Raising indices on the alternating tensor with the metric

[binbagsss]

Q) I am using index notation to show that ε$^{0123}$=-1 given that ε$_{0123}$=1.

The soluton is:

ε$^{0123}$=g$^{00}$g$^{11}$g$^{22}$g$^{33}$ε$_{0123}$=-ε$_{0123}$

where g$_{\alpha\beta}$ is the metric tensor.

I am struggling to understand the last equality.

Many thanks for any assistance.

 

[Dick]

Q) I am using index notation to show that ε$^{0123}$=-1 given that ε$_{0123}$=1.

The soluton is:

ε$^{0123}$=g$^{00}$g$^{11}$g$^{22}$g$^{33}$ε$_{0123}$=-ε$_{0123}$

where g$_{\alpha\beta}$ is the metric tensor.

I am struggling to understand the last equality.

Many thanks for any assistance.

Look up the definition of the metric tensor you are using and insert the values of the g components.

 

[HallsofIvy]

If you are using the standard metric tensor for relativity then $g^{11}= g^{22}= g{33}= -1$ while $g^{00}= 1$.