Hi /u/AdiSoldier245!

I think the best way to understand, why photons cannot escape from within the event horizon, is the following way:

According to General Relativity, gravity is the curvature of spacetime. The stronger the gravitational field, the more extreme is the curvature of spacetime. Inside the event horizon of black holes, the curvature of spacetime is so extreme, that no path through spacetime exist for photons, which lead anywhere else but to the singularity at the center. That is, spacetime itself is curved so much, that there is, physically and geometrically, simply no path that light can follow to the outside.

1. The speed of light is constant, so light can't slow down.
2. Black holes (and other massive objects) bend the space around them, so the path of a passing object (or light) bends as the object goes through that space. That doesn't slow the object or light down - it only changes its trajectory.

Black holes bend spacetime so much that direction called "the future" is pointed towards the centre of the black hole itself.

Light cannot fight the flow of time and it just so happens that the flow of time in black hole is hell bent on keeping you there. One cannot escape a black hole anymore than one can escape to the past.

If the speed of light can't slow down, why is it always referred to as "the speed of light in a vacuum" ?

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So light is actually slowed down through different mediums ie) to about 75% of it's speed through water, and 2/3 of it's speed through for instance glass. Gravity itself is not a medium, so does not impact the speed of light.

The speed of light does change depending on the medium it is passing through. For example, it is slower in water than through a vacuum and slower through glass than it is in water.

That, however, isn't relevant to the question being asked by OP.

Gravity curves the spacetime around it. We have a hard time visualizing what that looks like in three dimensions, but you can think of a massive body as bending spacetime inward toward itself. Being so massive, black holes bend spacetime to extremes. The curvature is so great that, for an object within the event horizon, there is no trajectory in spacetime that will take you outside the black hole. Rather, spacetime is so curved that all trajectories into the future converge on the singularity at the heart of the black hole.

Mass bend space time, thats how we get gravity. A black hole has so much mass that it completely warps space time to the point where outward is not an available direction anymore.

Sometimes people visualize gravity using a rubber sheet and various balls. In this analogy a black hole would be a ball so heavy that it tears a hole into the sheet and if another ball then would fall into that hole it is off the sheet and can't get back on it.

I'm not certain of this, but my understanding is that light in a vacuum is unhindered. When it's passing through a medium, it interacts with the medium and either doesn't travel straight, or is absorbed and emitted. Someone correct me if this is wrong.

There is a limit to how fast something can go. c is the universal speed limit. Photons and other massless particles travel at that speed.

There is not a limit to how much gravity something can have. So, for black holes, they have so much gravity that their escape velocity is higher than c.

The speed of light through any one medium (air, glass, a vacuum) is constant, so that is what is meant even we say "the speed of light is constant".

It is not changed, we preceive it as changed.

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Photon thropugh water or glass is moving with the same speed as in the vacuum.

But that photon is striking into every molecule/electron it finds on its way. So we preceive speed of ray of light as 2/3 c for example.

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Just like photon emitted in nuclear fussion in a core of a Sun - it needs about 100 000 years to be emitted to the Solar System, because there are so many molecules that its bumping into on its way.

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Other's gave the more relativistic/geometric explanation, but an easier ELI5 analogy I think is: imagine firing a bullet into the air. It'll fall back to the earth, unless you can shoot it so fast it can get past the gravitational pull back to earth. Imagine doing the same on a larger planet: you'll have to fire that bullet even faster to pass the gravitational pull. Now imagine a light gun, on a "planet" with so much gravity that even that light gun firing a bullet at the speed of light, it still doesn't have enough speed to escape the gravitational pull. Gravity bends the path of light, and while it moves at the same speed throughout, you don't have to slow something down to make it fall back in if you bend it enough.

That is incorrect. The light does actually slow down without getting absorbed or bouncing.

What is important to understand is that a photon is the oscillation of the EM field, not just a particle. Charges (like an electron) interact with the the EM field both eays, they are acted upon and act on it. Oscillations cause charges to move, but moving charges cause oscillations in the field. These effects interact with eachother in such a way that it causes the oscillation (a photon) to propagate slower in that medium than the maximum speed (speed of light) even without being absorbed.

The way you're describing it, transparency would be impossible, everything would be translucent or opaque. Like, say, the core of the sun that you mentioned.

That direction changing is it being affected by gravity. As a photon passes a star it's trajectory is changed. Not because the star is pulling on the photon but it has distorted space itself. In a black hole that's base is bent so severely that circles back in on itself.

You don't want to think of gravity as a force that is pulling on objects. But bending space. Earth isn't traveling in a circle around the Sun. It's traveling in a straight line. The sun has just bent space so that line circles back around in on itself.