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

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

-

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

-
the graph have good resemblance with space time around black hole but the image you showed of graph ln(|x|) is ugly !! –  alugnis-eloh Dec 19 '13 at 13:35
@alugnis-eloh You can't expect it to look like Mona Lisa –  Torsten Hĕrculĕ Cärlemän Dec 19 '13 at 13:36
@alugnis-eloh That was just a screen-shot from Wolfram|Alpha, I would be happy if someone could render the graph of the function in question with Mathematica. –  user93957 Dec 19 '13 at 13:38

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

Graph example

-
Graph of it please! –  alugnis-eloh Dec 19 '13 at 13:32
and is k a variable or a constant? –  alugnis-eloh Dec 19 '13 at 13:35
@alugnis-eloh , updated –  Arjang Dec 19 '13 at 13:47