Which function whose graph looks like the space time around a black hole?

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What function has a graph that looks like this but i just want 2 dimensions enter image description here

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2 Answers

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$$\ln(|x|)$$ where $\ln$ is the logarithmic function to the base $e$, and $|x|$ is the absolute value of $x$.

$Graph of the function $\ln(|x|)$$

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Seems like a simple function of the form :$$\dfrac{-k}{x^{2}+y^{2}}$$

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