# How dense must a light object be in order to significantly bend space-time?

We know that the mass of the sun bends the space time geometry. Collapsed onto an orange-sized sphere it can turn into a black hole.

The physicist Tippler has shown that time travel is theoretically possible by gathering the mass of a dozen of suns.

This sounds like all about very large masses. Could density work as well?

Rather than dealing with suns, let's assume I start with a jar of 1lb of taco salsa. Does collapsing this jar into a (?)-sized sphere bend the geometry in a more significant way?

Your question can be rephrased to "given a mass of X kg, how densely should I compact it to make it equivalent to a black hole in terms of space-time bending?"

To answer that, just use an online black hole calculator, like this one

For a mass of 1 kg the Schwarzschild radius $$R = M2G \over c^2$$ is $$1.5 \cdot 10^{-27}$$ meters, which is very small, about a million of millions times smaller than a proton, with its $$10^{-15}$$ meter size.

Apart from being too small to be practically usable for time travel, it would also live a very short life, evaporating in about $$10^{-17}$$ seconds.

• Thanks, so mass bends the geometry, but the mass itself is not enough to create a singularity, that's when mass density comes. So one 'could' have a lab created singularity without the need of a very large mass. Correct? Aug 12 '21 at 2:54
• @Xavier Prudent Correct. However, as it was pointed out in the answer, a lab created black hole would disappear faster than a blink of an eye. Aug 12 '21 at 4:06
• Xavier - Mass (or mass-energy) distorts spacetime so that futures point more inward (to the centre of mass) than usual. When it's distorted enough, all futures are inward, so nothing has any path to the exterior: thats an event horizon/black hole. But infalling mass still tries to reach the center, we don't know of any force that can stop it, so we theorise a singularity will form. If quantum effects prevent that, then an incredibly dense "something" will form instead. So a singularity's formation depends on how physics works. But not (as far as we know) on the amount of collapsed mass. Aug 13 '21 at 7:08

The Kugeblitz (1) is a black hole made out of radiation, like light. This is because mass and energy are interchangeable, so having enough energy in a small area means you can create a black hole as well. In this case by concentrating so much light through a single spot at a single moment that it collapses. This might also be the only way to feed a black-hole powered ship since it is exceedingly hard to feed a subatomic black hole with ordinary matter consisting out of atoms.

This does prove one thing: the mass of the object does not matter, what matters (heh) is getting enough density or energy in a single point of space, which will then form a black hole.

Just be sure to check that calculator from L.Dutch's answer. It also mentions something else: the lifespan of the black hole. Any black hole will evaporate (although this is actually an unconfirmed theory, but our best guess at how one works). This evaporation causes energy to be released, and the smaller a black hole is the faster than evaporation process. This process converts mass to energy, and the last seconds of a black hole surpass nuclear bomb levels of energy release. A black hole that lasts a day weighs 1.22928E7 kg for example. Your taco wont be close.

• Thank you, so in the scope of a Tippler cylinder where a frame-dragging effect has to take place (en.wikipedia.org/wiki/Tipler_cylinder), does the density also only matter? Aug 12 '21 at 17:53
• @XavierPrudent I dont know, I suspect so due to the fact they might need negative energy. The frame dragging effect also requires at least some mass, since the only other frame dragging effect I know off is of fast-spinning black holes. Aug 13 '21 at 7:45

There is no minimum density. The bigger your object the lower the required density. The universe itself is very close to being a black hole, yet most of it is a very hard vacuum.

Note, however, that anything that causes significant space-time bending exerts a gravitational force far higher than what chemistry can support--it's going to collapse into a sphere. Such forces obviously would also destroy any machine attempting to compress it--within the limits of the hard-science tag the only way to accomplish this is gravity.

Thus a Tippler cylinder can't be constructed by known physics even if infinite length isn't required.

• Its a bit different. The bigger the object, the more its own gravity will cause a higher pressure inside which increases its density. Aug 13 '21 at 7:46