# What is the formula that shows that gravitational waves can carry information and data?

Gravitational waves can carry information about its source but for further information. Is there any equation which shows that gravitational waves can carry information and data?

• Good question! However, could you possibly add a bit more information, in the question's current state, it's a little hard to understand exactly what you mean (or at least in my mind). May 4 at 20:17
• i meant, how it is possible load data in GW, for example EM wave can carry data but how about GW flux? it is better to say, i meant what we have in documents and papers about carry data in GW science ... i read only they can deliver us data about their source , but how? what kind of data? ... May 4 at 20:26
• Alright, now I understand. May 4 at 20:28
• This is kind of trivially "yes". There's no practical way of doing this, as we are unable to produce detectable gravitational waves. But as a simple thought experiment: place a ball on a string. whirl about yourself (this produces gravitational radiation) then stop (radiation stops) use this "on-off" to send a message in morse code May 4 at 20:39
• If you tell us what equation would be the equivalent for electromagnetic waves then you might get a sensible answer. Sep 24 at 13:58

Obviously they can, in the sense that at least the presence or absence of a gravitational wave can be detected. Hence you could send information by generating one or not, for example by either rotating two enormous masses around each other or not. Practically this is unlikely to be very useful.

What is the bandwidth you could send? Actually detected waves have had frequencies reaching a few hundred Hz, so that would give you a few hundred bits per second at most. Rotating deformed neutron stars might produce kHz waves, getting up to a kilobit per second at most. As noted in this answer, the frequency behaves roughly like $$\sim\sqrt{G\rho}$$ for gravitationally bound systems and hence to get decent bandwidth you need extremely high density objects. But to get a strong signal that you can detect at a distance they need to be very heavy and fast. So this is unlikely to be a very effective means of communication.

The theoretical maximum is likely given by a variant of Lachman's formula for electromagnetic waves, taking into account that these waves have slightly different statistics. One interesting observation is that this bound will scale with the energy: you need a lot of energy in the wave to have many gravitons that can carry information separately.

• thanks, you mentioned it is roughly like Gp, what do you mean by Gp? May 6 at 10:12
• G times by rho. G is the gravitational constant and rho is the density of the two orbiting bodies. More dense bodies can orbit more closely without colliding, and so can produce higher frequency gravitational radiation. May 6 at 12:24

$$f_{GW}$$ changes because the binary system radiates energy. It could also gain energy through mass transfer. $$f_{GW}$$ can also be phase modulated. When planets orbit a binary system, the binary system cannot remain at rest. Since it orbits the common center of mass, $$f_{GW}$$ is not constant but phase modulated. If you measure this PM, you can determine the orbital period of the planets and their masses. The PM is calculated using this equation:

$$f_{GW}=f_{GW0}+t\cdot\dot f_{GW0}+a_{planet}\cdot sin(2\pi t f_{planet}+\phi_{planet})$$

The parameters have the following meaning:

$$f_{GW0}$$ is the frequency of the undisturbed GW. This is calculated from the circulation period.

$$\dot f_{GW0}$$ is the frequency drift of $$f_{GW0}$$

$$a_{planet}$$ is the modulation index of the PM assuming that the planet describes a circular orbit around the GW source.

$$f_{planet}$$ is the orbital frequency of the suspected planet.

From the phase $$\phi_{planet}$$ it follows when the planet is in front of or behind the GW source from the point of view of the earth.

A GW may also transport other information. You only know this when you manage to receive continuous GW.