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

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If the energy momentum tensor (Tμν) is zero everywhere, it indicates a gravitational-free state, akin to a vacuum solution in general relativity. However, this does not imply the presence of anti-gravity; it simply represents empty space without mass or energy. The discussion draws parallels to electromagnetism, where a field exists due to a charge, but in the absence of energy momentum, no gravitational effects are present. The Schwarzschild black hole geometry exemplifies this, as it describes a vacuum solution with no stress-energy but still possesses a singularity. Ultimately, a zero Tμν signifies a lack of gravitational influence rather than an anti-gravitational effect.
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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?
 
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seonjunyoo said:
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.
 
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.
 
PeroK said:
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?
 
seonjunyoo said:
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.
 
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