Is the Schwarzschild metric dimensionless?

[help1please]

Homework Statement

The problem is I am wanting to know if the expression on the right hand side is dimensionless.

Homework Equations

$$ds^2 = (1 - \frac{2GM}{c^2 r})c^2 dt^2$$

The Attempt at a Solution

Since the Schwarzschild radius is $$r = \frac{2GM}{c^2}$$ would I be right in saying that

$$\frac{2GM}{c^2 r}$$

is dimensionless?

 

[Sourabh N]

The Attempt at a Solution

Since the Schwarzschild radius is $$r = \frac{2GM}{c^2}$$ would I be right in saying that

$$\frac{2GM}{c^2 r}$$

is dimensionless?

Yes, it is.

 

[vela]

Note that it would have to be if the formula is valid since you're subtracting that quantity from 1, which is dimensionless.

 

[karlzr]

Of course it is. Note that sometime we write metric in this form:$$1-\frac{2GM}{r}$$
just a matter of unit conventions.

 

[help1please]

thanks every1