What's the underlying principle to demonposite metrict fluctuation as scalar ,vector and tensor?(adsbygoogle = window.adsbygoogle || []).push({});

Is this decomposition complete?unique?

for scalar mode,

[tex]\begin{equation}

\delta g_{\mu \nu}=a^{2} \left( \begin{array}{cccc}

2\phi & -B,_{i} \\

-B,_{i} & 2(\psi \delta_{ij}-E,_{i,j})

\end{array}\right)

\end{equation}[/tex]

why should 00 term to be a "scalar"?but it is not a lorentz scalar?and why shoud 0i terms to look like a 3 vector? thank you.

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# Mathematical principle for decomposing metric fluctuation

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