Twin Paradox in Kerr Metric - Help Needed

In summary, the conversation is about the twin paradox in the Kerr metric. The discussion involves two twins at different radii in the Kerr metric, one performing equatorial circular motion and the other performing polar circular motion. The goal is to calculate the proper time elapsed for both twins when they meet again at the equatorial plane. The speaker mentions difficulty in calculating the proper time for the polar twin and asks for help. They also mention an old paper that may be helpful in understanding the polar and equatorial orbits in Kerr spacetime.
  • #1
dman12
13
0
Hi. I've been struggling with a formulation of the twin paradox in the Kerr metric.

Imagine there are two twins at some radius in a Kerr metric. One performs equatorial circular motion whilst the other performs polar circular motion. They separate from one another and the parameters of the motion are such that they meet again when the polar twin next crosses the equatorial plane (ie having traveled through theta=pi). I'm trying to calculate the proper time elapsed for both twins in this case.

I can work out the proper time for the equatorial twin by solving the equations of motion from a Lagrangian for the Kerr metric but am finding it difficult to work out proper times for the polar orbit?

Any help would be much appreciated!
 
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  • #2
I recall that this old paper discusses the polar and equatorial orbits in Kerr spacetime. It might be be helpful

arXiv:gr-qc/0202090v1 26 Feb 2002 (http://arxiv.org/abs/gr-qc/0202090v1)
 

Related to Twin Paradox in Kerr Metric - Help Needed

1. What is the "Twin Paradox" in Kerr Metric?

The Twin Paradox in Kerr Metric is a thought experiment in general relativity that involves two identical twins, where one stays on Earth while the other travels through a rotating black hole (Kerr Metric) and returns to Earth. This scenario highlights the concept of time dilation, where the twin who traveled through the Kerr Metric experiences a slower passage of time compared to the twin who stayed on Earth.

2. How does the Kerr Metric affect time dilation?

The Kerr Metric, which describes the spacetime around a rotating black hole, has a non-zero angular momentum. This results in a frame-dragging effect, where the spacetime is dragged along with the rotation of the black hole. This frame-dragging effect leads to an increase in the time dilation, causing time to pass slower for an object in the Kerr Metric compared to an object in flat spacetime.

3. What is the relationship between the Kerr Metric and the Twin Paradox?

The Twin Paradox in Kerr Metric is a specific case of the Twin Paradox, where the rotating black hole (Kerr Metric) plays a crucial role in the time dilation experienced by the traveling twin. This scenario allows us to understand the effects of a strong gravitational field on time dilation and the concept of relativity.

4. Can the Twin Paradox in Kerr Metric be observed in real life?

While the Twin Paradox in Kerr Metric is a theoretical thought experiment, some aspects of it can be observed in real life. For example, the effects of time dilation due to frame-dragging have been observed in experiments involving atomic clocks orbiting Earth. However, the extreme conditions of the Kerr Metric make it impossible for humans to experience it in reality.

5. What are the implications of the Twin Paradox in Kerr Metric?

The Twin Paradox in Kerr Metric has significant implications for our understanding of spacetime and the effects of gravity. It also highlights the importance of considering the frame of reference when measuring time. This thought experiment has been used to test and validate the principles of general relativity and has contributed to our understanding of black holes and their properties.

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