Can an object grow past the schwarzschild radius?
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Imagine the following: A massive star, VERY close to reaching the schwarzschild radius and become a black hole. It bends light quite a lot, but light coming out of it in a perpendicular angle is still able to escape.
Then this star absorbs a large planet, which contributes just enough mass to reach the schwarzschild radius and become a black hole, no light can escape anymore.
Why is it that scientists believe at that moment all the matter collapses into an infinitesimal point in space? Couldn’t the star keep existing and growing just as it was before, with the exception that light is “sucked” back in? An energy/mass sinkhole?
To start off with you don’t quite understand what the Schwarzschild radius is. It is not some limit of size where an object gets bigger and bigger, creeping up on it from below and when it is finally reached the object becomes a black hole.
Instead the Schwarzschild radius is the radius *below* which the force of gravity would cause it to irreversibly collapse. There would be a star which is balancing the force of its own gravity pulling inward against the force of the fusion in its core pushing outwards, until it runs out of fuel and gravity can crush it into a black hole.
Or you might have a neutron star which is cooled and prevented from further collapse just by neutron degeneracy pressure (you can’t pack neutrons any closer together) but that if somehow it was compressed into a smaller radius overcoming that pressure, below the Schwarzschild radius it would collapse into a black hole.
Based on the above what you really should be asking is if something could grow larger while **below** the Schwarzschild radius. And no, it can’t. Gravity pulls on things with mass, and *light doesn’t have mass*. An asteroid being tugged into a curved path by the gravity of a massive star is not the same thing as what happens when light’s path is bent by a massive object. Instead what is happening with light is that the light is not affected by gravity, the *space itself* is. Space itself is bent by gravity and light just follows along what to it is a straight line.
When a black hole is formed light is unable to escape not because it can’t claw itself away from the force of gravity, but because gravity warps space itself to the extent that **all directions point inward** to the black hole. There is no direction that light or anything else can travel to move away from deeper into the black hole so we can be certain it can’t become larger. There is literally “no way” for that to happen.
TL;DR – no matter that we know of can stably exist at a stage where it’s on the threshold of becoming a black hole, so the “just before” picture isn’t one we think is possible. Black hole densities are achieved during ongoing collapses that, as far as we known, have no mechanism to stop them. This is why we think it goes down to a singularity, but of course we don’t really have any way of knowing – there could be some sort of exotic particle sphere of finite size in there.
To explain: your scenario doesn’t work as stellar material isn’t stable at anything remotely close to those sorts of densities. A typical neutron star – *way* denser than a normal star – of 1.5-1.8 solar masses has a radius of about 10-15 km. The Schwarzschild radius of a 1.8 solar mass object is about 5 km – much smaller than even this densest known stable macroscopic form of matter. We think neutron stars behave weirdly – they may even get smaller as they get heavier – and aren’t stable over a very wide range of masses. We think that when two merge, they collapse into a black hole. But if we ignore that and assert that they could grow to something like 2.5 times their usual radius, at the same density, then yes they would at some point become, according to the outside world, a black hole with an event horizon past their surface.
Disclaimer: NOT a physicist, just someone who took undergrad physics.
My best understanding of the Schwarzchild Radius is that it is a solution to an equation. By rearranging a bunch of terms and solving for x, they found the number (or rather an equation that can give you the number). The argued about the number and what it means for a while, and it was originally determined to mean (or solved to mean) the radius (specifically, distance from the object’s center of mass) at which a body of a given mass has enough gravity that light cannot reach the escape velocity of the object. You probably already know all of this based on your comment.
What’s important to realize is that ABOVE the Schwarzchild radius (getting farther from the COM), the escape velocity for the object is no longer above the speed of light. Another important thing to remember is the terms on the other side of the equation giving the Schwarzchild radius: mass, the universal gravitational constant, and the speed of light. The last two are always the same, so the only thing determining a specific object’s Schwarzchild radius is its mass. In your example in your comment, adding the planet changes the mass of the star, and thus its Swarzchild radius.
“Couldn’t the star keep existing and growing just as it was before, with the exception that light is sucked back in?”
Well… this is where a trained physicist would really help me… but my best understanding of the event horizon tells me that a good answer here would be “we don’t really know, and there’s no way for us to know.” If light is sucked back in, then there is an event horizon, and there is no way for us to get information back “out” of the black hole, so there’s no way for us to study what’s happening in there. All we really know is that once an event horizon has developed, we are dealing with a black hole and can expect Hawking radiation and all that other stuff I definitely know about.
People who know more than me, please correct me…
Sure! The Schwarzschild radius represents the point where an object collapses under its own gravity and becomes a black hole
So, to answer your question, an object cannot grow past the Schwarzschild radius because it would require an infinite amount of mass and energy
It’s like trying to fit an elephant into a tiny box – just not possible!
After a certain point, the more mass you add to an object makes it smaller, as the increased gravity pulls it in more tightly. At a certain point, added mass will make the object smaller than its Schwarzschild radius and boom – you got a black hole.
Lots of answers. I’ll try a different approach and see if it sheds any light for you (or not). <– 2 puns! Maybe a superpositioning of puns?
Don’t think of light having an escape velocity – think of space-time being an escalator pulling everything down – space & time, and thus matter & energy & light, everything.
Imagine a neutron star like others have written here. With a radius of 10km and a schwarzschild radius of 15km.
Now imagine you’re a god who can alter the schwarzschild radius for this object like a human can adjust the lights with a dimmer switch.
Slowly crank down the schwarzschild radius to 14km – what would happen? 12km? 10.5km? 10.1km?
Eventually space-time is being warped more and more at that ever changing schwarzschild radius. Causing more and more of the surface of the star to be visible from your distant (we hope!) location. Check out https://www.youtube.com/watch?v=LSDNNfXYPq4#t=1m25 for a good idea.
But also, the light from the star will be traveling against space-time up the gravity well. It will get more and more red-shifted.
Until it’s infrared. Until it’s long radio waves. Until, there’s nothing left many many years from now.
Like an astronaut falling in, their light would get red shifted the closer they got to the event horizon and never totally cross it. Weird.
When an object “falls beyond” the schwarzschild radius of a blackhole (even if it’s the object itself) it goes red shifted into oblivion so to say.
Blackholes don’t form slowly by slowly getting more and more matter. But it’s fun it image what it would be like – it can help understand what effects are at play.
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