Dimensionless Time: Rindler & Minkowski Spacetime

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SUMMARY

The discussion focuses on the concept of dimensionless time in Rindler spacetime and its relationship with proper distance in Minkowski spacetime. Dimensionless time serves as a scaling mechanism for the time coordinate relative to the mass of a black hole, allowing for a clearer understanding of physical phenomena that remain consistent across different mass scales. Additionally, a dimensionless radial coordinate is introduced, which is derived from the standard radial coordinate divided by a constant related to the black hole's mass. This approach effectively isolates universal aspects of physics from mass-dependent variables.

PREREQUISITES
  • Understanding of Rindler spacetime concepts
  • Familiarity with Minkowski spacetime and its properties
  • Basic knowledge of black hole physics
  • Comprehension of dimensionless quantities in physics
NEXT STEPS
  • Research the implications of dimensionless time in general relativity
  • Explore the mathematical formulation of Rindler coordinates
  • Study the relationship between mass and spacetime curvature
  • Investigate the role of dimensionless quantities in theoretical physics
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Physicists, cosmologists, and students of theoretical physics interested in black hole dynamics and the mathematical frameworks of spacetime.

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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 )
 
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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.
 

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