# Could an object traveling at a significant fraction of light speed create a black hole?

Nothing with mass can reach the speed of light because the closer to the speed of light it gets the more mass it has tending toward infinite mass as it approaches light speed & the more mass it has the more energy needed to accelerate it any further tending toward infinite energy as it approaches light speed.

I'm assuming this mass is relative in the same way as time dilation from near light travel so that it's not felt by anything or anyone who might be traveling at these speeds.

Howsoever I also assume the gravity effects of this mass is felt by external objects that are passed by the items traveling at these speeds.

So (assuming I have all that sufficiently correct?) this seems to mean that passing through (or near enough to) a solar system with sufficient speed to replicate the gravity effects of a large black hole could be catastrophic (to say the least) with the potential to drag planets & even the systems star itself to the fast moving object & compact them around it into a new black hole.

I have so many thoughts, ideas & questions stemming from this ;) but I'm by no means sure I've got it entirely right at this stage, so it's probably prudent to limit myself to "have I got this right so far?"

• There's a related question which is answered by the splendidly named "Aichelburg-Sexl Ultraboost", but jdunlop's answer for this one is plenty good enough, saving me the effort of trying to explain it. Oct 30, 2021 at 8:33
• – Stef
Oct 30, 2021 at 12:39
• Seems like a better question for physics.stackexchange.com Oct 30, 2021 at 23:29
• – neph
Oct 30, 2021 at 23:44
• Agreed that this is just a physics question, not a worldbuilding question. The answer is no - however close to the speed of light the object is travelling, if it's moving at a constant velocity then in its own inertial frame it is not moving and has the same mass as it has at rest because it is at rest in that inertial frame. So it would not collapse into a black hole from moving at that velocity, unless it would also collapse into a black hole at rest, because the laws of physics are the same in all inertial frames. Oct 31, 2021 at 22:26

# No

Relativistic mass is not "real" mass. The gravity of an object travelling at relativistic speeds does not increase, because its mass does not increase. The "mass" added in the Lorentz equations is an expression of the asymptotic energy required to actually reach lightspeed when you have mass.

Edit: Forbes explains this at greater length, but the pertinent bit:

Understanding the answer is the key to understanding relativity: it’s because the “classical” formula for momentum — that momentum equals mass multiplied by velocity — is only a non-relativistic approximation. In reality, you have to use the formula for relativistic momentum, which is a little bit different, and involves a factor that physicists call gamma (γ): the Lorentz factor, which increases the closer you move to the speed of light. For a fast-moving particle, momentum isn’t just mass multiplied by velocity, but mass multiplied by velocity multiplied by gamma.

In high school physics, we use the Lorentz formulae and are told that the apparent mass/length/clockspeed of the object changes, but gravity warps spacetime, and so if the mass of the object changed, photons would behave differently around it for all observers, which is impossible. From the frame of reference of an observer on the accelerated object, the object cannot appear to gain mass. Which means that spacetime cannot be distorted... and therefore it cannot be distorted from the perspective of a stationary observer.

• Thankyou! I suspected this was likely hence the desire to check my thinking before letting it run any further :) I had similar issues with 'popular science' references to quantum entanglement & faster than light communication, that one took me days (maybe weeks) down the rabbit hole weeding daft media induced chaff from actual facts to get to the end of, was very muddy (rabbit holes can be like that) & disappointed by the end with a burning desire to see all popular science presenters executed, for taking the piss or impersonating a real scientist who knows his subject, either would do :) Oct 29, 2021 at 22:07
• Overall, the answer is "high school physics teaches lies that are useful". I remember a teacher drawing the electron orbitals. These are very useful when dealing with molecular bonds. They're also (mostly) not real, but it's a useful lie. Even the idea of an electron as thing you can (metaphorically) hold in tweezers is a useful oversimplification. Oct 29, 2021 at 22:10
• Implication of the blogpost linked is that black holes are made by rest mass, not relativistic mass aka energy. But how do the theoretical "light-only" black holes work then? Isn't the cause for gravity is ENERGY? Oct 30, 2021 at 13:20
• @NooneAtAll Relativistic mass isn't the same thing as energy either. The deal with a kugelblitz is that if you have enough photons densely packed into a small space, that space will produce gravity as if there were $E/c^2$ mass inside, even though none of the photons themselves have any mass.
– zwol
Oct 30, 2021 at 17:15
• This is false. Spacetime is curved by energy density. There's no difference between rest and "relativistic" mass as far as spacetime is concerned.
– neph
Oct 30, 2021 at 23:18

No. Gravity in General Relativity is not just about the mass. Einstein's equation sets the curvature of spacetime equal to the Energy-Momentum-Stress tensor, which contains one term for each pair of coordinates from x, y, z, t.

