Celestial Die Hards: Escape Velocity at 1 Planck Length

[kjones000]

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).

 

[pervect]

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
$$\gamma = \frac{1}{\sqrt{1-(\frac{v}{c})^2}}}=\frac{1}{\sqrt{1-\frac{2GM}{c^2r}}}$$

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

$$\gamma = \sqrt{\frac{2 G M}{d c^2}} = \sqrt{\frac{R_s}{d}}$$

this can be solved for v

$$v \approx (1 - \frac{d}{2 R_s})c$$

In Planck units, G=c=1