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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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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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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. T
- 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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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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General Relativity: An Informal Primer. David Kaiser. Center for Theoretical Physics, MIT. 1 Introduction. General relativity, and its application to cosmological models such as in ation, is a remark-ably beautiful and elegant theory. Yet newcomers to the eld often face at least three types of challenges: conceptual, mathematical, and notational.
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,
