I have a question about gravity -- If the value of the energy momentum tensor (Tμν) becomes zero, can it become gravitational-free?

[seonjunyoo]

R μν − 1/2g μν R= 8πG/c^4T μν

In this formula, if the value of the energy momentum tensor(Tμν) becomes zero, can it become gravitational-free?

 

[PeroK]

R μν − 1/2g μν R= 8πG/c^4T μν

In this formula, if the value of the energy momentum tensor(Tμν) becomes zero, can it become gravitational-free?

Only if it's zero everywhere. Think of electromagnetism. This is an EM field everywhere caused by a single charge.

 

[PeroK]

PS also, in the Schwartzschild black hole geometry, there is no stress-energy. It's a vacuum solution. There is however a characteristic mass and a singularity.

 

[seonjunyoo]

Only if it's zero everywhere. Think of electromagnetism. This is an EM field everywhere caused by a single charge.

Then, if the energy momentum tensor everywhere is zero, is it possible to assume that it is anti-gravity?

 

[Ibix]

Then, if the energy momentum tensor everywhere is zero, is it possible to assume that it is anti-gravity?

No, that's just empty space.