Graduate Covariant Derivative of Stress Energy Tensor of Scalar Field on Shell

Click For Summary
The discussion revolves around proving a specific formula related to the covariant derivative of the stress-energy tensor of a scalar field on a shell. The original poster shares their work and seeks feedback on potential errors in their approach. Participants are encouraged to provide insights or corrections to assist in the proof. The moderator has elevated the thread's importance level. Clarifications and collaborative problem-solving are central to the conversation.
thatboi
Messages
130
Reaction score
20
Hi all,
I am currently trying to prove formula 21 from the attached paper.
My work is as follows:
1.PNG


If anyone can point out where I went wrong I would greatly appreciate it! Thanks.
 

Attachments

Physics news on Phys.org

Thread 'Can a Gyroscope in a Satellite Detect Orbit?'

Einstein said, when describing someone falling off a building, that the Earth accelerating up to meet him/her. Without the Earth getting larger in all directions as the paradox goes, it curvature of space-time which is why you can have the acceleration up without the surface moving up as you follow a geodesic path. Any deviation from that geodesic will requires a force which is what causes you to have weight on a scale on earth. However, what if we consider an orbiting satellite which is...
View full post »

Similar threads

High School Prove that metric tensor is covariant constant
  • · Replies 11 ·
Replies
11
Views
1K
Undergrad Ricci Tensor: Covariant Derivative & Its Significance
  • · Replies 6 ·
Replies
6
Views
2K
Graduate Einstein Tensor and Stress Energy Tensor of Scalar Field
  • · Replies 4 ·
Replies
4
Views
3K
Undergrad Contracting the stress energy tensor
  • · Replies 33 ·
2
Replies
33
Views
4K
Undergrad Commutation between covariant derivative and metric
  • · Replies 16 ·
Replies
16
Views
4K
Graduate Weyl tensor and coordinate acceleration
  • · Replies 12 ·
Replies
12
Views
2K
High School Special Cases of Stress-Energy Tensor in GR
  • · Replies 10 ·
Replies
10
Views
2K
High School Understanding the Stress-Energy Tensor & Solar Mass in General Relativity
  • · Replies 14 ·
Replies
14
Views
2K
Undergrad Question about Stress-Energy Tensor: A First Course in GR
  • · Replies 8 ·
Replies
8
Views
2K
Undergrad Calculating Covariant Derivative of Riemann Tensor in Riemann Normal Coordinates
  • · Replies 5 ·
Replies
5
Views
2K