This is the first in a short series on black holes and we start with the falling in.
Ever wondered what would happen if you had the nasty fate of falling into a black hole or what you would see happen if you were at a safe distance watching your friend fall in? Well read on and find out…
To set up the scene we need two characters (or observers as is the language of theoretical physics). I’ve always fantasised about interstellar travel and this site has two authors so i’ll indulge myself. Joe and Mekhi are orbiting a black hole at a safe distance in their spaceship. By safe distance I mean their spaceship is at a stable radius, far enough away from the center of the black hole such that it does not spiral inwards as a result of the hole’s immense gravitational pull. Mekhi has decided she wants to die in the most spectacular way possible, being engulfed by a black hole and Joe, for science’s sake, is very keen to see what happens to Mekhi as she falls in. So, she puts on her spacesuit on to stop her exploding prematurely, waves goodbye and exits the spaceship.
[Black Holes have a very large gravitational pull and as such can distort even the paths of photons passing by, in a process called ‘lensing’ causing them to be whipped into an orbit around the black hole which leads to this eerie surrounding glow.]
Right, let’s flash back to special relativity for a moment (get it?). Remember one of the consequences of moving extremely fast? Time dilation. (You can read more about it here). This means, an observer, who watches an other observer travel at a high proportion of the speed of light measures the time between their events to be longer than the travelling observer does. For example Mekhi is about run a race at a high proportion of light speed and she has a stopwatch in her pocket. She starts the stopwatch when she starts running and stops it when she finishes the lap. Joe does the same, he starts the stopwatch when Mekhi starts running and stops it when she finishes the lap, all the while sitting still watching. The time measured on Mekhi’s stop watch will be less than the time measured on Joe’s. Remarkable but true, this is time dilation – a consequence of moving very fast. Now let’s get back to general relativity, which is the big theory in the case of Black Holes. Here’s the relevance – time dilation is also a consequence of a gravitational fields. Time runs slower in stronger gravitational fields. If you’re close to a large gravitational mass, the field will be subsequently stronger and your clock will run slower than somebody’s who is not. For example if you spent all your life at the top of a skyscraper, your clock would run slightly (almost negligible but slightly) faster than someone on the ground (closer to the Earth’s center of mass i.e. a stronger gravitational field) – general relativity decides your pay off for enjoying such a wonderful view would be having a slightly shorter life.
So as Mekhi approaches the Black Holes she gets closer and closer to the Black Hole an object with a colossal mass and as such a colossal gravitational field. Think of each tick on Mekhi’s clock (that she carries with her) as an event. When Mekhi and Joe were together in the spaceship the time between Mekhi’s ticks would coincide with the time between Joe’s clicks. But as she gets closer and closer to the black hole the time between Mekhi’s ticks/events, as measured by Joe, get further and further apart – time dilation. Now there is this special radius that every black hole has called the event horizon. It the radius (or distance) from the center of the black hole at which the gravitational pull is so strong that not even light can escape. The event horizon is determined purely by the mass of the black hole and is given by the equation: r = 2GM/c^2 Where r is the radius (distance), G is the gravitational constant, a fundamental universal constant, c is the speed of light and M is the mass of the black hole. So remember the ticks on Mekhi’s clock coincide with events in Mekhi’s experience for example the blinking of her eyelids or the kicking of her feet as she realises what she has done. As she gets closer and closer to the Black Hole the time Joe measures betweens these events gets longer and longer, it as though Joe essentially sees all Mekhi’s movements go in to hyper slow motion. Now how is Joe receiving this information? He is seeing her and how is he seeing her – he is seeing her through the transmission of photons which are carrying light from her towards him. Now here is the link with the event horizon part – when Mekhi crosses this radius during her fall the photons can no longer escape the gravitational pull and make it back to Joe. Joe cannot see the Mekhi who crosses the event horizon. Now, counterintuitively, it’s not that Mekhi disappears suddenly. The time as measured by Joe between her events just before she crossed the horizon became so so very dilated that he essentially sees her frozen image just before she crossed the point of no return. The light waves stretch to lower and redder frequencies and the image of Mekhi slowly dims and fades, over and out.
[A depiction of the warping of space time around the center of a black hole. The gravitational pull becomes so strong that the center of the black hole results in a singularity where the laws of physics break down.]
Now what about Mekhi’s experience of this whole thing, after all she’s the one doing the travelling. Well Mekhi sails through the event horizon without experiencing anything different at all, she probably couldn’t even tell it was happening. In fact as she crosses she can still look back and see the spaceship and the region outside the black hole horizon as normal and she can probably also just about make out Joe’s horrified face through the spaceship window. Now if the black hole is a small one tidal forces can come into play here and the force on her feet (which are closer to the center and hence experience a stronger gravitational pull) may be significantly stronger than the force on her head and thus she would experience spaghettification – one of my favourite words in theoretical physics – where she gets stretched so much that she becomes elongated like a piece of spaghetti until eventually she gets torn in two. If the hole is small and this effect is quite large she will see a lot of warping of the light around her as well as she undergoes this gruesome process. However if the black hole is a larger one these tidal forces will be much weaker and she will go on her merry way sailing down to the center of the black hole without noticing much difference. Moral of the story if you’re going to go off galavanting in a black hole, choose a large one! So on she goes down the center where most likely she will be torn apart before she reaches the singularity. The singularity is the point at the center of the black hole where the spacetime has been warped so immensely, density and the gravity have become infinite and the laws of physics as we know them have disintegrated. If Mekhi remarkably reaches the singularity without being spaghettified her only reward will be being crushed to an infinite density… probably, the truth is we don’t have a clue what actually happens at the singularity because our laws of physics completely break down. There are theories in modern day theoretical physics that believe the gravitational field does increase as your get closer to the black hole’s core but then eventually reduce as if you’re coming out the other end of the black hole, into what could be a new universe, this hypothetical exit region has imaginatively been named a white hole. Though it’s very likely a meek human being would not survive the crushing forces of gravity before this point occurred.
Forthcoming posts in the series will delve into mysteries surrounding black holes such as the information loss problem and the black hole firewall paradox. Black holes have always been a source of many cosmic problems and the answer to the paradoxes surrounding them may help us answer some of the most pressing questions in theoretical physics, such as how to reconcile general relativity with quantum mechanics. For now however we stop here having explained what it looks like when an observer falls in and how this contradicts with what the observer themselves experiences. I’d much rather be the one on the spaceship after all…