B Can Black Hole Gravity Be Overpowered?

[Picalilli]

TL;DR Summary

If a situation can exist where photons can escape black hole gravity, would “dark star” not be a more adequate name?

Summary: If a situation can exist where photons can escape black hole gravity, would “dark star” not be a more adequate name?

It is commonly accepted that once there is enough material put together to create a sphere with a mass big enough to prevent light from escaping, that this object then becomes some kind of death trap from which nothing can ever escape any more. This is commonly referred to as a “black hole” and the thesis then is that even no photon can ever escape a “black hole”.
Is this always the case?

Let's perform the following “Gedankenexperiment”:
Let's have two identical stars(S1 and S2) with diameter d and each having a mass between 101% and 103% of critical mass to prevent light from escaping. Both S1 and S2 qualify as “black hole”. Two parallel lines(a1 and a2)are at distance b from each other. S1 has it's center of mass on a1 and the center of mass of S2 is on a2. S1 and S2 are at least 300 000 light-years apart. S1 and S2 are sent flying towards each other along a1 and a2 at a relative starting speed between 75 and 85 % of the speed of light. Distance b has to be chosen such that the centers of mass of S1 and S2 come at least at one point closer to each other than 2.5 d and never closer than 2d, no matter what shape or mix the matter of S1 and S2 ever evolve to. As S1 and S2 approach each other and they both are composed of plasma and are not solid, a tidal effect will set in and both S1 and S2 will change shape (The force of gravity is directly related to the amount of mass, but so is the force of inertia). Losing their spherical shape results in weakening the gravity force on the edge of the system. If weakening the force of gravity results in photons escaping, the thesis doesn't hold water and black hole gravity can be overpowered. (2019-10-30)

 

[PeroK]

Are S1 and S2 stars or stars that have collapsed into black holes?

 

[Ibix]

critical mass to prevent light from escaping

There's no such thing - you can (in principle) have a black hole with a mass of 1kg, or 1g. They just don't form from gravitational collapse at that size. And conversely you can have stars way more than the mass of small black holes - they resist collapse due to fusion processes.

Losing their spherical shape results in weakening the gravity force on the edge of the system. If weakening the force of gravity results in photons escaping, the thesis doesn't hold water and black hole gravity can be overpowered.

This is a fairly critical misunderstanding of how black holes work. For a start, reference to "force" suggests that you are thinking in Newtonian terms, not relativistic ones.

You can certainly have black holes with event horizons that change shape as a result of interaction with other black holes (or other mass, more generally), but this never let's light escape.

 

[Ibix]

It's worth noting that Newtonian gravity would allow things called "dark stars", hypothesised as early as 1783. If one doesn't think too hard about (edit: or, in 1783, can't possibly know anything about) the status of light in a non-relativistic theory of gravity, these would behave broadly as the OP seems to be describing. One could deform such a thing enough that escape velocity from the top of the deformation was less than $c$.

Unfortunately, Newtonian gravity is wildly inaccurate outside very weak fields, and black holes don't behave anything like Newtonian "dark stars". Light was always hypothesised to leave the surface of a dark star - it just didn't make it all the way to our telescope, like a thrown ball falling back to Earth. In contrast, nothing can go upwards from the event horizon of a relativistic black hole.

 

[PeterDonis]

Let's perform the following “Gedankenexperiment”

Your scenario incorporates a number of unstated assumptions about how space and time work that are not valid for black holes, as well as some invalid assumptions about what black holes are. To list just a few that have not already been mentioned:

Black holes are not ordinary objects; they do not have surfaces at some constant radius less than their horizon radius. They are vacuum everywhere inside; the matter that originally collapsed to form the black hole continues to collapse all the way down to $r = 0$ where it forms a singularity. After that there is no matter anywhere inside the hole.

The centers of black holes at $r = 0$ are not points in space; they are moments of time, which are to the future of all other moments of time inside the hole's horizon. So it makes no sense to talk about how the centers of black holes move.

