- #1
CFDFEAGURU
- 783
- 10
Helo all,
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
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
Last edited: