# What would happen to a long ruler in a strong gravitational field?

So, let's say that we have an incredibly long, virtually indestructible ruler. We have advanced enough to move it wherever we want. Let's also say that we have another, identical ruler of the same length and other properties. If we put one of these rulers close to a black hole (remember, it's a really tough ruler) and another one parallel to it far away from the black hole (in empty space for our purposes), what would happen to the rulers with respect to one another? Let's say that the ruler next to the black hole is also suspended by a spaceship and is therefore not being sucked into the black hole. Would the endpoints of one ruler be closer together than the other? Would each 'tick' in the ruler in the gravitational field be closer to one another compared to the other ruler? I thought of this after reading about gravitational time dilation and I was curious about a length contraction (spacelike) analog. I am also just curious about just what happens to space in a gravitational field (using a ruler as a stand-in for space for the sake of intuition). Finally, to clarify, this is a non-charged, non-rotating black hole. Feel free to explain what would happen in these scenarios, but just a static, non-charged black hole is fine for a basic explanation.

• What about the fact the black hole curves space time? And how are you measuring it? Placing another ruler beside it? Aiming lasers from outside the black hole at each end and triangulating? Apr 8, 2021 at 3:06
• Vacuum solutions are Ricci flat meaning the volume of small spacetime balls is unchanged. So when time is dilated, length is radially contracted in the exact same proportion, as observed remotely. Your question is unclear, because "closer together" depends on who is measuring, where, and how. Apr 8, 2021 at 4:53