# Why can't electromagnetic radiation escape black holes?

## Main Question or Discussion Point

Why can't light escape black holes?

Isn't light as an electromagnetic radiation massless, thus not affected by gravitational pull?

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sylas
Why can't light escape black holes?

Isn't light as an electromagnetic radiation massless, thus not affected by gravitational pull?

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Even in classical physics, there is an expected divergence of light with gravity. I've never fully understood this myself, but as a start, note that the acceleration of a very light body in a gravitational field is independent of its mass.

If you drop a one kilogram weight, it falls at the same speed as a two kilogram weight.

This is because there is an equivalence of "inertial mass" (which says how much force is required to make something diverge a bit) and "gravitational mass" (which says how much force is applied in a gravitational field).

Light may be massless... but that's both inertial mass and gravitational mass, in classical physics. I think. You can apply a limit as both internal and gravitational mass tend to zero, and that (I think) is the classical expectation for light... assuming the equivalence of inertial and gravitational mass. (Someone correct me if I have this wrong).

Consider a particle of mass m being pushed around by a large mass M. The force involved is GmM/r^2. The amount of gravitational acceleration is F/m, or GM/r^2.

Note that the "m" term is now gone.

Although you actually need relativity to analyze a blackhole properly, you can calculate the boundary beyond which light cannot escape using classical physics.

Potential energy of a lightweight particle is -GMm/r. Kinetic energy is 0.5mv^2.

A particle is gravitational bound when GMm/r > 0.5mv^2, so the escape velocity at distance r is v=sqrt(2GM/r). The quantity "m" does not appear. If you use "c" as the escape velocity and solve for r, you actually get the Schwartzchild radius of a blackhole: 2GM/c^2

Classical physics is an approximation. For a full treatment, you need some quantum physics in which light does have inertia in the sense of having momentum; and some relativity to deal properly with gravity in terms of geometry rather than a force in Euclidean space. But it turns out you still get the same result for the limit at which light is trapped at a blackhole.

Cheers -- sylas

The fundamental idea of general relativity is that gravity is a geometrical effect due to the curvature of spacetime. Spacetime is curved, and objects follow paths which (to first approximation) are the curved-space analogues of straight lines; for example, if spacetime looked like a sphere, then objects would follow paths along great circles (lines of longitude). The same holds for light. The only way mass enters into the equation, so to speak, is as a component of the stress-energy tensor, which determines the geometry of spacetime. There is one other restriction placed on the motion of light, however: light must follow "null paths," i.e., light must travel in such a way that it experiences no proper time. (This is like saying that the time dilation factor for something moving at the speed of light is infinite.)

Another way of answering the question is that, in relativity, "mass" and "energy" are really the same thing (remember E = mc^2 ?), so it is perfectly logical that light should be influenced by gravity the same way as matter is.

rcgldr
Homework Helper
From what I've read, the speed of light isn't affect by gravity, just it's direction, which implies that gravity can only accelerate light perpendicular to it's direction of travel. If this is the case, then why can't a beam of light directed radially away from a black hole escape?

vanesch
Staff Emeritus
Gold Member
You shouldn't think of a black hole as a "big mass pulling on stuff in an Euclidean space", but rather as a place where spacetime is seriously warped. As another poster said here, in such a warped spacetime, "the next best thing to a straight line" which doesn't exist geometrically anymore, is what's called a geodesic. They are ensembles of "points" (events) in spacetime (so locations of the kind (x,y,z,t)) which would correspond, in flat spacetime, to "straight uniform motion". You can parametrize them (those points on a given geodesic) with a real parameter: x(s), y(s), z(s), t(s). In flat space, we usually do so, and usually (but not always) we take the parameter s to be equal to time ('universal time'). So we end up with x(t), y(t), z(t), and for a "geodesic" (straight line) in flat space, this becomes:
x(t) = vx t + x0
y(t) = vy t + y0
z(t) = vz t + z0

which is nothing else but "straight line motion" (uniform motion) in flat space, as you've learned it in high school.

But when spacetime is warped, the curvature of spacetime tells you what are now the geodesics. Light follows special geodesics, which are "null geodesics" (which correspond, in flat spacetime, to uniform straight motion such that vx^2 + vy^2 + vz^2 = c^2).

And it turns out that if you start out in certain regions in the spacetime of a black hole, you cannot leave a certain region - in fact all null geodesics end up in the singularity, no matter "in what direction" they start out. (at least for a Schwarzschild black hole ; for rotating black holes, it is way more involved).

Matter points follow "timelike geodesics" which is the equivalent in flat space of having vx^2 + vy^2 + vz^2 < c^2. Also all timelike geodesics starting out in an event in the neighbourhood of the black hole end up in the singularity, and are not able to leave a certain region.

I'm not 100% of this, but I think that there exist geodesics that can leave a point near a black hole, only they are not "timelike" nor "null geodesics" but are spacelike. But I could be wrong on this.

sylas
From what I've read, the speed of light isn't affect by gravity, just it's direction, which implies that gravity can only accelerate light perpendicular to it's direction of travel. If this is the case, then why can't a beam of light directed radially away from a black hole escape?
There is a distance at which light that is tangential to the hole will follow a circular path curving around the black hole. For a non-rotating black hole, this "photon sphere" is at 1.5 Schwartzchild radii.

