- #1

liu111111117

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- Homework Statement
- line element for Kottler-Møller coordinates

[tex] T = (x+\frac{1}{\alpha}) sinh(\alpha t) [/tex]

[tex] X = (x+\frac{1}{\alpha}) cosh(\alpha t) - \frac{1}{\alpha}[/tex]

Objective is to show that

[tex] ds^2 = -(1 +\alpha x)^2 dt^2 + dx^2 [/tex]

via finding dT and dX and inserting them into [tex] ds^2 = -dT^2 + dX^2 [/tex]

Incorrect attempt #1:

[tex] dT= (dx+\frac{1}{\alpha}) sinh(\alpha dt) [/tex]

Incorrect attempt #2:

[tex] dT= (\alpha x+1) cosh(\alpha t) [/tex]

[tex] X = (x+\frac{1}{\alpha}) cosh(\alpha t) - \frac{1}{\alpha}[/tex]

Objective is to show that

[tex] ds^2 = -(1 +\alpha x)^2 dt^2 + dx^2 [/tex]

via finding dT and dX and inserting them into [tex] ds^2 = -dT^2 + dX^2 [/tex]

Incorrect attempt #1:

[tex] dT= (dx+\frac{1}{\alpha}) sinh(\alpha dt) [/tex]

Incorrect attempt #2:

[tex] dT= (\alpha x+1) cosh(\alpha t) [/tex]