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

Question

What function has a graph that looks like this but i just want 2 dimensions

Answer 1

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

Answer 2

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

Graph example