A good starting point is On Continued Gravitational Contraction by J. R. Oppenheimer and H. Snyder. If I remember it correctly that is the nice paper where light cones fall graceful along the geodetic lines of the metric of the black hole into it, explaining the event horizon virtually by means of illustration ... a point that could be appealing to a graphic artist.

Dear Jofre,

Thank you for your reply. I don't see your response on the website but I did get an email. Unfortunately, I must be doing something wrong. My input is this:

1. time in rest frame (what or where is the rest frame?): 90 years
2. gravitational acceleration: 1.52 x 10^12g
3. radius: 30km

My answer is -1.423 x 10^9 i seconds. I don't know what i means, and I'm not seeing where I wait 63 years to watch my friend age 90 years. It also contradicts an astronomer who only would say I'd wait "less than a blink of an eye." I apologize for the confusion. This subject is a bit thicker than I'm used to :-)

You want to know the effect that a black hole has on time. The idea of rest frame is not at issue here. All relevant clocks are at rest. Imagine an infinite pole extending radially from the event horizon of a black hole. At places along the pole you mount clocks and also mark the radial distance of the clock from the center. The radial distance will be in terms of the radius of the event horizon of the black hole.

Identical clocks, wristwatches say, will run at different rates depending on their relative motion (not relevant here) and on what gravitation field they are in. The clocks at different radii on the pole will run at different rates and you can calculate that from the formula I gave you in my other answer. If we wanted to pick a standard clock we might pick the one at infinity. Why? Because it is in a region of space where the gravitational field is zero, which means flat spacetime. That might be the equivalent of 'being at rest' for the black hole problem. The formula I gave in my other answer gives the interval of time that will pass on one of the clocks on the pole as a fraction of the time that would pass on the 'clock at infinity'. If you look at the clock at the event horizon, no time will pass. Or you can make it as short as you want by getting close enough to the radius of the event horizon.

This whole discussion is getting a bit off the topic of Wolfram Language or Wolfram Alpha. If you know very little about general relativity (even though you might be a great graphic artist!) how can you write a small book about black holes for middle school students? Are you partnering with a physicist who is well versed in gravitational physics? Are you an expert in that yourself? If not, how good the students get a good book?

<<If you know very little about general relativity (even though you might be a great graphic artist!) how can you write a small book about black holes for middle school students? Are you partnering with a physicist who is well versed in gravitational physics? Are you an expert in that yourself? If not, how good the students get a good book?>>

First, thanks for your reply and the recommendation of Lawrence Krauss. I will see if I can get in touch with him.

You ask a very good question about how good the book will be. The book (really a reader) is twenty pages and 2000 words, plus pictures. I've been studying black holes for a year now and believe me, there's enough there for 2000 pages even for the average graphic artist. It's very hard to write about this subject without getting into the tall weeds, and some concepts are difficult to wrap the brain around. How do you explain general relativity in two sentences for a 10-year-old? That's the challenge. I'm working on the first draft of the manuscript, which will then go to my editor who's an expert in educational writing. It will then indeed be fact checked and discussed with a physics expert. And then the book will be leveled for the appropriate age, and then, most likely, be fact checked again. It's a long process.

Although I don't have a deep understanding of the physics, I have a reasonable comprehension of the facts and concepts. I do understand time dilation, the equivalence principle, and even a bit of the Lorentz transformation, but for the finer mathematical details I get lost in the equations. And yes, I did watch all two hours of Dr. Physics. Even grasped some of it :-) https://www.youtube.com/watch?v=foRPKAKZWx8

The purpose of the books isn't to provide a comprehensive study but an introduction. Hopefully, kids (and maybe even adults) will find black holes and relativity as fascinating as you and I do, and inspire "Hey Dad, I bet you didn't know about this . . . !!!"

Thanks again for your help and best regards,

Jack