Black Hole-Dark Energy Thruster?

[Jack Jectivus]

I am not educated on theoretical physics. I have very limited knowledge in the field and, from that knowledge, an idea came to me. I am more so looking to learn why the idea doesn't work than to prove that it does.

Imagine a black hole in expanding space. The black hole emits Hawking radiation in all directions from its event horizon in the form of thermal radiation, calculated with the surface area of the black hole to find it's blackbody radiation in degrees Kelvin. This equation can be simplified to J=(3.3367086×10^-42)÷R, R being the Schwarzchild radius of the black hole in meters, J being the thermal energy emitted by the black hole in joules. Finding energy emitted as a simple function of the black hole's radius shows us that as the radius decreases, the total energy emitted increases.

In this scenario, the black hole exists in a universe filled with dark energy, which powers the expansion of space. Dark energy cannot be obtained and measured as far as we know, but it does determine the Hubble constant, roughly 71 km/s/Mpc or 2.300953×10^-18 m/s/m, which can be measured. Presumably, the more dark energy, the higher the value for the Hubble constant. If there is an imbalance of dark energy on two opposing sides of a black hole, the Hubble constant in those opposing directions would be different. The side with a higher value for it's Hubble constant would be flattened, appearing like half of an ellipse split lengthwise. The acceleration of space away from the black hole on that side would be greater, therefore the escape velocity at what once was the event horizon would be lower, so the region where the escape velocity was once the speed of light is now traversable space. In order to mathematically compensate for this additional spatial acceleration outwards, the Schwarzchild radius on the side facing the higher density of dark matter must be lower. Using the equation to calculate blackbody radiation in Joules from the Schwarzchild radius, we can calculate that there would be differential radiation on either side of a black hole in this scenario. The differential would provide the black hole with thrust from the flattened side, pushing it away from the dark energy with immense speed depending on how flattened one side is compared to the other and the mass of the black hole.

If my ignorance on this topic has just revealed itself, please, educate me!

Edited May 31, 2020 by Jack Jectivus

[Markus Hanke]

6 hours ago, Jack Jectivus said:

Imagine a black hole in expanding space. The black hole emits Hawking radiation in all directions from its event horizon in the form of thermal radiation, calculated with the surface area of the black hole to find it's blackbody radiation in degrees Kelvin.

The original derivation of Hawking radiation was done for an idealised black hole called a Schwarzschild black hole, which is determined solely by its mass, and nothing else. In other words, this is a situation where you have an isolated black hole without rotation or electric charge, in an otherwise empty universe with vanishing cosmological constant (= no dark energy). If you change any of these parameters - e.g. by introducing a cosmological constant -, then the Hawking temperature of the black hole will depend on more than just the surface area of the event horizon, and even the horizon structure itself might change. 

I have not seen a general treatment of this, I only know of an exact solution where global curvature is positive - this is called the deSitter-Schwarzschild black hole. The problem here is that this spacetime is not asymptotically flat, so there is no way to actually define the horizon temperature. Also, there is more than one horizon in this type of spacetime. 

[Strange]

OK. There are a lot that is not quite right in this, so I'll start with the more obvious ones and we can see where we go from there...

6 hours ago, Jack Jectivus said:

In this scenario, the black hole exists in a universe filled with dark energy, which powers the expansion of space.

Dark energy is not responsible for the expansion of space. We knew, from both theory and evidence, that the universe was expanding for nearly 100 years before dark energy was discovered.

Dark energy is a (hypothetical) explanation for the observed accelerating rate of expansion. (It is the simplest way of mathematically explaining the acceleration. Whether it is correct or not is still to be seen.)

6 hours ago, Jack Jectivus said:

Dark energy cannot be obtained and measured as far as we know, but it does determine the Hubble constant, roughly 71 km/s/Mpc or 2.300953×10^-18 m/s/m, which can be measured.

That is determined by things like the average energy density of the universe. Dark energy has caused it to increase slightly in the last few billion years, but it would have a very similar value without dark energy.

