Newton's Theory
In the field theoretic elaboration of Newtonian gravity, the central quantity is the gravitational potential, which obeys the Poisson equation
where is the mass density of any matter present. Note that this equation implies that in a vacuum solution, the potential is simply a harmonic function.
The tidal tensor is given by the traceless part
of the Hessian
where we are using the standard Cartesian chart for E3, with the Euclidean metric tensor
Using standard results in vector calculus, this is readily converted to expressions valid in other coordinate charts, such as the polar spherical chart
Read more about this topic: Tidal Tensor
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“Where the statue stood
Of Newton with his prism and silent face,
The marble index of a mind for ever
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—William Wordsworth (1770–1850)
“If my theory of relativity is proven correct, Germany will claim me as a German and France will declare that I am a citizen of the world. Should my theory prove untrue, France will say that I am a German and Germany will declare that I am a Jew.”
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