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General relativity is the theory of space and time and gravity. The essence of the theory is simple: gravity is geometry. The effects that we attribute to the force of gravity are due to the bending and warping of spacetime, from falling cats, to orbiting spinning planets, to the motion of the cosmos on the grandest scale. The purpose of
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Introduction. General Relativity is the classical theory that describes the evolution of systems under the e ect of gravity. Its history goes back to 1915 when Einstein postulated that the laws of gravity can be expressed as a system of equations, the so-called Einstein equations.
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The general theory of relativity, together with the necessary parts of the theory of invariants, is dealt with in the author’s book Die Grundlagen der allgemeinen Relativitätstheorie (The Foundations of the General Theory of Relativity) — Joh. Ambr. Barth, 1916; this book assumes some familiarity with the special theory of relativity. v
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- Prologue
- (F 1o )0 = L1 L o ̄ F ® ̄ : (1.13)
- M(2) M(1)
- Curvature
- R 1o® ̄ = ¡R o1® ̄ = R ® ̄1o :
- R 1o = R o1 ;
- 9. Special coordinates.
General relativity is a beautiful scheme for describing the gravitational ̄eld and the equations it obeys. Nowadays this theory is often used as a prototype for other, more intricate constructions to describe forces between elementary particles or other branches of fundamental physics. This is why in an introduction to general relativity it is of ...
It is of importance to realize what this implies: although we have the well-known postulate that an experimenter on a moving platform, when doing some experiment, will ̄nd the same outcomes as a colleague at rest, we must rearrange the results before comparing them. What could look like an electric ̄eld for one observer could be a superposition o...
inert inert These objects would show di®erent accelerations ~ a and this would lead to e®ects that can be detected very accurately. In a space ship, the acceleration would be determined by the material the space ship is made of; any other kind of material would be accel-erated di®erently, and the relative acceleration would be experienced as a weak...
As for the Riemann curvature tensor de ̄ned in the previous chapter, we can now raise and lower all its indices:
By contracting two indices one obtains the Ricci tensor:
We can contract further to obtain the Ricci scalar,
In the preceding chapters no restrictions were made concerning the choice of coordinate frame. Every choice is equivalent to any other choice (provided the mapping is one-to-one and di®erentiable). Complete invariance was ensured. However, when one wishes to cal-culate in detail the properties of some particular solution such as space-time surround...
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Lecture Notes on General Relativity Sean M. Carroll Institute for Theoretical Physics University of California Santa Barbara, CA 93106 carroll@itp.ucsb.edu December 1997 Abstract These notes represent approximately one semester’s worth of lectures on intro-ductory general relativity for beginning graduate students in physics. Topics include
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ing with general relativity, which requires some practice to really get comfortable with. The methods are quite powerful and well worth the investment of e ort. One can only really hope to tackle the fascinating conceptual and mathematical challenges if one has rst gotten over the hurdle of understanding how to parse and manipulate the formalism.
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general theory of relativity. Only a few parts, including the treatment of the stress-energy tensor are adapted in accordance with later reformulations of the theory, and contravariant coordinates are consistently labeled by superscripts. In comparison with the special theory of relativity, which applies in flat spacetime,