6 hours ago, Jack Jectivus said:

Presumably, the more dark energy, the higher the value for the Hubble constant.

More accurately, the more dark energy the faster the Hubble constant changes.

6 hours ago, Jack Jectivus said:

If there is an imbalance of dark energy on two opposing sides of a black hole, the Hubble constant in those opposing directions would be different.

Dark energy is (I think - we are skirting the limits of my knowledge here!) a scalar field and the same everywhere. But I'm not sure we have enough data to be absolutely certain about that.

6 hours ago, Jack Jectivus said:

If there is an imbalance of dark energy on two opposing sides of a black hole, the Hubble constant in those opposing directions would be different. The side with a higher value for it's Hubble constant would be flattened, appearing like half of an ellipse split lengthwise. The acceleration of space away from the black hole on that side would be greater, therefore the escape velocity at what once was the event horizon would be lower, so the region where the escape velocity was once the speed of light is now traversable space. In order to mathematically compensate for this additional spatial acceleration outwards, the Schwarzchild radius on the side facing the higher density of dark matter must be lower. Using the equation to calculate blackbody radiation in Joules from the Schwarzchild radius, we can calculate that there would be differential radiation on either side of a black hole in this scenario. The differential would provide the black hole with thrust from the flattened side, pushing it away from the dark energy with immense speed depending on how flattened one side is compared to the other and the mass of the black hole.

The energy density of dark energy is very, very low. It is not going to have any significant effect on a black hole.

(Calculating what the effect of a varying external energy field would be on the form of a black hole is probably a difficult problem that can only be solved by simulation.)

Also, the expansion of space only takes place in the large areas of space between galaxies - because it only happens where there is a uniform mass distribution. There is no expansion of space inside galaxies (or even clusters of galaxies).

 

[MigL]

Next to a large deep gravitational well, such as a Black Hole, expansion and Dark energy would be insignificant.
We only note their effects where gravity is so weak that expansion/Dark energy exceeds the 'threshold' and its effects become apparent.
( we don't see expansion at solar system, galactic or even galactic cluster levels )
This is in the order of 100s of Megaparsec separation.

[joigus]

Totally agree with Markus Hanke: GR is (highly) non-linear. You cannot understand properties of solutions mixing different aspects in terms of (exact) individual solutions. You must solve Einstein's eqs. from scratch.

I just thought @Strange and @MigL (+1,+1) went more in the direction of what's troubling OP AFAI can tell. (Plus shortage of points.) Dark energy is small potatoes when it comes to BH dynamics. BHs are generally very very small in comparison to comparable cosmic masses. DE is only sizable at very long distances.

[Mordred]

Good points above. Black holes cannot drive expansion of the universe through Hawking radiation any more than stars can drive expansion through their much higher radiation emissions.

The radiation emitted by stars and BH's are miniscule compared to the mass density of the universe.

 Secondly radiation falls off in density as you move further from the source. 

 Lastly the cosmological constant whatever the cause has been around long before the first black holes even existed. Although miniscule in effect as the two prior eras (radiation dominant, matter dominant eras) overpowered DE.

 By this I will use the matter dominant era as an example. Radiation obviously existed however the main contributor to expansion during the era is matter. The cosmological constant was around as well.

 The same goes for the previous era (radiation dominant) the other two contributors still existed. Just that their contributions can be ignored.

Now here is where I really muddy the waters. The Hubble parameter is decreasing but the rate of expansion via the recessive velocity formula is increasing

Yet the cosmological constant stays constant in energy/Mass density....

At time Z=1080 The Hubble parameter is roughly 20,000  times greater than its value today 

 

 

Edited May 31, 2020 by Mordred

[Janus]

22 hours ago, Mordred said:

Good points above. Black holes cannot drive expansion of the universe through Hawking radiation any more than stars can drive expansion through their much higher radiation emissions.

The radiation emitted by stars and BH's are miniscule compared to the mass density of the universe.

In addition, any black hole more massive than the Moon is taking in more energy from just the cosmic background radiation than it is emitting via Hawking radiation.