There is an extensive literature on special and general relativity, and the spacetime-based
view2
of the laws of physics. For the student at any level interested in developing a working understanding we
recommend Taylor and Wheeler [109] for an introduction, followed by Hartle’s excellent recent text [51]
designed for students at the undergraduate level. For the more advanced students, we suggest two of the
classics, “MTW” [80] and Weinberg [117
], or the more contemporary book by Wald [114
].
Finally, let us not forget the Living Reviews archive as a premier online source of up-to-date
information!
In terms of the experimental and/or observational support for special and general relativity, we recommend
two articles by Will that were written for the 2005 World Year of Physics celebration [122, 121
]. They
summarize a variety of tests that have been designed to expose breakdowns in both theories. (We also
recommend Will’s popular book Was Einstein Right? [119] and his technical exposition Theory
and Experiment in Gravitational Physics [120
].) To date, Einstein’s theoretical edifice is still
standing!
For special relativity, this is not surprising, given its long list of successes: explanation of the
Michaelson–Morley result, the prediction and subsequent discovery of anti-matter, and the standard model
of particle physics, to name a few. Will [122] offers the observation that genetic mutations via cosmic rays
require special relativity, since otherwise muons would decay before making it to the surface of the Earth.
On a more somber note, we may consider the Trinity site in New Mexico, and the tragedies of Hiroshima
and Nagasaki, as reminders of
.
In support of general relativity, there are Eötvös-type experiments testing the equivalence of inertial
and gravitational mass, detection of gravitational red-shifts of photons, the passing of the solar
system tests, confirmation of energy loss via gravitational radiation in the Hulse–Taylor binary
pulsar, and the expansion of the Universe. Incredibly, general relativity even finds a practical
application in the GPS system: If general relativity is neglected, an error of about 15 meters
results when trying to resolve the location of an object [122]. Definitely enough to make driving
dangerous!
The evidence is thus overwhelming that general relativity, or at least something that passes the same
tests, is the proper description of gravity. Given this, we assume the Einstein Equivalence Principle,
i.e. that [122, 121, 120]
If the Equivalence Principle holds, then gravitation must be described by a metric-based theory [122]. This means that
For our present purposes this is very good news. The availability of a metric means that we can develop the theory without requiring much of the differential geometry edifice that would be needed in a more general case. We will develop the description of relativistic fluids with this in mind. Readers that find our approach too “pedestrian” may want to consult the recent article by Gourgoulhon [49], which serves as a useful complement to our description.
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