General relativity vs newtonian mechanics

Question

My high school textbook briefly touched the topic of black holes, and this is how it defined them:

"Consider a spherical body of mass $M$ and radius $R $. Suppose,due to some reason the volume goes on decreasing while the mass remians the same. The escape velocity from such a dense material will be very high. suppose the radius is so small that $ \sqrt (2GM/R)>c$.Thus, nothing can escape from such a dense material. These are called black holes."

My question is this definition right? If this is right then why do we need general relativity to explain them? PS I am a high schooler,so it will be more helpful to me if the solution avoids complicated math like tensors or stuff.

Answer 1

Very good question. This was also how I was introduced to black holes in high school: After introducing the concept of "escape velocity", if you assume a "cosmic speed limit" - the speed of light - then you can calculate the so-called Schwarzschild radius without understanding general relativity, or even special relativity except the existence of a speed limit.

But the thing is, although you can do this specific calculation even without general relativity, you can't do more sophisticated calculations without it. What if the object is slightly less dense than a black hole, and light can escape - how would gravity near this object behave? One of the first successes of GR was correctly describing the anomalous movement of the planet Mercury that could not be reproduced by Newtonian gravity. Just knowing the speed of light would not have helped doing this calculation.

There's another example of an idea that people usually assume come from GR, but in fact can be considered even without it: In Leonard Susskind's fantastic course on Cosmology (freely available online), he begins the course by explaining how we could understand the expansion or contraction of the universe without GR. Just normal masses in normal Newtonian gravity. GR is important for understanding the details and make correct calculations, but not always necessary to understand why a certain phenomenon should exist.

Answer 2

Well friend to the best of my knowledge, in physics, technically there's no such absolute concept as "Right;" merely "able to adequately model & predict."

So yes, it's "Right" in the teaching sense to convey a black hole's basic conceptual ideas to one whose grasp of Newtonian mechanics is stronger than it is of more advanced physics.

"Adequate" to explain & model the basic strength of the gravity and light's challenge of escaping it at high strength.

"Not adequate" to model the full behavior of light, gravity & time near a black hole (approximations of which you may have seen in modern visual effects like in Interstellar, the optical bending of its event horizon and such).

"Not adequate" to model the shape of space, (which it didn't recognize as a thing), or see the need to couple it intrinsically with time as spacetime.

As far as I know, that needed relativity. Which itself was the means by which black holes were first predicted and theorized, that we should be on the look for.

Once found, their simplified explanation then was distilled back into Newtonian mechanics, to introduce learners to the concept of them. So sure, Newtonian mechanics is "right," but GR is "more right."

I guess as you keep going, it might serve you to think in terms of "what more completely explains the most phenomena, vs. what can only get so far," rather than "right/not."

In over-simplified terms, Einstein observed that light does not move any faster if coming from a speeding body vs. stationary one, no matter where in space and time one was. Which Newtonian mechanics did not address, so something was needed to explain that.

The result was the more comprehensive physics of spacetime; special relativity. He then generalized it to incorporate gravity, which he modeled as a curvature, not a force. That model has been able to predict and explain much more of what's since been observed, than Newton's has.

But Newtonian mechanics are still plenty right for plenty of calculations and models here on the ground, in aeronautics, and in space. They'll just only take one so far, only to certain degrees of accuracy or quantity of phenomena.

So they can't for instance, sync the clocks on GPS satellites with those in the stronger gravity in which your phone sits, (which gives it a different relative time rate), to put your car in the right place on your map. That'd hafta be Einstein, as far as I know. Good question.