# Light & Black Holes: Exploring the Paradox

• Gank

#### Gank

Hey guys, I was reading that even light can't escape black holes due to the huge gravitational force which they have. I have been mulling it over for awhile now and I am still stumped. How can a force dependent on the mass of the two bodies act on a body-light/photons which have no mass?

Gravity depends on energy, and photons have energy.
The classical formula from Newton is just an approximation for slow objects, and light is not slow.

Hey guys, I was reading that even light can't escape black holes due to the huge gravitational force which they have. I have been mulling it over for awhile now and I am still stumped. How can a force dependent on the mass of the two bodies act on a body-light/photons which have no mass?
In addition to mfb's correct response consider the question: according to Newtons second law, how much force is required to accelerate a massless object?

General Relativity provides another answer to this question: the spacetime path of a massless particle (the photon) is always a null geodesic. Geodesics are the shortest (or sometimes the longest) path between points. On a plane surface they are straight lines, on a sphere they are the great circles.

For spacetime the measure of a path is the relativistic invariant known as the spacetime interval: s^2 = (ct)^2 - (x^2 + y^2 + z^2) where I have taken the initial event (our spacetime point) as the origin to simplify the expression. Since light travels at the speed of light, the temporal portion is equal and opposite to the spatial portion, and hence its spacetime interval is always zero: a geodesic connecting two events which has a zero spacetime interval is called a null geodesic.

When you solve the field equations for General Relativity you will find an interesting boundary: the event horizon is never crossed by null geodesics which start on the interior of the event horizon. Hence you can see no events from the interior.

This description uses spacetime geometry, and does not involve any forces. It is the presence of mass and energy, concentrated in one location, which results in this severe curvature of spacetime.

There are some nice movies here: http://jila.colorado.edu/~ajsh/insidebh/schw.html

How can a force dependent on the mass of the two bodies act on a body-light/photons which have no mass?
Even in Newtonian gravity the gravitational acceleration is independent of the mass of the particle. General Relativity uses a different model including gravitational time dilation and spatial distortions which affect how light propagates.

Hey guys, I was reading that even light can't escape black holes due to the huge gravitational force which they have. I have been mulling it over for awhile now and I am still stumped. How can a force dependent on the mass of the two bodies act on a body-light/photons which have no mass?

As has already been stated, a photon has energy and thus mass and so is affected by gravity. But I too had problems with the idea that gravity could overwhelm light, such that a radially outward photon at the EH would 'stay at the EH'.

The problem as I saw it was that at the EH, the 'force' of gravity was finite and therefore, so was the energy required to move any given mass out to infinity (to escape). There appeared to be no validity to the assertion that an EH would form at any non zreo radius.

But then I read that space 'flowed' toward massive bodies - at a speed equal to that of the Newtonian escape velocity. I cannot say I was comfortable with the idea that space flows or moves - but it did make a black hole black.

I would dearly like to know what the 'official', scientifically accepted version of this is. Can space be said to flow or to move or not? And if not then what (in English rather than Math) is going on?

But while the jury is out, the idea of a flowing space certainly simplifies things. Take the word 'curvature' for example. I always asked 'curved where?' and never got an answer. The flowing space model as described by http://jila.colorado.edu/~ajsh/insidebh/waterfall.html suggests a very simple answer. Curved directly inwards. An outgoing photon is still outgoing but is swept directly backwards like a swimmer overwhelmed by a river faster than the swim speed.

I would dearly like to know what the 'official', scientifically accepted version of this is. Can space be said to flow or to move or not? And if not then what (in English rather than Math) is going on?
I believe that this manuscript represents the "official scientifically accepted version".
http://arxiv.org/abs/gr-qc/0411060

Note, the authors are clear that this is a model which works well to describe two specific spacetimes. It is not a general model which can be applied to arbitrary spacetimes.

DaleSpam, thank you for this. At least I know I wasn't on a complete wild goose chase! I don't have access to the complete document but the intro makes clear that space can be said to flow. I do note the caveat however, that the river model is just that, a model. I note also the paper is recent (2008). I wonder if the concept of flowing space had any credence before?

By the 'official version' I had really meant the official, academically accepted description of space in a gravity well - rather than the official version of the river model. I was thinking that if I was sitting an exam in GR and I said that space fell towards concentrations of mass, with or with reference to the arxiv paper, would I have passed the exam?