# Would a black hole passing next to a star create a deadly focal point due to gravitational lensing?

Black holes bend all kinds of radiation thanks to their giant gravity. Now imagine that a black hole passes close to some star (we know of cases when black hole devours a star). Star emits massive amounts of radiation in all directions, so naturally the radiation just outside the event horizon will be bent by the black hole. Many rays will be focused into a single point.

Wouldn't that create a "certain death zone" on the opposite side? Could this be a real threat for celectial bodies from far-away black holes (for example for earth)? If this effect in fact happens, would different radiation types be focused farther away - for example UV, visible, X-Ray etc. in it's own zones (EDIT: meaning basically - do black holes work similar to prisms by lensing different types of wavelengths differently)?

In the draft above the yellow circle is a star, black dot is black hole, gray circle is event horizon and red circle is the "death area where rays are focused by the black hole

• Remember that a stellar black hole is very tiny, so the portion of a nearby stars light that it could focus would also be tiny; too small to have any "destructive" effect. – antlersoft Nov 12 '20 at 21:22

tl;dr: seen at a distance, the lensed object will appear as an annulus or "ring" around the lensing object, and while that will be brighter than if there were only empty space, sadly it won't be death-ray bright!

Let's first think about what makes a familliar lens a lens. Near the center the thickness doesn't vary much, but as you move farther from the center the thickness changes faster and faster.

If we measured the slope or angle of the surface, we'd see that the angle increased roughly linearly with distance from the center.

In the thin lens approximation the angle that the lens bends the light $$\Delta \theta$$ is proportional to the distance from the center of the lens $$r$$ where the light hits it. The bending power increases linearly with distance.

$$\Delta \theta \approx \frac{r}{f}$$

where $$f$$ is the focal length of the lens.

How do concentrated points of mass bend light? Wikipedia's Gravitational lens give us

$$\Delta \theta \approx \frac{4 G M}{r c^2}$$

and that's a problem because now $$r$$ is on the bottom!

Single concentrated objects like black holes do not act like the familliar lenses we use to focus. They do have some ability to concentrate somewhat compared to empty space, but nowhere near as much as real lenses do. From a source that's a certain distance away, there will be only one angle that gets bent parallel into a "beam", angles slightly larger or smaller passing slightly farther or closer from it will be bent much less or much more, either diverging or converging from the axis afterward.

Thus seen at a distance, the lensed object will appear as an annulus or "ring" around the lensing object, and while that will be brighter than if there were only empty space, sadly it won't be death-ray bright!

In the case of your star/BH pair, exactly how bright it will be along that axis depends on the details, but one can get a good estimate by ray tracing, either with a few lines of Python or pencil and paper for estimate purposes.

If the star were close then it is an extended object, a wide disk, and those can't be focused to points even by lenses (we can't concentrate blue sky with a magnifying glass) so there wouldn't be much of a death effect. If it were far, you could concentrate it better (because it's more point-like) but it would be a lot dimmer to begin with because it would be farther away.

A Horseshoe Einstein Ring from Hubble The bright thing in the middle is the lensing mass, the ring is the lensed object behind it. It's not a "beam" but just a distorted view, but it is brighter than if the lens weren't there.

• intriguing, thanks for your in depth answer! Interesting to know, that lensed objects are in fact brighter. Using this I can speculate that this setup in a solar scale - where the star is considered an area emitter, not a point light - could result in more power per surface, if only the "halo" surface of lensed image were bigger than the surface of undistorted image. And as a clarification to the main question - do different wavelengths get lensed differently (think black hole acting as prism by splitting radiation into components - X-Ray, UV, visible etc.)? – Tooster Nov 13 '20 at 0:23
• @Tooster it's a really fun and intriguing scenario and I think you're on to something interesting for sure! The best way to think about gravitational lenses is to forget the gravity and just think of the black hole (or any object with mass for that matter) as "bending space". Photons will travel in a "straight line" and aren't "pulled" towards the object, it's the "straight lines" in space itself that are bent. Then we can see that the wavelength doesn't matter, there's no chromatic aberration from a gravitational lens. I think there's a Q&A here about that somewhere, I'll add a link shortly. – uhoh Nov 13 '20 at 0:32
• @Tooster answers to the following questions mention that there is no chromatic aberration: When is optical refraction important in astronomy? and Gravitational lensing of quasars – uhoh Nov 13 '20 at 0:37

I believe there are systems where a black hole and a star orbit each other. So possibly such systems shoot deadly radiation beams outward from the plane that the two objects orbit in.

In the Lensman series by E.E. Smith, a gigantic space war results in the constant invention of newer and more powerful weapons. TV Tropes has a trope Lensman Arms Race named after the series.

One weapon developed in the Lensman arms race is the Sunbeam, which artificially focuses all the radiation which a star emits in all directions into a single narrow beam of destruction. Thus it does artifically what a black hole passing close to a star might do naturally.

If I remember correctly, sunbeams were only useful within a solar system and were not used to project beams to destroy planets in other solar systems.

And it seems intuative to me that a black hole could not focus radiation tightly enough for the beam to be deadly at interstellar distances.

But possibly someone will be able to calculate at what distance range a beam of deadly radiation from a star/black hole combination might be dangerous.