#### PeterDonis

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**Re: "Locally Lorentz"**

But this transformation, if it is to be valid globally in a curved spacetime, cannot be a Lorentz transformation. If you insist on writing it in the form you gave, then the coefficients [itex]\beta[/itex] and [itex]\gamma[/itex] will vary from event to event in a curved spacetime (i.e., in the presence of gravity). A global Lorentz transformation must have constant coefficients.While the "globally lorentz" behavior applies to the global coordinates

[tex]\begin{pmatrix}

c t_{global}'

\\

x_{global}'

\end{pmatrix}=

\begin{pmatrix}

\gamma & -\beta \gamma \\

-\beta \gamma & \gamma

\end{pmatrix}

\begin{pmatrix}

c t_{global}

\\

x_{global}

\end{pmatrix}[/tex]