The tt term is the energy, and because of the rest mass energy usually pointing in this direction when things are going slowly, this is usually by far the biggest term. That's why it is usually valid to ignore all the other terms and treat gravity as if it was purely sourced by accumulations of mass.

The xt, yt, and zt terms are the linear momentum. When things are moving very fast, these terms get big. However, because of the peculiar geometry of spacetime, it tends to cancel out the effect of the mass. More on that in a moment.

The xx, yy, and zz terms are the pressure. This is one of the main reasons why stars collapse into black holes - as the star gets bigger, the pressure in the centre grows, which makes the gravity even stronger, raising the pressure even further. There's a positive feedback loop that means beyond a certain point infinite pressure is needed to balance the forces. Since nothing can supply infinite pressure, nothing can stop the collapse.

The xy, xz, yz terms are the shear stresses. Those are usually small, because no matter is strong enough to resist such forces. With compression, there's nowhere for the matter to go, but with shear the matter flows like taffy.

If you rotate your coordinate system, the numbers change. But it's still the same underlying geometry - just described differently. Rotating about planes involving only x, y, z axes behaves like you would expect, but rotating in any plane involving time works a bit differently. In Euclidean geometry Pythagoras says the squared length of a vector is $$x^2+y^2+z^2$$, which rotations don't change. In Minkowski geometry, the t coordinate has the opposite sign. So we can define the squared length of a vector using a modified Pythagoras theorem as $$t^2-x^2-y^2-z^2$$, which doesn't change under 4D rotations. This leads to a relationship between energy and momentum: $$E_0=E^2-p_x^2-p_y^2-p_z^2$$, where $$E_0$$ is the rest energy (or mass), the length of the energy-momentum vector and a fixed constant in any reference frame, $$E$$ is the relativistic energy (or mass, the thing that increases with speed), and $$p_x$$ etc. are the components of the momentum.

When you shift to a reference frame where the object is moving, the momentum terms obviously get bigger, and so the energy term gets bigger too. This is the kinetic energy. The increase in size of one is counterbalanced by the other, to yield exactly the same rest energy. The energy-momentum vector is not any longer - it's just viewed from a coordinate system where the components in each direction are bigger numbers. And so the 'size' of the whole energy-momentum-stress tensor, and hence the gravitational space-time curvature, is no different.

This does not mean that kinetic energy is irrelevant for gravitational purposes. If you have a fast moving particle confined in a box, then it bounces backwards and forwards, resulting in momentum currents in opposite directions that cancel out. But the kinetic energy term doesn't cancel. If particles are bound together, then the kinetic energy of their confined motion contributes to their mass, because the momentum terms cancel out. It turns out that much of the mass of ordinary matter is not the bare mass of the constituent particles themselves, but comes from the binding energy that is the result of their confinement, being stuck to one another.

# Frame shift: how about two objects...?

Lead answer is right that one object can't make a black hole with relativistic mass. But it is wrong in another way: relativistic mass IS real mass! Most of the "mass" in the protons and neutrons of every everyday object is the "relativistic mass" of quarks moving around.

If you need any extra convincing, consider what happens if two of your particles crash together. Suddenly all that relativistic energy is spewing out as vast numbers of particles and antiparticles and photons and so forth. So it is certainly conceivable that these two objects could make a black hole with all that mass. (Note the "rest mass" is determined by the velocities of these objects relative to each other, because that cannot be reduced to zero by simply picking another frame of reference)

The caveat being that of all the ways to round up the mass to make a black hole, delivering it as free energy has got to be the most painful way to do it.

• This is overcomplicated. There's no difference between energy & mass. If smashing things together gets enough energy in one space to achieve the energy density required to make a black hole, it doesn't matter what form it's in.
– neph
Oct 30, 2021 at 23:30
• I never suggested there was. Oct 31, 2021 at 0:55

If we take our solar system as reference, an object like the one you describe would cross it from one end to the other of Pluto's orbit in about half a day.

