Understanding E subscript R Notation in the Context of General Relativity

[robotkid786]

Homework Statement

It's not homework, it's a query about the book "spacetime and geometry"

Relevant Equations

F=GMm/r^2 e subscript r in brackets

All I know is that e subscript r must be a vector cos the book says so, but what does it mean, is it, a konstant in vector form? I'm confused by it (page one, chapter one spacetime and geometry by SeanCaroll)

Help is appreciated

Edit. Is vector r describing the curvature that takes place ?

 

[haruspex]

It's the unit vector in the radial direction, also written ##\hat r##.

 

[PeroK]

Homework Statement: It's not homework, it's a query about the book "spacetime and geometry"
Relevant Equations: F=GMm/r^2 e subscript r in brackets

All I know is that e subscript r must be a vector cos the book says so, but what does it mean, is it, a konstant in vector form? I'm confused by it (page one, chapter one spacetime and geometry by SeanCaroll)

Help is appreciated

Edit. Is vector r describing the curvature that takes place ?

That's Carroll's notation for a unit vector in the direction of separation of the masses. The more usual notation involves the position vectors of the two masses ##\vec r_1, \vec r_2##. In which case, the force on mass ##m_2## is:
$$\vec F_2 = \frac{Gm_1m_2}{|\vec r_1 - \vec r_2|^3}(\vec r_1 - \vec r_2)$$

 

[PeroK]

It's the unit vector in the radial direction, also written ##\hat r##.

That's not actually what Carroll means in this context.

 

[Delta2]

It's the unit vector in the radial direction, also written ##\hat r##.

If by radial direction you mean the direction of separation of masses M and m then ok, but if you mean the unit vector in polar, spherical or cylindrical coordinates, then you are not ok :D.

 

[haruspex]

If by radial direction you mean the direction of separation of masses M and m then ok, but if you mean the unit vector in polar, spherical or cylindrical coordinates, then you are not ok :D.

##e_r, e_\theta## are often used to denote unit vectors in the radial and tangential directions in polar coordinates. Likewise ##e_x## etc. in Cartesian. See e.g. https://www.chegg.com/homework-help...-z-r-right-rangle-unit-radial-vect-q114756124.

Per @PeroK, it seems that Sean Carroll is here, in effect, electing to take one of the masses as being at the origin.

 

[PeroK]

Per @PeroK, it seems that Sean Carroll is here, in effect, electing to take one of the masses as being at the origin.

It's actually his own slighty idiosynchratic notation. In any case, it's only the prelude and only the briefest summary of Newtonian gravity before he introduces the Einstein Field Equations.

 

[robotkid786]

So, does this mean. The hat notation is equivalent to the subscription notation here?

In which case, as above, the vector here being referred to is in reference to the circular distance between m and M?

Sorry if I'm getting it wrong. I havent even done vectors in my degree yet and I can hardly remember the topic either

 

[PeroK]

So, does this mean. The hat notation is equivalent to the subscription notation here?

In which case, as above, the vector here being referred to is in reference to the circular distance between m and M?

Sorry if I'm getting it wrong. I havent even done vectors in my degree yet and I can hardly remember the topic either

If you haven't studied vectors yet, you are wasting your time with a graduate textbook on GR. Moreover, you cannot seriously learn GR until you have mastered SR.

 

[Delta2]

The vector being referred is the unit vector in the direction of the line that connects the centers of the two masses.

If we consider a coordinate system in spherical or polar coordinates and we put its origin in mass M or the mass m, then the vector being referred is also the radial unit vector of the coordinate system.

 

[robotkid786]

Got you, thanks man

 

[Delta2]

If you haven't studied vectors yet, you are wasting your time with a graduate textbook on GR. Moreover, you cannot seriously learn GR until you have mastered SR.

Don't cut the wings of possibly I have to admit overambitious young students.