- #1

member 657093

- TL;DR Summary
- What are the effects on a stationary observer at a specific distance from a Kerr Black Hole?

A Kerr Black Hole (BH) is a spinning BH. There is an Event Horizon (EH) which is $$r_H^\pm = \frac{r_S \pm \sqrt{r_S^2 -4a^2}}{2}$$ where ##a=\frac{J}{Mc}## and ##r_S## is the Schwarzschild radius. My question is, suppose I'm in a spacecraft, not in orbit, but stationary at a distance ##r##. I want to have a comprehensive understanding of the effects of that BH on the spacecraft, and by extension on me. I would like to know, if I'm subjected to the effects of:

To prevent ambiguity, let me edit the question with the following (please note that I'm currently dealing in SI units):

- Time Dilation: If this is present, the formula should be derived from the ##g_{tt}## component of the Kerr metric, which is $$ \gamma = \frac{1}{\sqrt{1-\frac{r_S r}{r^2 + a^2 cos^2 \theta}}}$$
- Tidal Force: What is the formula for this in a Kerr metric? Normally the equation is $$\frac{2GMd}{r^3}$$ with ##d## being in the instance of a human being, about 2 meters.
- Acceleration due to the gravitational attraction of the BH at that distance (surface gravity from an arbitrary distance). Normally the formula is $$ \frac{GM}{r^2}$$ But I've read here that this should be multiplied by ##\gamma##
- Escape velocity I need for my spacecraft from this distance ##r##; normally the formula is $$\sqrt{\frac{2GM}{r}}$$

To prevent ambiguity, let me edit the question with the following (please note that I'm currently dealing in SI units):

- Kerr BH mass is: ##10^8## times that of Solar mass (Solar Mass ##=1.98847e+30 kg##)
- Spin Parameter: ##0.999999999999986673399999999999954##
- Distance ##r##: ##252083284394.398975225334674476303## m
- ##\theta##: ##45^0##

Last edited by a moderator: