at a rate too slow to be detected by present-day technology. This means that the universe remains essentially the same for all time, hence the "steady state" theory. Thus matters went from bad to worse. From the "cosmic egg" to matter created out of nothing! The two rival theories slugged it out for over a decade.

The very fact that so many serious scientists were prepared to accept Hoyle’s fantastic notion that matter was being created out of nothing is itself absolutely astonishing. In the event, this theory was shown to be false. The steady state theory assumed the universe to be homogeneous in time and space. If the universe were in a "steady state" for all time, the density of a radio-emitting object ought to be constant, since the further we look out into space, the further back in time we see. However, observations showed that this was not the case; the further they looked out into space, the greater the intensity of the radio waves. This proved conclusively that the universe was in a constant state of change and evolution. It had not always been the same. The steady state theory was wrong.

In 1964, the steady state theory received the coup de grace with the discovery by two young astronomers in the USA, Arnas Penzias and Robert Wilson, of background radiation in space. This was immediately taken to be the "after-echo" of the big bang, predicted by Gamow. Even so, there were inconsistencies. The temperature of the radiation was found to be only 3.5°K, not the 20°K predicted by Gamow, or the 30°K predicted by his successor, P. J. E. Peebles. This result is even worse than it looks. Since the amount of energy in a field is proportional to the 4th power of its temperature, the energy of the observed radiation was actually several thousand times less than that predicted.

Robert Dicke and P. J. E. Peebles took over the theory where Gamow had left off. Dicke realised that there was a handy way of getting round the sticky question of what happened before the big bang, if only they could get back to Einstein’s idea of a closed universe. It could then be argued that the universe would expand for a time, then collapse to a single point (a "singularity"), or something near it, and then bounce back into expansion, in a kind of everlasting cosmic ping-pong game. The trouble was that Gamow had calculated the energy and density of the universe at levels just short of what would be needed to close the universe. The density was about two atoms per cubic meter of space; and the energy density, expressed as the predicted temperature of the background radiation, supposed to represent the remnants of the big bang, 20°K, i.e., 20 degrees above absolute zero. In fact, Gamow had fixed these figures in order to prove that the big bang produced heavy elements, something nobody now accepted. So Dicke unceremoniously ditched them, and selected new and equally arbitrary figures, which would fit in with his theory of a closed universe.

Dicke and Peebles predicted that the universe would be filled with radiation, mainly radio waves, with a temperature of 30°K. Later, Dicke claimed his group had predicted a temperature of 10°K, although this figure does not appear anywhere in his published notes, and is anyway a 100 times more than the observed result. This showed that the universe was more diffuse than Gamow had thought, with less gravity, which aggravated the basic problem of where all the energy for the big bang came from. As Eric Lerner points out:

"Far from confirming the Peebles-Dicke model, the Penzias-Wilson discovery clearly ruled out the closed oscillating model." (55) Thus arose a third version of the big bang—which became known as the standard model—an open universe in a permanent state of expansion.

Fred Hoyle did some detailed calculations, and announced that a big bang would produce only light elements—helium, deuterium and lithium (the latter two are actually quite rare). He calculated that if the density of the universe were about one atom per eight cubic metres, the amounts of these three light elements would be quite close to those actually observed. In this way, a new version of the theory was put forward which was nothing like the older theories. This no longer mentioned the cosmic rays of Lemaître, or the heavy elements of Gamow. Instead, the evidence put forward was the microwave background and three light elements. Yet none of this constitutes conclusive proof for the big bang. A major problem was the extreme smoothness of the background microwave radiation. The so-called irregularities in the background are so small that these fluctuations would not have had time to grow into galaxies—not unless there was a lot more matter (and therefore a lot more gravity) around than appears to be the case.

There were other problems, too. How does it come about that bits of matter flying in opposite directions all managed to reach the same temperature, and all at the same time (the "horizon" problem)? The partisans of the theory present the alleged origins of the universe as a model of mathematical perfection, all perfectly regular, a regular "Eden of symmetry whose characteristics conform to pure reason," as Lerner puts it. But the present universe is anything but perfectly symmetrical. It is irregular, contradictory, "lumpy." Not at all the stuff that well-mannered equations are made of down at Cambridge! One of the problems is why did the big bang not produce a smooth universe? Why did not the original simple material and energy just spread out evenly in space as an immense haze of dust and gas? Why is the present universe so "lumpy"? Where did all these galaxies and stars come from? So how did we get from A to B? How did the pure symmetry of the early universe give rise to the present irregular one we see before our eyes?

Do you want me to continue to prove you wrong?