# How big a black hole is needed for this story?

The story begins in classic disaster film style. A small rogue black hole is approaching our Solar System. It isn’t going to get close enough to destroy everything, but it will agitate our Sun, causing horrific solar flares as it reaches perihelion. Those flares are going to bake the Earth’s surface in fatal levels of radiation. Conservative estimates suggest that it will take a thousand years for the planet’s magnetic fields to recover, at which time it will be fit for recolonization.

We don’t have FTL travel and we’ve only got a decade to prepare, so the world unites in an effort to build a fleet of generation ships capable of holding ten thousand souls, plus a Noah’s ark assortment of domesticated animals. The trick will be to keep that viable gene pool alive for a thousand years in deep space. The finest minds alive work on the problem, but there is just no way to bring even a fraction of the oxygen, food and water needed.

In desperation, an insane plan is adopted.

The ships will launch about a year before perihelion and will proceed on a collision course with the approaching black hole. At the moment when the singularity passes closest to our Sun, the ships will dive into its gravity well, slingshoting in close enough to the event horizon to cause significant time dilation.

Emerging after half an orbit of the hole (by firing Orion nuclear engines to reach escape velocity), they will race back towards earth, arriving just before the life support supplies run out. If the time dilation does what it should, the fleet's two year round trip, will find an Earth more than a thousand years older and completely healed.

Now for my question…

What combination of black hole size/mass and distance from our Solar System would make this story viable?

• It needs to get close enough that an Orion nuclear drive (and maybe a sun-dive/slingshot outbound maneuver) can get our ships there in a relatively short time (so that we don’t run out of life support on the way there).
• It needs to be small enough that it doesn’t rip Earth out of its orbit as it passes by. It can take the rest of the planets, but Earth and our moon have to survive.
• It needs to be big enough that it can generate enough time dilation that a thousand years can pass on Earth during the fleet’s one or two year journey.

Is it believable that a cosmically short-term interaction with a distant black hole, could temporarily cause our sun to intensify, throwing off solar flare for a few years before settling back down to normal?

This question asks for hard science. All answers to this question should be backed up by equations, empirical evidence, scientific papers, other citations, etc. Answers that do not satisfy this requirement might be removed. See the tag description for more information.

• With a powerful and reliable energy source, the ship doesn't need to carry 1000 years of food, water, oxygen, it can recycle everything. With enough energy, if the ship can maintain 1G of acceleration for 30 years, time dilation means 30 years of ship time is 1000 years of earth time. I think that any black hole long enough to allow survivable surfing of the event horizon would be so massive that it would absorb the entire solar system, including the Sun. Though the best chance of survival is probably in deep caves on earth until the fatal radiation passes rather than a hastily built ship. – Johnny Apr 17 '15 at 5:59
• Getting that close to a black hole will likely cause significant en.wikipedia.org/wiki/Tidal_force, to the point where your ship will be ripped apart. – Dan Smolinske Apr 17 '15 at 6:29
• If the black hole passes too near to the earth , wont it cause time dilation on earth as well? Can somebody please educate me on this? – Abhishek Apr 17 '15 at 7:10
• There is another big problem here as well - time dilation means the ship will only experience 30 years...however the black hole will still have flown through space for 1000 years. When you complete the sling shot you will be a LONG way from earth. – Tim B Apr 17 '15 at 8:07
• @Lightning..., Intuitively, I didn't agree with you about the effect of loosing planets, so I jumped over to the physics stackexchange to check. I found a question on exactly that subject and It turns out you are right (+1), at least in terms of Jupiter and Saturn. I will edit my question later tonight. Thanks! – Henry Taylor Apr 17 '15 at 18:43

That's some extreme time dilation.

It is possible, but the black hole needs to be insanely massive for your ship to orbit it without falling into the event horizon and have the proper amount of time pass.

Gravitational time dilation goes like this:

$$t_0 = t_f \sqrt{1-{{r_0}\over{r}}}$$

Where,

• $t_0$ is the proper time between events A and B for a slow-ticking observer within the gravitational field
• $t_f$ is the coordinate time between events A and B for a fast-ticking observer at an arbitrarily large distance from the massive object
• $r$ is the radial coordinate of the observer (which is analogous to the classical distance from the center of the object, but is actually a Schwarzschild coordinate)
• $r_0 = {{2GM}\over{c^2}}$ is the Schwarzschild radius of M.

