Exploring the Mystery of an Equation in Spacetime

[nomadreid]

In my reading I came across the equation
ds² = −dt² + 2t/r dtdr + (1 − (t/r)²)dr² + (BKr)²(dθ² + sin² θdϕ²)

where s is spacetime, t is time, r is radius and the others are not important for my question.
What I do not get is the "1" in the (1 − (t/r)²)dr², or

dr²− ((t/r)²)dr² .

This seems to lead to a mismatch in units, with the rest of the members of the equation ending up in time (squared) units, but the dr² being in distance (squared) units. What gives?

(The paper itself is at http://arxiv.org/abs/grqc/9909016 )

Thanks.

 

[Dadface]

When you click on the link you provided you will see that "the paper has been withdrawn by the author,due to a fatal error"

 

[nomadreid]

I should have specified [v4], sorry. [v1] was the one that was withdrawn; [v4] has not been withdrawn.

 

[phyzguy]

Relativity is often done with the implicit assumption that c=1. In this system of units, time and space have equal units. To recover normal units, just replace t with ct everywhere. Then the units will match.

 

[nomadreid]

Phyzguy: Thanks. That makes sense.