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The two largest contributions that come to mind are both in the realm of general relativity. The first is his contribution to the singularity theorems. These are purely general relativistic results (i.e. no quantum mechanics involved), and they mathematically prove that generically one expects to find singularities in spacetime. That is, except in somewhat ...


26

You can check this yourself using this very long link which will give you a list of Hawking's work that has been published in refereed journals, ordered by the number of times they have been cited in other papers (a measure of how influential they are on other scientists). This is a way of providing at least some non-opinion based answer to this question. ...


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Fluctuations of density in the universe naturally become greater with time because matter is attracted to regions that are denser than average, and as a result they get denser still and the other regions less dense. So if there were even tiny density fluctuations in the early universe they would have grown into the density variations we see today - ...


4

First off, spherical symmetry isn't really the best description. Cosmological models usually assume that the universe is (approximately) homogeneous and isotropic. That's a higher degree of symmetry than spherical symmetry. Spherical symmetry would normally be used to describe something that has a lower degree of symmetry, so that there is a center. The ...


1

One can treat the spacetime coordinates as complex and therefore turn spacetime integrals into contour integrals in the complex plane. The value of the integral of a function that is holomorphic except at certain (singular) points is now determined by its singularity structure: the Cauchy's residue theorem tells us that the integral is given solely in terms ...



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