I initially solved this by estimating the insane minimum distance of 1km from the event horizon. This was supposed to be a minimum bound for the size of the black hole, but it appears to not be insane enough. You said you wanted half an orbit, a slingshot, it's hard to say how long that would take. I'm guessing a tenth of one year; about five weeks.

$$0.1\ year = 1000\ years \sqrt{1-{{r_0}\over{r_0 + 1000\ meters}}}$$

Solving this gives a Schwarzschild radius of about 99,999,999,000 meters. Which requires 33,851,584 solar masses to produce. This would be a supermassive black hole larger than the one at the center of our galaxy. Larger by almost an order of magnitude.

To have such a thing pass near enough to our solar system that the ship could get there in one year is likely to do more than make our sun fizzle a bit. Placing the black hole farther away means it needs to be even more massive in order to make up for the extra travel time. Which might not work anyway because the ship would also have to orbit in less time, which starts to become impossible as the black hole gets larger.

To make this story plausible, the elapsed time needs to be significantly reduced. Unfortunately that reduction would likely need to be to less than ten years. Even getting closer to the black hole doesn't solve it. Getting to just ten meters away still requires a black hole of around 338,500 solar masses. But, 1km was already insane and very likely impossible to achieve.

I don't think a passing black hole is a viable method for "intensifying" our Sun's weather. I can't think of anything you could do to the Sun to make it act weirdly for only 1000 years, it's been around for so much longer than that.

• Thank you for your help. It appears to be one of those cases where a good story premise and science have no common ground, so the story will die unwritten. +1 for all your efforts with the math. Thanks again! – Henry Taylor Apr 17 '15 at 11:38
• Great answer ... and you neglected to mention the complicating effects of tidal stresses such close approaches would impose. While 100 km from the event horizon might be safe for a 33,000,000 solar mass black hole, I sincerely doubt 10 km from the event horizon for a 330,000 solar mass black hole is. – Jim2B Apr 17 '15 at 12:35
• @HenryTaylor Don't let it die, this is a brilliant story, and I want to read it. I do believe that a sufficient amount of Unobtanium in the hull will allow a ship to pass very close to the event horizon with only minimal adverse effect! Let's not let boring fact get in the way of a good story! – Marv Mills Apr 17 '15 at 12:48
• You get back within a generation and 1000 years have passed on Earth. As far as the black hole causing the sun to fry the Earth being unlikely, maybe just have some other catastrophe that will make the Earth uninhabitable for 1000 years, perhaps even our own doing or otherwise unrelated to the black hole. Then, the black hole showing up could actually be the savior of mankind. – Bryon Apr 17 '15 at 13:43
• Please don't let this die. It sounds incredible. – Pureferret Apr 17 '15 at 16:29

This is probably more of a comment than an answer, but as I don't have enough reputation to comment I'll see how this goes:

Have you considered using a cosmic string instead of a black hole? You might be able to still get the time dilation effect due to the string acting like it has high mass, and the crew could travel along the length of the string as it passes near the solar system so they exit at the other end of the string, still near the solar system but at a time when the string has passed out of harm's way (rather than with the black hole where they would exit very far from where they started).

• Good idea! I've been reworking the question over the weekend, and no matter how I play with the numbers, I can't seem to get the non-ftl ships far enough away from the solar system to make the wandering black hole harmless. I will look into your cosmis strings as an alternative. Thanks. – Henry Taylor Apr 19 '15 at 23:39

I suppose I'll address the solar flares angle, since nobody appears to have tried that yet.

My main objection here is that an external source will have a very hard time causing solar flares. Solar flares are, at their hearts, magnetic phenomena. While the exact mechanism behind them is unknown, one fundamental component is charged particles traveling along magnetic field lines, formed inside the star. There are various ideas as to the events that lead to these particles being ejected: kink instabilities in coronal loops (Wood & Priest (1979)), coronal mass ejections (discussed in Zhang et al. (2001)), or more exotic structures (Kusano et al. (2012)). A good overview of many different theories is given in Shibata (2011).

The point is, an external source is most likely not going to cause solar flares. It's true that black holes can have magnetic fields, but, as I explained here, they are generated by the accretion disk surrounding the black hole, not the black hole itself. You would need to have it bring its accretion disk along with it for it to have a magnetic field itself, which would really screw up the Solar System in other ways - and still probably not cause solar flares, unless you take into account the other extreme consequences of a black hole entering the Solar System.