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I have a very simple question about basis Four-Vectors and Components. In Hartle's book, Gravity, he uses the following equation to show the components of the 4-vector, a

a =a[tex]^t{}[/tex]e(sub t) + a[tex]^x{}[/tex]e(sub x) + a[tex]^y{}[/tex]e(sub y) + a[tex]^z{}[/tex]e(sub z)

Sorry for the half LaTex half something else but I couln't get the subscript LaTex command to work right. All it did was create another superscript.

Here is my question:

The e(subs) are a unit vector so there value should be -1 for the t component and 1 for the x, y, and z components correct?

For example, (this is problem 5.1)

The components of the 4-vector a[tex]^\alpha{}[/tex] are (-2,0,0,1)

Is a timelike, spacelike, or null?

The value of a[tex]\alpha[/tex] = -2(-1) + 0(1) + 0(1) + 1(1) = -1

Since -1 < 0, a is timelike.

Is the above correct ?

Thanks

Matt

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# Hartle Gravity - Simple basis vector question

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