If I make two rods with 1 meter length here on the surface of earth, and send one of them near a black hole that is at rest relative to earth, would I see the rod close to the black hole with a length shorter than 1 meter, (would the black hole rod be perceived as shorter than the rod here on earth)?
Then, if I go close to the rod near the black hole, would I see it with its original length, while the rod on earth would appear longer than 1 meter?
Below are some assumptions before we can discuss the problem:
Let assume that the bar is made with a very high youngs modulus and tensile strength material, so that the stretching/rupture due to tidal forces near the black hole be negligible when compared to the total length of 1 meter.
For calculus purposes, one should consider that the rod is "stationary", because the measurement will be made "instantly" at a given moment. (but we know that the rod will be circularly orbiting the black hole.)
The distance between the observer and the rod that is far away is known at any given moment, so that at first glance, the lenght will be measured using apparent angular size from a side view of the rod, not considering gavitational lensing (naive aproach).
The mass of the black hole and the distance between the rod that its near it and the black hole center is also known, so that in a second time, the length will still be measured using apparent angular size from a side view of the rod, but, considering the influences of the gravitational lensing.
The capacity to measure meter-scale lengths over cosmical distances should not be considered a problem, given that this question must be seen as a fundamental problem instead of a engineering one.
So, in short, my question is: Does matter (with known dimensions) in curved spacetime appears to have its dimensions distorted when viewed from a region with flat spacetime?