What happens to photons leaving very large massive objects?

Question

Consider a particle falling into a black hole. Just before it reaches the Schwartzchild radius sphere it emits a photon, and just after it passes into the sphere it emits another one, both moving radially away from the central mass.

The photon emitted outside the sphere is moving away at the speed of light, obviously, and losing energy, therefor becoming longer in wavelength. As it leaves the gravity well, at what rate does it's frequency change?

The photon emitted just inside the sphere also travels away from the central mass, but it doesn't have enough energy to escape the gravity well entirely, and eventually simply runs out of energy and ceases existance.

How far from the black hole does that photon go before it ceases existance?

So what color is a black hole at some point, say at the point where the pull of the black hole is equal to the pull of Gravity at the Earth's surface?

Answer 1

Well, gravitational redshift can be calculated from the energy conservation law and general relativity. It follows, that $$\nu_1=\nu_2\sqrt{\frac{R_1(R_2-r_s)}{R_2(R_1-r_s)}}$$ as you can read from wikipedia.

As for the inside of the event horizon, the law of energy conservation has to hold even there(the only problem is the singularity in the middle), so the light can not simple cease to exist. If we are considering the photon as a massless particle, it will just fall into the center of the black hole.

In relativity, we talk about gravity using light cones. If you draw a graph with space on $x$ axis and time on $y$ axis, the speed of light can be visualized as a cone, this is called a light cone, because it represents the trajectory of light. The cone that runs to positive numbers is called a future light cone, the cone that runs from negative numbers is called a past light cone(see figure).

Gravity has a property that it rotates this light cone, it bends the light. The event horizon is a place, where the future light cone is paralell to it, meaning that all light that is emitted there either stays inside the event horizon and will orbit the black hole forever, or falls inside. Below the event horizon all of the future light cones point to the center of the black hole.

Inside the black hole, you can literally not see anything below you, you can see only things above. Also, had you somehow managed to fall into a black hole and not get spaghettified to death by its gravity outside the event horizon(which can be achieved given a sufficiently big black hole), you would be killed by the radiation orbitting the black hole on the event horizon that particles that fell into it before you left there.