Space is not Euclidean around a black hole. So you cannot rely on Euclidean geometry when reasoning about how things move when black holes are present.

The horizons of black holes are not ordinary surfaces in space. They are null surfaces formed by radially outgoing light rays. They do not mark "places" and you cannot reason about them as if they did.

You can't stop two black holes that are falling towards each other from merging. There is no way to push on them to stop them from falling.

 

[Picalilli]

Are S1 and S2 stars or stars that have collapsed into black holes?

Thanks for bringing this to my attention, this was a helpful comment.
Too loosely defined start conditions. My bad. Apologies.

Allow me to redefine S1 and S2 as follows: let’s take an average star (e.g: the sun) and freeze it in time. We now start adding matter to it, one helium atom at the time until gravity prevents any photon to escape. At this point we stop the addition of matter and let’s refer to the obtained object as “Scm”. S1 and S2 are identical and are formed in the same way as Scm but we continue adding helium atoms until they have a mass between 1.01 and 1.03 Scm mass.

In a further attempt to improve on parameter definition, let’s define diameter d as the greater value of either the objects diameter or the diameter based on the Schwarzschild radius (d=2*rs).

 

[Picalilli]

It's worth noting that Newtonian gravity would allow things called "dark stars", hypothesised as early as 1783. If one doesn't think too hard about (edit: or, in 1783, can't possibly know anything about) the status of light in a non-relativistic theory of gravity, these would behave broadly as the OP seems to be describing. One could deform such a thing enough that escape velocity from the top of the deformation was less than $c$.

Unfortunately, Newtonian gravity is wildly inaccurate outside very weak fields, and black holes don't behave anything like Newtonian "dark stars". Light was always hypothesised to leave the surface of a dark star - it just didn't make it all the way to our telescope, like a thrown ball falling back to Earth. In contrast, nothing can go upwards from the event horizon of a relativistic black hole.

Thank you for your comments.
I assumed that most people were aware that the concept “dark star” was first mentioned in the nineteenth century, so two mistakes with one assumption, not my finest hour. First of all apologies to the fine people of the eighteenth century and I’ll try to be more careful in the future.
Please find further comments underneath.

 

[Picalilli]

Your scenario incorporates a number of unstated assumptions about how space and time work that are not valid for black holes, as well as some invalid assumptions about what black holes are. To list just a few that have not already been mentioned:

Black holes are not ordinary objects; they do not have surfaces at some constant radius less than their horizon radius. They are vacuum everywhere inside; the matter that originally collapsed to form the black hole continues to collapse all the way down to $r = 0$ where it forms a singularity. After that there is no matter anywhere inside the hole.

The centers of black holes at $r = 0$ are not points in space; they are moments of time, which are to the future of all other moments of time inside the hole's horizon. So it makes no sense to talk about how the centers of black holes move.

Space is not Euclidean around a black hole. So you cannot rely on Euclidean geometry when reasoning about how things move when black holes are present.

The horizons of black holes are not ordinary surfaces in space. They are null surfaces formed by radially outgoing light rays. They do not mark "places" and you cannot reason about them as if they did.

You can't stop two black holes that are falling towards each other from merging. There is no way to push on them to stop them from falling.

