Einstein metric and Space-time metric

[wam_mi]

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?

 

[Mentz114]

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.