Einstein metric and Space-time metric

  • Thread starter wam_mi
  • Start date
  • #1
81
0

Main Question or Discussion Point

Hi there,

I have a few queries and they are as follows:

(i) What is the difference between the Einstein metric and the Space-time metric?

(ii) What does the curvature of the metric really mean? Does one calculate the Riemann curvature tensor, but what does that really tell you if it ends up 'a constant divided by r squared'?

(iii) In the context of string theory, why is it that the space-time metric ceases to be well defined once the curvature of the string metric is of order the string scale?
 

Answers and Replies

  • #2
5,428
291
1. the Einstein metric is an example of a space-time metric. It is cosmological solution of the field equations.

2. The Riemann tensor in 4-D has 44 components. Do you mean the Riemann scalar ? If the scalar is as you describe it, it means that the curvature scalar decreases as 1/r2

3. Because the strings would bend. I suspect the strings need a locally flat space-time. The size of a locally flat patch decreases with the curvature.
 

Related Threads on Einstein metric and Space-time metric

  • Last Post
Replies
2
Views
1K
  • Last Post
Replies
8
Views
2K
  • Last Post
Replies
5
Views
2K
  • Last Post
Replies
1
Views
435
Replies
30
Views
8K
  • Last Post
2
Replies
49
Views
4K
Replies
6
Views
642
Replies
3
Views
551
  • Last Post
Replies
19
Views
7K
  • Last Post
Replies
1
Views
690
Top