How do I calculate the event horizon?

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Discussion Overview

The discussion centers around the calculation of the event horizon of black holes, exploring both theoretical and mathematical approaches to understanding this concept. Participants are attempting to derive equations related to escape velocity and the Schwarzschild radius, while also addressing the implications of using mass in calculations involving photons.

Discussion Character

  • Exploratory
  • Technical explanation
  • Mathematical reasoning

Main Points Raised

  • One participant discusses the event horizon as the limit beyond which not even photons can escape, expressing uncertainty about the equations used for calculation.
  • Another participant suggests that the first equation presented is correct but questions the second equation, proposing that it should be the Newtonian kinetic energy equation and suggesting a rearrangement to derive escape velocity.
  • A participant reiterates the use of the kinetic energy equation but raises concerns about dividing by the mass of a photon, which is zero, and mentions an alternative energy calculation for photons using the equation Ep = hf.
  • There is a clarification that while photons have zero rest mass, they are not at rest, and higher frequency implies higher energy, which may affect escape dynamics.

Areas of Agreement / Disagreement

Participants express uncertainty and differing views on the appropriate equations to use for calculating the event horizon, indicating that there is no consensus on the correct approach or understanding of the concepts involved.

Contextual Notes

Participants highlight limitations in their calculations, particularly regarding the treatment of mass in equations involving photons and the assumptions underlying their mathematical approaches.

Spring
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I am clearly talking about black holes. The event horizon is the limit where even a photon won't escape it.

I tried to calculate it in the easy way using enegry calculation

m * MG/R = mc^2 / 2

but I do not know if I am using the right equation or even if I can divide by the m because it equels to zero, deviding by which is mocking the foundations of math and physics.

If the way to calculate it is tricky and scientific I will be disappointed because I want to understand it well but I will still try and listen.
 
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The first equation is correct but the second one (to my knowledge) should be the Newton equation for kinetic energy-

[tex]E_k=\frac{1}{2}mv^2[/tex]

If you replace the second equation with this one, then you should be able to rearrange to get the equation for escape velocity and from that, you should be able to establish an equation for the event horizon (or the Schwarzschild radius). This is a basic way of establishing the EH, for a more accurate and GR related solution, you should look at the Schwarzschild metric. You might also find the following thread of interest-

Deriving the Schwarzschild radius?
 
Last edited:
The second equation is ½mv2 but I used c (speed of light) to calculate it for light.

Once again, I am unsure because I devided by m of photon which equals to zero, deviding by nothing.
Also because there is a different way to calculate the energy of a photon. Ep = hf .
That way it means that every where there is a photon who can escape with high enough frequency.
 
Spring said:
The second equation is ½mv2 but I used c (speed of light) to calculate it for light.

Once again, I am unsure because I devided by m of photon which equals to zero, deviding by nothing.
Also because there is a different way to calculate the energy of a photon. Ep = hf .
That way it means that every where there is a photon who can escape with high enough frequency.

Zero is the rest mass of a photon. Of course, photons are not normally at rest. High frequency implies high energy.
 

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