Is there any 2D surface whose metric tensor is eta?

  • #1
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16

Main Question or Discussion Point

Does there exist any 2D surface whose metric tensor is,
##\eta_{\mu\nu}=
\begin{pmatrix}
-1 & 0 \\
0 & 1
\end{pmatrix}##
 

Answers and Replies

  • #2
haushofer
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Yes. Two-dimensional flat spacetime. Or the worldsheet of a string. What are you looking for in particular?
 
  • #3
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Yes. Two-dimensional flat spacetime. Or the worldsheet of a string. What are you looking for in particular?
I am looking for a surface in 'space'.
 
  • #4
Orodruin
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Your question is unclear. If you are asking if you can get that metric on a two-dimensional surface induced by its embedding in a higher-dimensional Euclidean space, then no. The metric tensor induced by an embedding in a Riemannian space is going to be positive definite.
 
  • #5
haushofer
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I am looking for a surface in 'space'.
You mean ordinary space? But you have a Lorentzian signature. Seems to me like looking for complex Majorana spinors.
 

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