in which both parameters $\lambda$ and $\Omega$ have a specific physical meaning, it will be the physics that will impose the functional dependence $\Omega(\lambda)$ in particular sub-cases.

Gauges in perturbation theory and the two–parameter case {#gauges}
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Let us consider for the moment a spacetime $\{g^{\rm b},\cM_{0}\}$ which we call the background, and a physical spacetime $\{g,\cM\}$ which we attempt to describe as a perturbation of $\{g^{\rm b},\cM_{0}\}$.[^4] In relativistic perturbation theory we are used to write expressions of the form g\_(x) = g\^[b]{}\_(x) +g\_(x), \[metricpert\] relating a perturbed tensor field such as the metric with the background value of the same field and with the perturbation. In doing this, we are implicitly assigning a correspondence between points of the perturbed and the background spacetimes [@bi:schutz]. Indeed through (\[metricpert\]), which is a relation between the images of the fields in ${\rm I\! R}^{m}$ rather than between the fields themselves on the respective manifolds $\cM$ and $\cM_{0}$, we are saying that there is a unique point $x$ in ${\rm I\! R}^{m}$ that is at the same time the image of [*two*]{} points: one (say $q$) in $\cM_{0}$ and one ($o$) in $\cM$. This correspondence is what is usually called a gauge 