Gravity is a small force and, especially at large distances, would need time to produce significant effects. Time that is not given by the quick dashing through the system.

Considering that the probability of an impact is minuscule, the most likely effect is a small perturbation of some orbit, negligible in the short term, maybe less in the long term.

That apart, consider that to double the mass the object would need to travel at 0.8c, to decuplicate it it would need to move at 0.99 c, an it would still be far from being anything close to a black hole. However, as jdunlop noted in the comment, that relativistic mass does not increase the gravitational pull of the object under acceleration.

• I'm assuming that you're saying that yes basically I've got this right? but that you think it would have to pass pretty damn close to anything to even perturb its orbit (which wasn't really the question yet, though yes that is the direction I was headed with my thoughts, how fast and how close does an object of a given mass need to be before it starts having serious consequences). Oct 29, 2021 at 21:08
• Worth noting (as in my answer) that relativistic mass does not increase the gravitational pull of the object under acceleration, so the only concern you'd have from this object zipping through the solar system would be if it hit something and released its kinetic energy. Oct 29, 2021 at 21:59
• @jdunlop "relativistic mass does not increase the gravitational pull of the object under acceleration" wouldn't this allow to determine a privileged reference frame which is at rest? A pulls like a mass of 8 kg but has a mass of 10, while B pulls like 8 and have a mass of 8, thus B is standing still.
– L.Dutch
Oct 30, 2021 at 3:23
• @L.Dutch No, because mass is invariant. $\gamma$, the Lorentz factor, is incorporated into momentum, accounting for the requirement that infinite energy is required to accelerate any mass to the speed of light, but an observer can only measure the mass of the accelerating object by its effect on spacetime. The "stationary" observer sees it pull like a mass of 8kg, and the observer in the same FoR also sees it pull like a mass of 8kg. The only strange thing is that it requires more and more energy to increase its momentum (and velocity), accounted for by the Lorentz factor. Oct 30, 2021 at 4:52

# Yes, as you're travelling through the solar system.

If you travelled fast enough, which is probably going to be a very weird number like 99.99999999% of the speed of light, collisions with protons and other particles will cause micro black holes to form.

This was a fear for the LHC, that it would form micro black holes. You could use much more energy.

The gravity would of course be negligible, since relativistic mass isn't real mass and doesn't change the underlying space time geometry. But, the explosions of energy could certainly do some damage to the solar system, if there was enough speed.

• It was a fear only for people who weren't paying attention. Everyone else knew that some cosmic rays have higher energies than particles in the LHC, and noted a distinct lack of micro black holes bombarding the Earth.
– Mark
Oct 31, 2021 at 1:48
• The likely reason for that being that the micro black holes either evaporate quickly or require higher energies. Oct 31, 2021 at 7:09
• Why would someone fear a micro black hole? I think some folks have some strange ideas about how blackholes work.... If a black hole has a few nanograms of mass (and to be clear, thats many many orders of magnitude bigger than whats proposed) it'd still only exert that much gravity, just with a sharper gradient near the planck scale. Oct 31, 2021 at 9:56
• They asked about creating a black hole, not saying it had to cause damage. As I noted, it wouldn't cause any notable damage. The explosions would do the damage. Oct 31, 2021 at 13:45

# Yes.

A black hole does not form because you reach a certain rest mass energy. A black hole forms because a region of space reaches a certain energy density. Accelerating a mass to a sufficiently high velocity that the region of space it occupies achieves this energy density would form a black hole.

Note that black holes form because of energy density, not total amount of energy. As a result, you can have very low-mass black holes--space is highly curved, but only very close to the singularity. Accelerating things to very high speeds will produce these type of black holes unless the total energies involved (rest mass + kinetic energy) are on the order of solar masses. Such small black holes will rapidly cease to exist thanks to hawking radiation; their energy will be released as a flash of other particles.

• This is wrong. Neutrinos have mass, and thus a frame of reference. In the frame of reference of the typical neutrino, almost everything in the universe is moving at near-c. You're either demanding the existence a preferred frame of reference, or that the existence of a single neutrino causes everything in the universe to collapse into a black hole. Oct 31, 2021 at 10:13