Dimensionless Time: Rindler & Minkowski Spacetime

[felici95]

What does the dimensionless time in Rindler spacetime signifies? And how something dimensionless can be regarded as time and coupled up with proper distance in Minkowski spacetime?

(Page 7: https://www.perimeterinstitute.ca/images/files/black_holes_and_holography_course_notes.pdf )

 

[PeterDonis]

The "dimensionless time" is just a way of scaling the time coordinate in relation to the mass of the hole. Some sources also use a dimensionless radial coordinate which is constructed basically the same way, as a ratio of the usual radial coordinate to a constant times the hole's mass. The idea is to separate out aspects of the physics that are the same regardless of the mass of the hole.