- #1
Logarythmic
- 281
- 0
I have been told that using a metric
[tex]g_{00} = -a^2(\eta)(1+2\psi)[/tex]
[tex]g_{oi} = g_{i0} = a^2(\eta)\omega_i[/tex]
[tex]g_{ij} = a^2(\eta) \left[(1+2\phi)\gamma_{ij} + 2\chi_{ij} \right][/tex]
and a gauge transformation
[tex]x^{\bar{\mu}} = x^{\mu} + \xi^{\mu}[/tex]
with
[tex]\xi^0 = \alpha[/tex]
[tex]\xi^i = \beta^j[/tex]
gives the changes in the amplitude as
[tex]\delta \psi = \alpha' + \frac{a'}{a} \alpha[/tex]
and so on.
But how do I calculate these changes? How do I start?
[tex]g_{00} = -a^2(\eta)(1+2\psi)[/tex]
[tex]g_{oi} = g_{i0} = a^2(\eta)\omega_i[/tex]
[tex]g_{ij} = a^2(\eta) \left[(1+2\phi)\gamma_{ij} + 2\chi_{ij} \right][/tex]
and a gauge transformation
[tex]x^{\bar{\mu}} = x^{\mu} + \xi^{\mu}[/tex]
with
[tex]\xi^0 = \alpha[/tex]
[tex]\xi^i = \beta^j[/tex]
gives the changes in the amplitude as
[tex]\delta \psi = \alpha' + \frac{a'}{a} \alpha[/tex]
and so on.
But how do I calculate these changes? How do I start?