How is it possible for light to be unable to escape from a black hole, given the fact that the speed of light through a vacuum must be the same for all observers?
If light is unable to escape from a black hole, does this mean that light slows down and then reverses direction as it tries to escape?
The answer is no, the speed of light through space-time is still the same for all observers.
It is space-time itself which is falling into the black hole.
Gravity affects the rate at which time flows.
Though, this effect appears different to different observers.
Different observers have different coordinates for space-time.
This is shown from the perspective of an object falling into a black hole, where the black hole has no rotation and no electric charge.
Far away from the black hole, the light is still able to escape.
But close to the black hole, space-time is falling into the black hole faster than light can travel through the space-time.
The demarcation between the region where light can still escape and the region where it cannot is what we call the "Event Horizon."
For a non-rotating black hole, the Event Horizon forms a sphere and people often refer to the size of this sphere as the size of the black hole, even though all the mass is concentrated in the center.
In theory, any amount of mass can form a black hole, if concentrated into a sufficiently small volume.
However, in almost all circumstances, this is prevented from ever happening by electromagnetic and nuclear repulsive forces.
An exception where these repulsive forces are overcome is when a star with sufficiently large mass dies in a supernova explosion, which can form either a neutron star or a black hole.
Let us consider the light emitted either directly towards or directly away from the black hole.
The distance between the arrows represents the wavelength of the light.
As the distance between the arrows increases, the light becomes more and more red-shifted.
From the perspective of an object falling into the black hole, the distance between the arrows increases due to how space is stretched as it falls into the black hole.
So far, we have only been considering the perspective of the falling object, and this appears very differently to an observer far away.
Let us now consider this other perspective.
To an observer far away, the distance between the arrows increases not because space is stretched, but because gravity affects the rate at which time flows.
From this point of view, the closer an object is to the event horizon, the slower the object’s internal clock, causing the object to emit light with a lower frequency.
From this perspective, time at the event horizon stops completely and the object therefore never actually crosses the event horizon.
However, from the perspective of the falling object, its internal clock is always running normally, and it passes through the Event Horizon without noticing that anything special has happened.
From the object’s perspective, as it approaches the event horizon, it takes light from the object a longer and longer time to reach us, and light emitted exactly at the event horizon will take an infinite amount of time to reach us.
This is why the object appears frozen in time to us, from the object’s perspective.
Although the object’s light signals from beyond the event horizon will never reach us, two different falling objects inside the Event Horizon will still be able to see each other’s light signals.
Therefore, life for the object inside the event horizon will still appear normal, at least until the object is torn apart.
Suppose we drop a large sphere into the black hole.
Different parts of the sphere, relative to each other, will accelerate into the black hole at different rates.
This will inevitably cause the sphere to be torn apart, though whether this happens inside or outside the event horizon depends on how massive the black hole is.
The larger the mass of a black hole, the larger the radius of the event horizon.
Objects falling into extremely massive black holes will safely pass through the event horizon and happily continue falling, only to be torn apart much later.
Less massive black holes have a much smaller radius for the event horizon.
Objects falling into less massive black holes will be torn apart long before they reach the event horizon.
In either case, the object will be destroyed before it reaches the center of the black hole.
At the center of the black hole, both General Relativity and Quantum Mechanics become important.
Therefore, no one yet really knows what happens at the center of a black hole, as we presently don’t yet know how to combine these two theories.
Though, we can talk about what General Relativity alone says happens at the center of a black hole.
It says that space-time forms a point of infinite curvature which we call a singularity.
Throughout this video, this curved sheet has represented two of the three spatial dimensions, with a singularity at the center.
In order to understand a singularity, we need to understand intrinsic curvature.
This is described in detail in the video titled "Intrinsic Curvature and Singularities."
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