Rest Energy and a 1 million solar mass black hole

In summary, the conversation discusses a scenario where a 1 million solar mass black hole is producing electron-positron pairs at various distances from the event horizon. The positron's vector is directly "up" away from the singularity and reaches an apogee before falling towards the singularity. Another pair is produced at a distance 1/2A from the event horizon and the electron's vector is also directly "up" with the same initial vector as the positron. The electron reaches its apogee at distance C at the same time as a collision occurs with the positron. It is asked whether the annihilation photons will have more, equal, or less energy than 1.022 MeV combined when measured from the center
  • #36
You will need to solve the geodesic equations for a massive particle falling in a Schwarzschild spacetime. In Schwarzschild coordinates you would start with a four-velocity with no spatial components as your initial condition. There are other coordinate systems that may be better adapted for this part of the problem, such as the "rain" coordinates, but in those determining the location of B/2 will be more challenging.
 
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  • #37
Dale said:
need to solve the geodesic equations for a massive particle falling in a Schwarzschild spacetime

Will these corrections generally increase or decrease the expected KE relative to the over-simplified "falling halfway to a planet surface" approximation as distance B decreases?
 
  • #38
metastable said:
Will these corrections generally increase or decrease the expected KE relative to the over-simplified "falling halfway to a planet surface" approximation as distance B decreases?
I don't know, I would have to do the calculation to find out. In all likelihood those calculations have already been done somewhere, but I don't have a reference ready.
 
  • #39
metastable said:
Thanks for your answer DrStupid, but the quote is misattributed- its says "metastable" made that quotation but it was Dale.

Sorry. I fixed it.
 
  • #40
Dale said:
Assuming that the atom is very massive then the atom can receive any of the momentum without significantly impacting the energy. That is what I assumed.

That makes sense. Within the given accuracy of four significant digits for the total energy, everything heavier than hydrogen should do the job.
 
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  • #41
DrStupid said:
That works for the energy but not for the momentum.

That can be easily fixed by having the electron-positron pair produced by a pair of photons instead of a single photon. The photons would just have to be such that they had zero total linear momentum relative to an observer momentarily at rest at the given altitude.
 
  • #42
Can the black hole be modeled as having its mass in a thin shell at the event horizon?
 
  • #43
metastable said:
Can the black hole be modeled as having its mass in a thin shell at the event horizon?

If you are restricting yourself to events outside the horizon, the distribution of mass inside the horizon does not matter at all. The only thing that matters is that there is vacuum outside the horizon and that the spacetime is spherically symmetric. The total mass is the only relevant parameter in this regime.

If you want to model events at or inside the horizon, then no, you obviously can't model the hole as having its mass in a thin shell at the horizon, since that's not a valid solution to the EFE (except at some instant in the original gravitational collapse to form the hole, if the collapse happened to be of a thin, spherically symmetric shell, which is extremely unlikely).
 
  • #44
So if I understand you correctly, during the core collapse of a supernova, we won't see matter at the core "falling upwards" towards an over-density at the forming event horizon.
 
  • #45
metastable said:
during the core collapse of a supernova, we won't see matter at the core "falling upwards" towards an over-density at the forming event horizon.

Huh? Where did this come from?

This is not the first thread where what question you appear to be asking changes drastically during the course of the thread. What exactly are you trying to find out?
 
  • #46
Perhaps this last question was leading me down the wrong path towards a solution. I’m still just looking at how to correctly model the expected KE when distance B is relatively close to the event horizon.
 
  • #47
metastable said:
I’m still just looking at how to correctly model the expected KE when distance B is relatively close to the event horizon.

What you need are the equations describing geodesic (free-fall) motion in the Schwarzschild spacetime geometry. Most GR textbooks cover this; I believ Sean Carroll's online lecture notes do as well:

https://arxiv.org/abs/gr-qc/9712019
 
  • #48
PeterDonis said:
I believ Sean Carroll's online lecture notes do as well:

https://arxiv.org/abs/gr-qc/9712019
Around equation 7.38-7.43, from memory 7.43-7.48 in fact. You'll need something capable of solving differential equations - Maxima is free, but there's a bit of a learning curve.
 
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  • #49
metastable said:
I’m still just looking at how to correctly model the expected KE when distance B is relatively close to the event horizon.
I told you how to correctly model it. You have to solve the geodesic equation.
 
<h2>1. What is rest energy?</h2><p>Rest energy is the energy that an object possesses due to its mass. It is a form of potential energy that is equivalent to the mass of the object multiplied by the speed of light squared (E=mc^2).</p><h2>2. How is rest energy related to black holes?</h2><p>Black holes are objects with extremely high mass and gravitational pull. As objects get closer to a black hole, their rest energy increases due to the strong gravitational force. This means that the closer an object gets to a black hole, the more energy it possesses.</p><h2>3. What is a 1 million solar mass black hole?</h2><p>A 1 million solar mass black hole is a black hole that has a mass equivalent to one million times the mass of our sun. This is an extremely large black hole that can have a significant impact on its surrounding environment.</p><h2>4. How is a 1 million solar mass black hole formed?</h2><p>A 1 million solar mass black hole is formed when a large amount of matter collapses under its own gravity. This can happen when a massive star dies and its core collapses, or when two or more smaller black holes merge together.</p><h2>5. What are the implications of a 1 million solar mass black hole?</h2><p>A 1 million solar mass black hole has a strong gravitational pull that can affect the motion of nearby objects and even distort space and time. It can also emit powerful radiation and jets of matter, making it an important object for studying the universe and its evolution.</p>

1. What is rest energy?

Rest energy is the energy that an object possesses due to its mass. It is a form of potential energy that is equivalent to the mass of the object multiplied by the speed of light squared (E=mc^2).

2. How is rest energy related to black holes?

Black holes are objects with extremely high mass and gravitational pull. As objects get closer to a black hole, their rest energy increases due to the strong gravitational force. This means that the closer an object gets to a black hole, the more energy it possesses.

3. What is a 1 million solar mass black hole?

A 1 million solar mass black hole is a black hole that has a mass equivalent to one million times the mass of our sun. This is an extremely large black hole that can have a significant impact on its surrounding environment.

4. How is a 1 million solar mass black hole formed?

A 1 million solar mass black hole is formed when a large amount of matter collapses under its own gravity. This can happen when a massive star dies and its core collapses, or when two or more smaller black holes merge together.

5. What are the implications of a 1 million solar mass black hole?

A 1 million solar mass black hole has a strong gravitational pull that can affect the motion of nearby objects and even distort space and time. It can also emit powerful radiation and jets of matter, making it an important object for studying the universe and its evolution.

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