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

[arpon]

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

 

[haushofer]

Yes. Two-dimensional flat spacetime. Or the worldsheet of a string. What are you looking for in particular?

 

[arpon]

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'.

 

[Orodruin]

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.

 

[haushofer]

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.