# The Schwarzschild metric

## 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?

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## 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
Staff Emeritus
Of course it is. Note that sometime we write metric in this form:$$1-\frac{2GM}{r}$$