I'm working through A. Zee's new EGR book, and I came to a step on tidal forces I couldn't follow. He presents the gravitational potential(adsbygoogle = window.adsbygoogle || []).push({});

[itex]V(\vec{x})=-GM/r[/itex]

and asks us to verify that the tensor [itex]R^{ij}(\vec{x})\equiv\partial^{i}\partial^{j}V(\vec{x})[/itex] is, in this case,

[itex]R^{ij}=GM(\delta^{ij}r^{2}-3x^{i}x^{j})/r^{5}[/itex].

(From all context I can find within the chapter, his notation [itex]\partial^{i}[/itex] refers to [itex]\frac{\partial^{i}}{\partial x^{i}}[/itex]). Can anyone tell me how to derive this expression explicitly? I've experimented with a lot of differentiation but I can't figure out how to get the term with the 3 in it. All I can do is see that the formula does provide the result he wants, namely that

[itex]

R=\frac{GM}{r^3} \left( \begin{array}{ccc}

1 & 0 & 0 \\

0 & 1 & 0 \\

0 & 0 & -2 \end{array} \right)\

[/itex]

Many thanks!

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# Question about Newtonian Tensor from Zee's EGR book

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