It's a bit like a conventional circular orbit, in which the speed remains the same but the velocity vector is endlessly pulled sideways, orthogonal to the direction of motion.

This shows that the classical ideas I used above have broken down -- because such photon is "gravitationally bound" in a sense, and yet outside the point where classical physics says c is the escape velocity.

As everyone has noted, the proper description of gravity in these extremes is geometric, using relativity. Different co-ordinate systems do strange things near the Schwatzchild radius. If you try and set up co-ordinates in which a photon moving radially is always moving at "c", you end up with something that looks like space itself getting sucked into the hole. Very weird; it makes my head hurt.

Cheers -- sylas

From what I've read, the speed of light isn't affect by gravity, just it's direction
And it's energy. Light climbing up out of a gravity well shifts red. Whimsically put, if you shine a flashlight straight up, the beam gets tired.

Isn't the inability of light to escape just the definition of a black hole? (otherwise it wouldn't be black)
Regardless of whether it actually exists or not.

Many reasons. You can see it in many ways but all point to the same result
one is:
it's got to do with the inertial and gravitational equivalence principle.
According to it, i suppose, there is no physical experiment that can determine if a reference frame is an accelerated frame or is in a gravitational field having the same value of g as that of accl frame
so if you imagine a straight light beam in a lift accelerating upwards, you should see it bends slightly, like in projectile motion as if you throw a ball
Einstein said that the equivalence principle demanded that the same is true if gravity is present because you cannot distinguish between the two inside the frame.
that's one of the reasons to believe gravity bends light, since velocity of light is so large, you need a lot of acceleration or equivalently a strong gravitational field to actually notice the slight bend.
a black hole is just the extreme case, it bends light so forcibly that it never actually escapes, as in you consider escape velocity of a particle, same here.

another way:
light has to spend energy while traveling in a gravitational field. if you shine yellow light at the moon, the beam slowly loses energy on the way, and at some distance, might appear red. if you consider a black hole , its the extreme case.

Although these are what is called as the 'layman's way' of understanding gravity and black holes. If you know deep physics, then you'll find a mathematical expression too.
As pointed out, black holes were invented by mathematicians (at least they gave the idea)

DaveC426913
Gold Member
Isn't the inability of light to escape just the definition of a black hole? (otherwise it wouldn't be black)
Regardless of whether it actually exists or not.
No. They exist. And they do capture light. The reason light cannot escape is because strong gravity bends space-time. Light follows curved space-time. Inside the extremely curved space-time of a black hole, it is so curved that all paths bend back on themseves to the singularity. Light, which follows these paths through space-time, bends back on itself and ends up at the singularity.

No. They exist. And they do capture light. The reason light cannot escape is because strong gravity bends space-time. Light follows curved space-time. Inside the extremely curved space-time of a black hole, it is so curved that all paths bend back on themseves to the singularity. Light, which follows these paths through space-time, bends back on itself and ends up at the singularity.
You say that all path are bent so that light end up back in the black hole. So, if you imagine a line/path goint radial out from the center of a black hole, in what direction is it bent? up? down? left? right?
I know that there is no absolute up and such, but what i mean is in what direction is the path bent from our perspective?

The biggest reason for which light cannot escape a black hole is the fact that the black hole bends space. Light always travels in a straight line in relation to space, so if the space is curved, then light will curve with it. Light is simply following the curved space into the black hole. Light will never come back out again because space is constantly warping even more at the speed of light. Its like running on a treadmill that always goes as fast as you do: you will never move in relation to it.

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DaveC426913
Gold Member
You say that all path are bent so that light end up back in the black hole. So, if you imagine a line/path goint radial out from the center of a black hole, in what direction is it bent? up? down? left? right?
In that case, it is infinitely red-shifted.

In that case, it is infinitely red-shifted.
I see, so you are saying that if light wasn't redshifted, then it could escape. Isn't it just a matter of time before the light find the radial path then?
if yes, doesn't that mean that without redshift, it would be shining just as bright as a normal star?
The reason I ask is that I have not hear that the only reason that light can't escape a black hole is because of redshift. Is redshift the only reason that light can't escape?
What happens with the light when it's red shifted? Is it destroyed?

DaveC426913
Gold Member
I see, so you are saying that if light wasn't redshifted, then it could escape.
No it couldn't.

But I see your point. I can't really describe what would happen to infinitely red-shifted light.

Isn't it just a matter of time before the light find the radial path then?
if yes, doesn't that mean that without redshift, it would be shining just as bright as a normal star?
The reason I ask is that I have not hear that the only reason that light can't escape a black hole is because of redshift. Is redshift the only reason that light can't escape?
What happens with the light when it's red shifted? Is it destroyed?

No it couldn't.

But I see your point. I can't really describe what would happen to infinitely red-shifted light.
Okay. Thanks for trying anyway.