Einstein metric and Space-time metric

In summary, the conversation covers three topics: the difference between Einstein metric and Space-time metric, the meaning of curvature in the metric, and the impact of string curvature on space-time metric in string theory. The Einstein metric is a specific example of a space-time metric and is a cosmological solution. The Riemann curvature tensor has 44 components in 4-D, and if the Riemann scalar decreases as 1/r2, it means the curvature decreases with distance. In the context of string theory, the space-time metric becomes undefined when the curvature of the string metric is of the same order as the string scale due to the bending of strings and the need for a locally flat space-time.
  • #1
wam_mi
81
1
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?
 
Physics news on Phys.org
  • #2
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.
 

1. What is the Einstein metric?

The Einstein metric, also known as the Einstein-Hilbert metric, is a mathematical concept used in the theory of general relativity. It describes the curvature of space-time caused by the presence of massive objects.

2. How does the Einstein metric differ from the space-time metric?

The Einstein metric is a specific solution to the more general space-time metric, which describes the overall geometry of space-time. While the space-time metric includes all possible solutions, the Einstein metric is a specific solution that satisfies the equations of general relativity.

3. What is the significance of the Einstein metric in physics?

The Einstein metric is significant because it is the foundation of general relativity, which is one of the most successful theories in modern physics. It explains the force of gravity as the curvature of space-time caused by massive objects, and has been confirmed by numerous experiments and observations.

4. Can the Einstein metric be applied to all objects in the universe?

Yes, the Einstein metric can be applied to all objects in the universe. It is a universal concept that describes the curvature of space-time caused by any type of matter or energy, from planets and stars to galaxies and black holes.

5. How does the Einstein metric relate to the theory of special relativity?

The Einstein metric is a direct result of the theory of special relativity, which describes the relationships between space and time for objects moving at constant speeds. General relativity, which incorporates the Einstein metric, builds upon the principles of special relativity to explain gravity and the curvature of space-time.

Similar threads

  • Special and General Relativity
Replies
5
Views
821
  • Special and General Relativity
Replies
16
Views
1K
  • Special and General Relativity
Replies
12
Views
1K
  • Special and General Relativity
Replies
2
Views
915
  • Special and General Relativity
Replies
12
Views
2K
  • Special and General Relativity
Replies
18
Views
1K
  • Special and General Relativity
3
Replies
95
Views
4K
  • Special and General Relativity
Replies
14
Views
1K
  • Special and General Relativity
Replies
3
Views
1K
  • Special and General Relativity
Replies
2
Views
1K
Back
Top