# Escaping light

#### Päällikkö

Homework Helper
What happens to light "trying to escape" from a black hole? Does it lose all its energy?
Does the light leaving the sun lose some of its energy as it goes "uphill" the geometry of spacetime? And as E=hf, does this mean that the light shifts color?
As light rides "downhill" as it comes to Earth, does it gain energy?
Is this energy sort of like potential energy? If so, is there a level where this potential energy is zero (maybe black holes)?

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#### quasar987

Homework Helper
Gold Member
A teacher of mine once explained this to me in these terms: "Light cannot escape the black hole because space-time itself is flowing inside the black hole faster than the speed of light (the same way water is flowing down a drain). So as light travels 1m towards the surface of the BH, the space in which the photon travels as traveled 2m (for exemple) towards the center of the BH."

I would like to know how accurate this model is.

#### pervect

Staff Emeritus
Päällikkö said:
What happens to light "trying to escape" from a black hole? Does it lose all its energy?
Does the light leaving the sun lose some of its energy as it goes "uphill" the geometry of spacetime? And as E=hf, does this mean that the light shifts color?
As light rides "downhill" as it comes to Earth, does it gain energy?
Is this energy sort of like potential energy? If so, is there a level where this potential energy is zero (maybe black holes)?
First of all, your description of "gravitational redshift" is correct. As light falls downhill to earth, it gains energy and is blueshifted. As light goes "uphill" away from Earth, it loses energy and is redshifted.

Now let's go on to black holes.

If you consider the light that is emitted exactly at the event horizon of a Schwarzschild (non-rotating) black hole, it basically "hangs there" in space.

Because its distance to the black hole is constant, it does not gain or lose any energy. The only person who can see it is someone who falls thorugh the black hole in the exact same spot the light was emitted, though. When they reach the event horizion, they will see the light, just as it was originally emitted (no frequency shift) - assuming it hasn't been absorbe by some other body travelling through the black hole.

Of course this is a highly unstable situation. Light emitted even a fraction closer to the event horizon will escape - light emitted even a fraction inside the event horizon will fall into the singularity. So the number of photons that will actually be "trapped" exactly at the event horizon in this manner for long periods of time is very close to zero - it's like trying to balance a pencil on its tip, it will balance for a short time, but if you wait a minute or two, the pencil will fall over.

#### pervect

Staff Emeritus
quasar987 said:
A teacher of mine once explained this to me in these terms: "Light cannot escape the black hole because space-time itself is flowing inside the black hole faster than the speed of light (the same way water is flowing down a drain). So as light travels 1m towards the surface of the BH, the space in which the photon travels as traveled 2m (for exemple) towards the center of the BH."

I would like to know how accurate this model is.
The accuracy of the model isn't great. It does accurately describe how light travels near a black hole, and may be somewhat satisfying because it achieves it's result in that respect. However, according to relativity, there is not any way that one can actually measre the "flow" of space-time with any sort of small mechanical instrument, even in principole. No matter what sort of instrument you use, you'll always get the same reading, because the laws of physics are the same no matter what one's state of motion is. So for the purpose of doing science, you are explaining something that you can observe as being caused by something that you cannot measure, something that relativity says is impossible to measure.

#### Päällikkö

Homework Helper

What happens to light when it goes closer to the center of a black hole? Shoudn't its energy grow to almost an infinite amount?

#### Dr.Brain

Päällikkö said:
What happens to light "trying to escape" from a black hole? Does it lose all its energy?
Does the light leaving the sun lose some of its energy as it goes "uphill" the geometry of spacetime? And as E=hf, does this mean that the light shifts color?
As light rides "downhill" as it comes to Earth, does it gain energy?
Is this energy sort of like potential energy? If so, is there a level where this potential energy is zero (maybe black holes)?
Our Universe is expanding and so is the spacetime fabric, so light coming from far off powerful sources, will lengthen, that is , its wavelength increases as it travels long distances, and it appears to lose energy , and thus called 'red-shifted'. A light coming from a star far away would appear to be red-shifted , but a light escaping earth would not, but this escaping light earth would be red-shifted for a far off star/planet.Therefore light escaping from location A to a location B would appear to have different shifts for different locations.

Near a black hole , the spacetime fabric is completely hindered and yes light coming from near a BLACK hole or trying to escape from a black hole(though not possible) will appear to lose energy as it travels to our eyes through a telescope.

BJ

#### Päällikkö

Homework Helper
Dr.Brain said:
Our Universe is expanding and so is the spacetime fabric, so light coming from far off powerful sources, will lengthen, that is , its wavelength increases as it travels long distances, and it appears to lose energy , and thus called 'red-shifted'. A light coming from a star far away would appear to be red-shifted , but a light escaping earth would not, but this escaping light earth would be red-shifted for a far off star/planet.Therefore light escaping from location A to a location B would appear to have different shifts for different locations.

Near a black hole , the spacetime fabric is completely hindered and yes light coming from near a BLACK hole or trying to escape from a black hole(though not possible) will appear to lose energy as it travels to our eyes through a telescope.
Surely light emitted "before" the even horizon will leave the black hole.

Your claims are rather contradictory: You state there is no redshift due to Earth's gravitational field, but on the hand you said that light loses energy as it tries to escape from a black hole's gravitational field.

Is the redshift seen on light emitted from distant galaxies due to the spacetime fabric being expanded or due to the fact the galaxy is moving away from us (which ultimately is due to the expanding spacetime fabric, though).

#### pervect

Staff Emeritus
Päällikkö said:

What happens to light when it goes closer to the center of a black hole? Shoudn't its energy grow to almost an infinite amount?
The frequency and hence the energy of the light depends on the frame in which you measure it.

Inside the event horizon of the black hole, it's impossible to "stand still". There isn't any stationary frame to measure it's energy from, so I'm not sure how to answer the question of what the energy is from the "inside" viewpoint, there isn't any single answer.

The important viewpoint is from the observer outside the black hole, anway. The viewpoint at infinity is the viewpoint from which energy is conserved. One finds that from this viewpoint at infinity, the total energy of the black hole is a constant, and is equal to the amount of energy that has fallen into the hole.

Energy conservation in GR can be quite tricky - see for instance

http://math.ucr.edu/home/baez/physics/Relativity/GR/energy_gr.html

Is Energy Conserved in General Relativity?

In special cases, yes. In general -- it depends on what you mean by "energy", and what you mean by "conserved".

#### DaveC426913

Gold Member
Päällikkö said:
What happens to light "trying to escape" from a black hole? Does it lose all its energy?
Does the light leaving the sun lose some of its energy as it goes "uphill" the geometry of spacetime? And as E=hf, does this mean that the light shifts color?
Yes. Light climbing out of a gravitational well is red-shifted. Light climbing out of a black hole is infinitely red-shifted.

#### Päällikkö

Homework Helper
Yet another series of questions about light. I suppose these are easier to answer, as they're about SR and the Doppler effect:
Is the Doppler effect on light due to a combination of the following: time dilation, relative movement and the growth of space?

Does the growing of space have a direct impact on light? I know it's the phenomena that makes the distant galaxies move relative to us. But if there was light in a vacuum, would it lose energy (frequency) due to the stretching of the fabric of spacetime?

Does Lorentz-contraction have an effect? Does time dilation always cause redshift (instead of blueshift, that is) from the observer's point of view (ie. not the source's)? Must both time dilation and Lorentz-contraction be taken into account (separately) (my thoughts got tangled up here :). My guess'd be no, though)?

As frequency increases, does intensity increase too? Why?

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