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
Voyaging through strange seas of thought, alone.”
—William Wordsworth (1770–1850)
“There could be no fairer destiny for any physical theory than that it should point the way to a more comprehensive theory in which it lives on as a limiting case.”
—Albert Einstein (1879–1955)