Thanks for all the above comments, especially for bringing up the use of models (Newtonian, relativistic or other). I always try to keep in mind and never to ignore the following quote: “All models are wrong, but some are useful”.
Allow me to bring a bit more structure in my paper and let’s start with a proposition and then bring forward the supporting arguments.
Proposition:
Black hole gravity can be overpowered
Argumentation:
Argument 1:
The discovery of a dark massive object in the center of our galaxy lead to the search for “black holes” in other spiral galaxies. Based on observations it seems now to be accepted that most spiral galaxies have a “black hole” at their center. Observations of other galaxies that are at different distances from our galaxy are thus observations at a different moment in the past. It seems very improbable that the black hole at the center of a galaxy is just there at the moment of our observation and somewhere else when not under observation. It seems safe to conclude that the black holes at the center of galaxies remain at the center of their galaxies. According to observations, galaxies move relatively to each other. In order to keep the “black hole” at the galaxy center, the “black hole” must move with the galaxy, thus “black holes” can move in space. If a “black hole” moves in space it makes sense to state that it’s center also moves in space. The easiest way for a black hole to move in sync with it’s galaxy is to move by the same laws of motion as the rest of the masses in the galaxy.
From observing the center of our galaxy we know that photon emitting stars can orbit in close vicinity of massive dark objects with apparently strong gravity. These orbits have not been observed to be perfectly circular. So there is no reason to exclude the possibility of elliptical, parabolic or hyperbolic approach of a “black hole”.
Since the discovery of the black hole at the center of our galaxy multiple observations of the close vicinity of that black hole have been performed, as far as I know no observation has indicated a violation of the laws of nature regarding motion. Until proven wrong by an observation it makes sense to state that in the part of the universe that allows photons to escape all that exists, including black holes move according the known laws of nature. As the inside of an event horizon is not visible (observable by using photons) the above cannot (based on observations) be guaranteed nor denied to be valid inside an event horizon.
If all that exists in our universe started moving from one spot and moves now further outwards in all directions, galaxies containing one or more black holes can move in all directions and thus black holes can move in all directions. So, S1 and S2 can have their starting velocity vectors in opposite direction on parallel lines.

As mentioned in the “gedankenexperiment” the shortest distance between S1 and S2 is big enough to guarantee that the event horizons of S1 and S2 never come in contact. That means that we expect S1 and S2 to move following the known rules for movement.

As described before:
“Gedankenexperiment”: Let's have two identical stars(S1 and S2) with diameter d (redefined above) and each having a mass between 101% and 103% of the mass of Scm. Both S1 and S2 qualify as “black hole”. Two parallel lines(a1 and a2)are at distance b from each other. S1 has it's center of mass on a1 and the center of mass of S2 is on a2. S1 and S2 are at least 300 000 light-years apart. S1 and S2 are sent flying towards each other along a1 and a2 at a relative starting speed between 75 and 85 % of the speed of light. Distance b has to be chosen such that the centers of mass of S1 and S2 come at least at one point closer to each other than 2.5d and never closer than 2d, no matter what shape or mix the matter of S1 and S2 ever evolve to.
There are two cases to consider: S1 and S2 are collapsed into singularities and S1 and S2 are not collapsed into singularities, in which case they stay blobs of plasma.

Let’s consider the plasma blobs first: As S1 and S2 approach each other and they both are composed of plasma they are not solid, a tidal effect will set in and both S1 and S2 will change shape (The effect of gravity is directly related to the amount of mass, but so is the effect of inertia). Losing their spherical shape results in weakening the gravity force on the edge of the system. If weakening the force of gravity results in photons escaping, black hole gravity can be overpowered.

Now the case that S1 and S2 are singularities:
Both S1 and S2 can be approached by photons from all directions in different ways. Let’s do away with photons approaching S2 and continue with photons moving towards the S1 vicinity. From these photons we only are interested in those who curve into the S1 event horizon at the shallowest angel possible. Now we take out all photons that do not cross the line between the S1 and S2 singularities after their first entry into the event horizon and at or close to the moment that the distance between S1 and S2 is at it’s shortest. Some photons that enter the event horizon just before or at the beginning of the effect of S2 gravity will then come into the area where gravity is the sum of opposing gravitational effects of S1 and S2. With S1 and S2 having their centers of mass at a distance below 2.5d the effect on the photons under consideration of S2 gravity is in the same realm as the effect of S1 gravity as the photons move towards and trough the line between the singularities. These photons enter S1 event horizon when under control of mainly S1 gravity and then move into the area where S2 gravity counteracts S1 gravity resulting in allowing the photons to stop curving inwards and follow a curving outward course. Some of these photons will curve further outwards and move away from the S1 event horizon. These photons have been inside the event horizon of S1 and using the S2 counteracting gravity moved out of the S1 event horizon.

