Electron Falling in Kerr Metric: Release of 40% Rest Energy?

In summary, the conversation discusses the concept of releasing an electron into a black hole and the loss of its rest energy during this process. The quote from Hartle's Gravity states that about 42% of the rest energy can be released when transitioning from an unbound orbit to the most bound innermost stable circular orbit. This is due to the binding energy, which is the difference between the energy at rest and the energy in orbit, expressed as a fraction of the rest energy. This explains how the electron can lose about 40% of its rest energy during the process.
  • #1
jfy4
649
3
I have here a quote from Hartle's Gravity, page 321:

"The fraction of rest energy that can be released in making a transition from an unbound orbit far from an extremal black hole to the most bound innermost stable circular orbit is [itex](1-1/\sqrt{3})\approx 42\%[/itex]".

My question is about releasing an electron into a black hole in precisely this fashion. An electron is a fundamental particle, hence, cannot decay into other fundamental particles. Then how is the electron losing about 40% of its rest energy during this process?
 
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  • #2
I would guess that they're just expressing the loss of potential energy as a fraction of the rest energy.
 
  • #3
bcrowell said:
I would guess that they're just expressing the loss of potential energy as a fraction of the rest energy.

After re-reading over and over again, that seems right. This appears to be the key in that paragraph:

"The binding energy of any orbit is the difference between the energy of a particle at rest at infinity (including rest energy) and the energy of the same particle moving the orbit as measured from infinity. Since [itex]\mathbf{e}[/itex] is the energy measured from infinity per unit rest mass, the binding energy per unit rest mass is [itex]\mathbf{(1-e)}[/itex]. This is the fraction of rest energy that can be released in the process of gravitational binding".

So another way to say this is:

This is the amount of binding energy expressed as a fraction of the rest energy that can be released in the process of gravitational binding.

?
 

1. What is the Kerr metric?

The Kerr metric is a mathematical description of the geometry of spacetime around a rotating black hole. It was developed by New Zealand mathematician Roy Kerr in 1963.

2. What is an electron falling in Kerr metric?

An electron falling in Kerr metric refers to the motion of an electron as it falls into a rotating black hole, following the curvature of spacetime described by the Kerr metric.

3. What is rest energy and why is it important in this scenario?

Rest energy is the energy that an object possesses due to its mass, even when it is not moving. In the case of an electron falling in Kerr metric, the release of 40% of its rest energy is important because it represents the conversion of mass into energy as the electron falls into the black hole.

4. How is the release of 40% rest energy calculated?

The release of 40% rest energy is calculated using Einstein's famous equation, E=mc^2, where E represents energy, m represents mass, and c represents the speed of light. In this scenario, the mass of the electron is converted into energy as it falls into the black hole, resulting in the release of 40% of its rest energy.

5. What are the implications of an electron falling in Kerr metric and the release of 40% rest energy?

The implications of an electron falling in Kerr metric and the release of 40% rest energy are significant in terms of our understanding of black holes and the conversion of mass into energy. This scenario also has implications for the study of gravity and the behavior of matter in extreme environments.

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