Abstract
Understanding special relativity is a prerequisite for understanding general relativity. In this chapter, we review special relativity and introduce the basic notation for describing flat spacetime in terms of general curvilinear coordinates. We also review Newtonian gravity so that it can later serve as a useful limiting case in the context of the Einstein field equations.
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Notes
- 1.
Galilei, Galileo, Italian mathematician, physicist and philosopher, *Pisa 15.2.1564, †Arcetri (today a part of Florence) 8.1.1642.
- 2.
Lorentz, Hendrik Antoon, Dutch physicist, *Arnheim 18.7.1853, †Haarlem 4.2.1928; Nobel Prize in physics 1902 together with P. Zeeman.
- 3.
This connection is made in electrodynamics.
- 4.
The only requirement is that the velocity along an alternative path is less then 1.
- 5.
In the remainder of this subsection upstairs numbers are exponents and not indices!.
- 6.
The following is adopted from [4].
- 7.
In examples involving the Earth’s gravitation, we shall always approximate Earth as a radially symmetric mass distribution.
- 8.
The reason for putting indices downstairs instead of upstairs will be explained in the next section. Here we merely adhere to the rule that summation over paired indices requires one index to be downstairs (e.g. \({}_\alpha \)) and the other one to be upstairs (e.g. \({}^\alpha \)).
- 9.
We consider this experiment ‘remarkable’, because it made general relativity effects tangible.
- 10.
Mössbauer, Rudolf, German physicist, *Munich 31.1.1929 , †Grünwald 14.9.2011; Nobel Prize in physics 1961.
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Hentschke, R., Hölbling, C. (2020). Review of Concepts and Some Extensions Thereof. In: A Short Course in General Relativity and Cosmology. Undergraduate Lecture Notes in Physics. Springer, Cham. https://doi.org/10.1007/978-3-030-46384-7_2
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