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

Click For Summary
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.
seonjunyoo
Messages
5
Reaction score
1
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?
 
Physics news on Phys.org
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.
 
Reply
  • Like
Likes Vanadium 50 and PeroK

Thread 'Question about Parallel Transport'

In this video I can see a person walking around lines of curvature on a sphere with an arrow strapped to his waist. His task is to keep the arrow pointed in the same direction How does he do this ? Does he use a reference point like the stars? (that only move very slowly) If that is how he keeps the arrow pointing in the same direction, is that equivalent to saying that he orients the arrow wrt the 3d space that the sphere is embedded in? So ,although one refers to intrinsic curvature...
View full post »

Similar threads

Undergrad Conservation of matter energy momentum tensor beyond GR
  • · Replies 3 ·
Replies
3
Views
2K
Questions about Properties of the Godel Metric
  • · Replies 6 ·
Replies
6
Views
2K
Undergrad Does potential energy curve spacetime?
  • · Replies 28 ·
Replies
28
Views
2K
Undergrad Deriving Weak-Field Schwarzschild Metric from LEFEs
  • · Replies 2 ·
Replies
2
Views
2K
Graduate Dirac on localization of energy in the gravitational field
  • · Replies 16 ·
Replies
16
Views
2K
Graduate Can gravitational energy be localized in the case of plane waves?
  • · Replies 8 ·
Replies
8
Views
2K
Graduate Dirac's integral for the energy-momentum of the gravitational field
  • · Replies 38 ·
2
Replies
38
Views
1K
Solving Dimensional Analysis Problems in Stress Energy Momentum Tensor
  • · Replies 38 ·
2
Replies
38
Views
5K
High School Does gravitational force act on system or its components?
  • · Replies 5 ·
Replies
5
Views
1K
Exotic stress-energy tensor and causality
  • · Replies 5 ·
Replies
5
Views
3K