# The gravity of light

Iridium
If I shine my new yottawatt laser onto a black hole (yotta = 10^24), I expect that the mass of the black hole will increase, along with it's gravity. I know that 'massless' photons can also be converted into electron/positron pairs, (and vice versa). But can the light itself generate it's own gravitational field? If so, I assume that it's own gravity can't affect itself, since gravity can't propagate faster than light, and I expect the beam won't 'gravity focus' itself (not sure though), but how about an observer who is close to the beam? I had planned to try these experiments myself, but found the electricity costs to run the laser are a bit on the high side.

Iridium
Darn ... I calculate that my yottawatt laser beam only contains a mass-energy equivalent of about .037kg/meter of beam. 'Light-Gravity', (if any) would be small for a yottawatt laser.

1 yottawatt ~= 1,000,000,000,000,000,000,000,000 watts (joules/sec)
1kg mass ~= 90,000,000,000,000,000 joules
1 yottawatt ~= 11,111,111 kg/sec mass-energy
length of 1 second laser beam ~= 300,000km
beam density ~= (11,111,111 kg/300,000km) = 37kg/km = .037kg/meter (mass equivalent)

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DaTario
what if you try mirrors a la Fabry-Perot to obtain reinforcement and localization?

I found your post very interesting in deed. I am also concerned with the gravitational effects light can have on light itself.

Is it possible to have an estimative on the power existing inside an star like the Sun, just where particles are formed ? Through your calculations we could get the notion of how big is the gravitational effect of this amount of radiation.

Best Regards,

DaTario

Spin_Network
Iridium said:
If I shine my new yottawatt laser onto a black hole (yotta = 10^24), I expect that the mass of the black hole will increase, along with it's gravity. I know that 'massless' photons can also be converted into electron/positron pairs, (and vice versa). But can the light itself generate it's own gravitational field? If so, I assume that it's own gravity can't affect itself, since gravity can't propagate faster than light, and I expect the beam won't 'gravity focus' itself (not sure though), but how about an observer who is close to the beam? I had planned to try these experiments myself, but found the electricity costs to run the laser are a bit on the high side.

The Equivalence:http://relativity.livingreviews.org/open?pubNo=lrr-2001-4&page=node3.html [Broken]

has to be taken into considerations?

What is local and what is non-local? In an Einstein Thought experiment, a light beam enters a spacecraft, and "bends" downwards, before leaving the window on the other side of the craft, according to the local spacemen onboard, the acceleration and gravitation are equivalent, so the local cause is the fact the craft is moving in a certain direction.

If one performs experiments onboard the craft, then there will be other factors that have to be considered, for instance, what if there are no windows(they are blocked out), and the light source from the thought experiment is replaced with an apparatus that shines a light form one side of the craft to the other?..will the onboard light source follow the geodesics of the external lightsource?

One has to apply certain factors to certain events, in "your" thought experiment, the 'windows' are the Event Horizons, which does not allow light to re-emerge from another side. Now one can also conclude that the lightbeam itself does not "Enter" the Blackhole, but collects around the Mass source. Think of a water hose that sends a finite jet of water at a target, make the target a basketball, the water hits the ball, and dissapates over the SURFACE, it is 'bent' locally around the surface-horizon.

Locally, one can not confirm that water penetrates the surface horizon, but far away one can conclude that there exists a "ball-of-fluid", that is behaving with a Mass different to that of just Water?..one can conclude that there must be some sort of 'basketball', with a Mass that is preventing the water from splashing back to source.

If the water generated its own 'gravitational field', then it would not reach the surface-horizon, it would be comparable to a person taking aim with a water-pistol, at a student friend, pulling the trigger..the water comes out so far, then turns around like a 'WATER-FOUNTAIN', and falls backwards and drenches the person pulling the trigger!

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Staff Emeritus
Iridium said:
If I shine my new yottawatt laser onto a black hole (yotta = 10^24), I expect that the mass of the black hole will increase, along with it's gravity. I know that 'massless' photons can also be converted into electron/positron pairs, (and vice versa). But can the light itself generate it's own gravitational field? If so, I assume that it's own gravity can't affect itself, since gravity can't propagate faster than light, and I expect the beam won't 'gravity focus' itself (not sure though), but how about an observer who is close to the beam? I had planned to try these experiments myself, but found the electricity costs to run the laser are a bit on the high side.

If you take the limit of the gravitational field of a bunch of moving particles, as the energy is kept constant and v->c, you arrive at the conclusion that there will not be any self focusing effects.

Googling, I find this old usenet post by Steve Carlip which makes a similar point. Carlip is a good source, with numerous published papers in GR and quantum gravity.

Steve Carlip Nov 19 2001, 10:24 am show options
Newsgroups: sci.physics
From: Steve Carlip <car...@dirac.ucdavis.edu> - Find messages by this author
Date: Mon, 19 Nov 2001 17:17:25 +0000 (UTC)
Local: Mon, Nov 19 2001 10:17 am
Subject: Re: Photon Gravity
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Ryan Morris <rmor...@home.com> wrote:
> Say two photons were simultaneously shot from two lasers, such that they
> were traveling perfectly parallel to each other and 1mm apart. If there
> were no external forces or interference, would they (very) gradually come
> closer together?

It depends on their direction, which isn't completely clear from your
question. If they are moving parallel to each other in the same direction,
then according to our best available theory of gravity, general relativity,
there will be no net attraction, and they'll remain parallel. If they're
moving along parallel paths but in opposite directions, there will be an
attraction.

> Basically the question is do photons have gravity?

Yes. It's a bit complicated, though: the source of gravity is not just mass,
but the stress-energy tensor, which depends on mass, energy, momentum,
pressure, and internal stresses. Photons don't have rest mass, but they do
have energy and momentum, and energy and momentum gravitate.

> Has this been experimentally investigated?

Not for free photons---the effect is far too small. But it has been tested,
to very good accuracy, that the electrostatic energy of an atomic nucleus
contributes to its gravitational mass.

Steve Carlip

I stumbled across a useful link to the literature while looking at these archived usenet posts:

If this really intrigues you, get R.C. Tolman's classic book "Relativity,
Thermodynamics and Cosmology" first published in 1934, now available from
Dover rather reasonably priced. See Ch 8, Relativistic Electrodynamics, Part
II, section 112 "The Gravitational Field Corresponding to a Directed Flow of
Radiation. also 113 and 114 for the gravitational field of a pencil of light.

I don't have it personally, but it looks like it's \$11.16 from amazon.com

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Iridium
Thanks for a good post, pervect. After thinking about this last night I realized that based on a simple thought experiment, light must indeed gravitate:

I have a box containing hydrogen ... the walls of the box are 'perfect' mirrors (they even reflect neutrons!). I make the hydrogen undergo fusion, and now a percentage of the mass has been converted to light that is bouncing around inside. It would not make sense for an outside observer to sense a sudden large change in the gravity from the box.

As an interesting side-note, the measured gravity from the box might be allowed to change slightly. As far as I know, we still have not experimentally confirmed that matter and antimatter have identical gravitational characteristics. Some physicists think that there may be slightly higher attraction between two objects if one is made of matter and the other of antimatter, compared to the attraction resulting if both objects are made of matter (or both of anti-matter). Thus if some of the light was converted to anti-matter (by converting the light to electron/positron pairs), the measured gravity could increase (although most likely by a very small amount). Many experiments have been proposed to look for such a difference, but as far as I can tell, they still have not been able to settle this one way or the other.