Ex 4 of 4.9 "Spacetime and Geometry: an introduction to general relativity", Carroll :Show that the...

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Ex 4 of 4.9 "Spacetime and Geometry: an introduction to general relativity", Carroll :
Show that the energy-momentum tensors for electromagnetism and for scalar field theory satisfy the dominant energy condition, and thus also the weak, null, and null dominant conditions. Show that they also satisfy w > -1.

Robert · Accepted Answer

Ans. 
The equation for momentum tensor, 
1
( ( )
2
T g                 
The case for WEC is, 
0T U U    
Here, U

 is an a arbitrary non space like vector (null). 
If U

 is the null vector,

Ex 4 of 4.9 "Spacetime and Geometry: an introduction to general relativity", Carroll : Show that the energy-momentum tensors for electromagnetism and for scalar field theory satisfy the dominant...

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