Celestial Die Hards: Escape Velocity at 1 Planck Length

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In summary, the escape velocity at 1 Planck length from an event horizon is approximately equal to the speed of light, with a slight decrease as the distance from the event horizon increases. The equation for computing the escape velocity is v = (1 - d/2R_s)c in Planck units, where d is the distance from the event horizon and R_s is the Schwarzschild radius. This equation is an approximation and does not apply to rotating black holes.
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kjones000
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What is escape velocity at 1 Planck length from an event horizon? Or, if it varies with the mass, is there a simple equation for computing the escape velocity? (No rotating black holes please, they hurt my brain).
 
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kjones000 said:
What is escape velocity at 1 Planck length from an event horizon? Or, if it varies with the mass, is there a simple equation for computing the escape velocity? (No rotating black holes please, they hurt my brain).

Well, I get that
[tex] \gamma = \frac{1}{\sqrt{1-(\frac{v}{c})^2}}}=\frac{1}{\sqrt{1-\frac{2GM}{c^2r}}}
[/tex]

but I could use a double-check. Assuming this is right, if we let R = Rs +d, where Rs is the schwarzxshild radius 2GM/c^2, we can approximate this as

[tex] \gamma = \sqrt{\frac{2 G M}{d c^2}} = \sqrt{\frac{R_s}{d}} [/tex]

this can be solved for v

[tex] v \approx (1 - \frac{d}{2 R_s})c [/tex]

In Planck units, G=c=1
 
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FAQ: Celestial Die Hards: Escape Velocity at 1 Planck Length

What is "Celestial Die Hards: Escape Velocity at 1 Planck Length"?

"Celestial Die Hards: Escape Velocity at 1 Planck Length" is a hypothetical video game that explores the concept of escaping a black hole at the smallest possible length scale, known as the Planck length. It is purely a thought experiment and does not currently exist as a physical game.

How is the Planck length related to black holes?

The Planck length is the smallest possible length scale in the universe, at approximately 1.6 x 10^-35 meters. It is also the length scale at which the effects of quantum gravity become significant. In the context of black holes, the Planck length is important because it represents the point at which the gravitational pull becomes so strong that it collapses into a singularity.

Is it possible to escape a black hole at the Planck length?

Currently, it is not possible to escape a black hole at any length scale, including the Planck length. This is because the laws of physics, particularly the theory of general relativity, dictate that nothing can escape the event horizon of a black hole once it has crossed it.

What is the significance of exploring the concept of escaping a black hole at the Planck length?

Exploring this concept allows us to better understand the limits of our current understanding of physics and to contemplate the possibility of a theory of quantum gravity. It also allows us to think about the extreme conditions that exist at the smallest length scale in the universe.

Are there any real-life applications of this thought experiment?

While there may not be any direct applications, the thought experiment can inspire new ideas and theories in the field of physics. It also highlights the need to continue studying and researching the concept of quantum gravity, which could have significant implications for our understanding of the universe.

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