# I Measuring the mass of an object near the event horizon of a black hole and observing the results at a distance

#### metastable

It isn't. It is hanging radially, and the only motion involved is the slow unrolling of the string as the object is lowered. All motion is purely radial.
If this is the description of the scenario, won't the person doing the "lowering" "plummet" "like a rock"?

#### PeterDonis

Mentor
won't the person doing the "lowering" "plummet" "like a rock"?
No. They are assumed to be supported by something; since the central mass is a black hole, the support would presumably be a rocket or something similar that could exert thrust to hold itself stationary. The person doing the lowering is assumed to be very far away from the hole, so the thrust required to remain stationary is minimal.

#### metastable

No. They are assumed to be supported by something; since the central mass is a black hole, the support would presumably be a rocket or something similar that could exert thrust to hold itself stationary. The person doing the lowering is assumed to be very far away from the hole, so the thrust required to remain stationary is minimal.
So in the scenario, we are saying the amount of thrust required to "remain stationary" isn't the amount of thrust it would take to keep an "untethered" "lowerer" stationary with respect to the black hole at that coordinate, plus the additional force exerted on the "lowerer" through the string?

#### PeterDonis

Mentor
So in the scenario, we are saying the amount of thrust required to "remain stationary" isn't the amount of thrust it would take to keep an "untethered" "lowerer" stationary with respect to the black hole at that coordinate, plus the additional force exerted on the "lowerer" through the string?
No, it is the sum of those two things. The force exerted at the lowerer's position due to the tether having to support the object being lowered is redshifted, so it does not increase without bound as the object at the lower end of the tether approaches the horizon.

You are correct, though, that unless the black hole is supermassive, the thrust required to hold station even at a very large distance, once the force on the tether is included, will not be "minimal". Since this is a thought experiment, a large amount of thrust being required is not a problem.

#### metastable

No, it is the sum of those two things. The force exerted at the lowerer's position due to the tether having to support the object being lowered is redshifted, so it does not increase without bound as the object at the lower end of the tether approaches the horizon.

You are correct, though, that unless the black hole is supermassive, the thrust required to hold station even at a very large distance, once the force on the tether is included, will not be "minimal". Since this is a thought experiment, a large amount of thrust being required is not a problem.
Does this not imply then that the "lowerer" will always be using more power in the experiment than is "gained" back via the tether?

#### PeterDonis

Mentor
Does this not imply then that the "lowerer" will always be using more power in the experiment than is "gained" back via the tether?
So far we have been ignoring any power requirements for exerting thrust. This is typical for these kinds of thought experiments.

Since this thread is about how we would measure the mass of the object being lowered, not about whether any net energy can be extracted from the lowering process once the energy requirements for holding station are included, ignoring the power required to exert thrust for this thread does not seem objectionable. If you want to discuss the net energy extraction question, it would be fine to start a separate thread on that topic.

#### Heikki Tuuri

https://en.wikipedia.org/wiki/Ultimate_tensile_strength
I calculated a practical example. Make a 1 x 1 millimeter^2 thick tether of graphene and put it between the Moon and the surface of Earth.

Its mass is 380 metric tons, weight 60,000 newtons, and it can lift a load of 7 tons from Earth.

The redshift from the surface of Earth is less than 10^-9. That is too small. We cannot measure the increase in the inertial mass of the 7 ton load.

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"Measuring the mass of an object near the event horizon of a black hole and observing the results at a distance"

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