Abstract
It has been said that Newton was the first to state, with exemplary modesty, “If I have seen further it is only by standing on the shoulders of giants.” While we would place Newton and Einstein, as the ultimate giants at the very highest level of achievement in the history of physics, there is much wisdom and justification in Newton’s homage to earlier researchers. After all, the greatest advances were made with the help of important advances by those who preceded Newton and Einstein. Arguably the greatest of these was made by Copernicus who replaced the Earth with the Sun as the central body in what we now recognize as the Solar System.
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- 1.
Readers with a more mathematical bent might wish to see the explicit form of the field equations for spherical symmetry and how they are solved in [3].
- 2.
Setting \(c=1\) means that we are setting \(3.10^8\,\text{ m/s} = 1 \), a pure number. This implies that \(3.10^8\) \(\text{ m} = 1 \text{ s}\). What this means is that with this choice, we replace every second that appears by \(3.10^8\,\text{ m}\) in any subsequent point in the analysis. Similarly, setting \(G=1\) enables the replacement of every kilogram that appears by an appropriate number of meters. Thus, all quantities that follow are expressed in numbers of meters. While this procedure, highly favoured by relativists, might seem strange, it is really very sensible. Quite apart from simplicity of expression, it enables one to compare quantities meaningfully in terms of size as they all appear in terms of the same units, meters. In the end of the calculations, we can readily revert to conventional units if we wish.
- 3.
For the benefit of the more mathematically-inclined reader, the equation of motion is \(\frac{d^2(1/r)}{d{\phi }^2} + 1/r =\frac{M}{l^2} +\frac{3m}{r^2}\) where \(l\) is the angular momentum per unit mass of the planet.
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We will have more to say about the binary pulsar when we discuss gravity waves.
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This is a reminder to us of the importance of proper measures in Relativity.
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For simplicity, we consider here the case of a non-rotating body. Rotation injects additional complexity.
- 7.
S. Hawking has theorized that quantum-mechanically, black holes will actually evaporate particles that emerge to cross out of the \(r=2m\) sphere but the process is very slow for stellar-sized bodies.
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© 2012 Springer-Verlag Berlin Heidelberg
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Cooperstock, F.I., Tieu, S. (2012). Testing Einstein’s General Relativity. In: Einstein's Relativity. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-30385-2_5
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DOI: https://doi.org/10.1007/978-3-642-30385-2_5
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