When we experiment with General Relativity on Earth, a tissue bends according to the experiment due to the placement of a mass, but of course there is a gravitational pull that causes bending. If we did the experiment outside the Earth, the tissue would not bend and the masses would not attract.
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The bending in your experiment is mainly due to the earth gravitational field. Outside earth, in the space, you can observe the same effect if you are in the attractive field of any other body such as the Sun, Jupiter, the Moon, ... or a black hole. There is nothing specific to the Earth field. Of course amount of bending will depend on the intensity of the gravitational field.
Jean-Louis
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