Transformation on the minkowsky metric

Thread starter michiherlin
Start date Jan 13, 2011
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Metric Transformation

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A linear bijective map T from R^4 to R^4 that preserves the light cone must maintain the structure of the Minkowski metric. To show that T* ds^2 = (constant)^2 * ds^2, one can utilize the properties of Lorentz transformations, which are known to preserve the light cone and the form of the metric. The key is to demonstrate that T acts as a scaling transformation on the metric, leading to the conclusion that the pullback of the Minkowski metric is proportional to the original metric. Further insights or detailed steps are requested to solve the problem. The discussion emphasizes the need for guidance in applying these concepts to the specific problem presented.

Jan 13, 2011

michiherlin

hi,

in my textbook there ist a problem, i cannot solve: let T be a linear bijective map from R^4 to R^4, which preserves the light cone. show: T* ds^2 = (constant)^2 * ds^2, where ds^2 ist the minkowsky metric and T* ist the pullback of the metric.

can someone show how to do it.

michiherlin

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Jan 13, 2011

michiherlin

hi,
does anyone have a hint for me :)?

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