Does it make a sense to define the Taylor expansion of the square of the distance function? If so, how can one compute its coefficients? I simply thought that the square of the distance function is a scalar function, so I think that one can write(adsbygoogle = window.adsbygoogle || []).push({});

$$

d^2(x,x_0)=d^2(x'+(x-x'),x_0)=d^2(x',x_0) + (x-x')^\mu\partial_\mu d^2(x',x_0)\\+1/2(x-x')^\mu(x-x')^\nu\nabla_\mu\partial_\nu d^2(x',x_0)+\dots

$$

Is this anywhere near correct?

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# Taylor expansion of the square of the distance function

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