If we describe the above accepting that you can have black holes with event horizons that change shape as a result of interaction with other black holes (or other mass, more generally), we can state that S2 puts a substantial dent into the S1 event horizon and if we now look into the photons that curve into the rim of the dent under the shallowest angle possible, curve down trough the rim for less than a 100m (e.g: 1mm),with more than half of the trajectory inside the event horizon before the top of the rim and then cross the event horizon again into the horizon crater to follow their path towards the line between the singularities, some of these photons can now outside the S1 horizon curve out away from S1.

Argument 2:
Allow me to propose another “Gedankenexperiment”:
“Gedankenexperiment 2”: Let’s start with a star like the sun and freeze it in time. We now start adding matter to it, one helium atom at the time and between the mass of the moon and 10kg - give or take a pound (.5kg) - before we reach the mass of Scm we stop the addition of helium and we now start tossing in protons. We know that the effect of electrostatic repel per proton outperforms the effect of gravity per proton and that electrostatic repel and gravity are both cumulative effects. This means that from the start of the addition of protons the gravitational effect is a slower growing value than the electrostatic repel effect. By continuing the addition of protons we must reach the point where the electrostatic repel effect overcomes the gravitational effect and from that point on no more proton can be added, meaning that black hole gravity is overpowered.

Question: How do you keep a photon inside the event horizon using only the black hole gravity under the following circumstances: The photon leaves it’s source – i.e: gets launched at velocity c - in the area between the event horizon and one billionth of a nanometer below the event horizon and it’s velocity vector pointing in the opposite direction as the direction of the black hole gravity effect?

 

[Ibix]

We now start adding matter to it, one helium atom at the time until gravity prevents any photon to escape.

This only happens when the object collapses into a black hole. I imagine adding helium to a star would eventually cause it to undergo core collapse and it may form a black hole - whether it does or not probably depends on what mass and age of star you started with.

I think the problem is that you are imagining that you can create a Newtonian-type dark star. You can't.

 

[PeterDonis]

let’s start with a proposition and then bring forward the supporting arguments.

You are spending a whole lot of words on pointless arguments. You would do a lot better to take some time to understand how our model of black holes actually works. You can't reason correctly about something if your model of it is wrong. In fact, the vast majority of your post is not even worth trying to refute: in Wolfgang Pauli's words, it's "not even wrong".

As far as your "Argument 1" scenario is concerned, your basic idea seems to be that black holes should follow the same "laws of movement" as other objects. If we substitute "laws of physics" for "laws of movement", this is perfectly true: black holes obey the same laws of physics as everything else. However, you don't seem to have a correct understanding of what those laws are. They are the laws of General Relativity: the Einstein Field Equation. You are not using those laws to reason about black holes, so of course you are getting wrong answers.

As far as your "Argument 2" scenario is concerned, your basic idea, of taking a static object and adding mass to it until it becomes a black hole, is impossible according to the laws of General Relativity. A black hole is not a static object that happens to have just enough mass to prevent light from escaping, and you cannot form one by slowly adding mass to a static object while having it remain static. A theorem called "Buchdahl's Theorem" says that the minimum size that any static object can have is 9/8 of the size of a black hole with the same mass. That means there is a finite gap between any static object and a black hole; the only way for black holes to form from any ordinary object is for that object to collapse, dynamically, because it is unable to support itself against its own gravity. That collapse will always have to cross a finite "gap" between the size of the original object and the size of the black hole that forms from it.

Question: How do you keep a photon inside the event horizon using only the black hole gravity under the following circumstances: The photon leaves it’s source – i.e: gets launched at velocity c - in the area between the event horizon and one billionth of a nanometer below the event horizon and it’s velocity vector pointing in the opposite direction as the direction of the black hole gravity effect?

This one is easy: the photon launched under the conditions you specify will fall inward, not rise outward. Anything released anywhere inside a black hole's event horizon will fall inward, even light. This is an invariant property of the spacetime geometry inside the horizon, which is nothing like any ordinary spacetime geometry you are used to.