Large-scale structure of space-time

Author: (UK) S·W·Hawking, (South Africa) G·F·R·Einstein/Nationality: Mainland China
Publisher:
Publishing Date: 2006-06-01
Features: Up to this point, we have not considered the relationship between exact solutions and the physical universe. Following Einstein's line of thought, we ask, can we find a certain spacetime as an exact solution of an appropriate form of a material field, which can well explain the large-scale properties of the observable universe? If the answer is affirmative, then we can claim to have a reasonable "cosmological model" or a model of the physical universe. However, without synthesizing and selecting some existing ideas, we cannot construct a cosmological model. In early cosmology, humans placed themselves at the center of the universe as its master. Since the time of Copernicus, our status has been reduced to that of a medium-sized planet orbiting a medium-sized star at the edge of a medium-sized galaxy, and this galaxy itself is merely a member of a local group of galaxies. In reality, we have little to be proud of today, no longer claiming that our position in space has any significant special meaning. As Bondi (1960) put it, we call this assumption the Copernican principle. A reasonable interpretation of this somewhat ambiguous principle is to understand it as meaning that, from some appropriate scale, the universe is approximately uniform in space. Here, the uniformity of space refers to the existence of a free acting on M. isometric transformation group, whose transitive surfaces are three-dimensional spacelike surfaces. In other words, any point on these surfaces is equivalent to any other point on the same surface. Of course, the universe is not strictly spatially uniform, and there are local inhomogeneities such as stars and galaxies. Nevertheless, we can reasonably assume that the universe is spatially uniform on sufficiently large scales. Although we can construct mathematical models that satisfy this uniformity requirement (see the next section), directly verifying this uniformity through observation is extremely difficult, as there is no simple method to measure the distance between us and distant celestial bodies. This difficulty can be overcome because, in principle, we can easily observe isotropy (i.e., whether the observations in different directions are the same) in the study of extragalactic star systems, and isotropy is closely related to uniformity. The results of isotropy observations to date indicate that the universe around us is approximately spherically symmetric. In particular, observations show that the distribution of extragalactic radio sources is approximately isotropic, and the most recent observations of the cosmic microwave background radiation are also highly isotropic in the regions we have detected (further discussion see Chapter 10). We can certainly write and verify the metrics of all spherically symmetric spacetimes, especially the Schwarzschild and Reissner-Nordstr?m solutions (see §5.5), but they are all asymptotically flat spaces. Generally speaking, a spherically symmetric space may exist at most at two points, from which the space appears spherically symmetric. Although they can serve as models of spacetime near massive celestial bodies, they can only be models consistent with isotropy as seen from a very special position. The exception is those models where the universe is isotropic at every point in spacetime. Therefore, we should interpret the Copernican principle as meaning that the universe is approximately spherically symmetric with respect to every point (because it is approximately spherically symmetric to us). P123-124