Gravitoelectromagnetic circuits

Question

Looking into gravitoelectromagnetism, a strong analogy is drawn between gravity-torsion to electro-magnetism. Continuing this line-of-thought, I would imagine a "gravitational circuit"- a closed loop of mass flow (mass carriers replacing charge carriers)- would behave in similiar manners to electromagnetic circuits.

While a resistor in such a circuit is fairly understandable (a bottleneck-in-a-pipe description would perhaps do), I am very much intrigued by the idea of a capacitor (large massive gravitodes seperated by vacuum?) and an inductor (a "coil" of flowing mass?) and their behavior. Would oscilating gravitational fields be achievable this way, using an alternating current of mass? How about circuit resonance- would that create a zero field? Would a gravitational RLC circuit produce the known behaviour of it's electric counterpart?

I would naively assume so, as the behaviour of electrical circuits is derived at it's core from Maxwell's equations, and these apply here as well. The main prblem is the positivity of mass- while there exists negative charge, a gravitational counterpart is missing. How will that affect the results? How about the fact (as mentioned by Wendy Krieger) that positive momenta repel in a similiar manner to charge repulsion?

Can the analogy even be stretched that far? If so- can it be stretched even further? Can a gravitotransistor be created (my intuition is that the lack of negative mass means the answer is no)? How about a gravitocomputer?

in short: does the analogy between gravity and electromagnetism allow certain behaviours of electronic circuits to exist in a purely gravitational system? If so, which devices can be imitated this way?

Thank you!

Answer 1

My reaction to gravitoelectromagnetism was to rewrite the definitions of magnetism and the fields in terms of momenta.

$\vec s = \hat r / \gamma r^2$ where $\gamma = 4\pi_{SI} = 1_{cgs}$

$\vec D = Q\vec s \qquad \vec H = \vec P \times \vec s$ 'fluxes'

$\vec F = Q \vec E \qquad \vec F = \vec P \times \vec B$ 'fields'

$ zcD = \kappa E \qquad \vec cB = z\kappa H$ constituant equations

$\kappa = 1_{SI} = c_{cgs}$ is an EM velocity constant in $Q = \kappa It$. It corresponds to inverse turns, in 'Ampere-turn'.

This converts current into a flow of momentum, in that P here is Qv. This makes gravity easier to understand, since Qv becomes a moving mass, rather than some supposed 'current of mass'.

Maxwell's equations are correspondingly paired as

Ampere: $\qquad \nabla D = \rho Q / \beta\qquad \kappa\nabla H = \rho P/\beta + \tau D$

Faraday: $\qquad \nabla B = 0 / \beta\qquad \kappa\nabla E = - \tau B$

Snell: $\qquad zcD = \kappa E = c\vec B = z\kappa H$

Here we have $\tau = \frac d{dt}$ as a time-operator, and $\rho = \frac d{dv}$ as a volume operator. $\beta = 1_{SI} = 1/4\pi_{cgs} = \frac 1{\gamma}$. The existance of maxwell's equations in both electricity and gravity are a precursor to the rationalisation, or going from cgs to si style formulae.

These are the generic SI/cgs forms of the equations, written to reduce repetition.

The form of snell's equations is the 'photon continuity relation', where you shoot a single photon through a defraction, and keep the vertical D,B continuious and the horizontal E,H.

Note we write it in the form in z and c, viz $\epsilon = \kappa/zc$ and $\mu = \kappa z/c$. In this form, we see that c arises from space-time and z is a property of the field. z_SI = 376.730313462 Ohms.

I have come across a number of demonstrations that if a field travels at a finite speed, then a co-field of opposite sign and magnetic in nature exists (Heaviside), and the consequences of a flux in SRT is to produce equations such as in D and H above.

This means that GEM or gravitoelectromagnetism is a consequence of SRT.

Of course, gravity has z as negative, and q can only be positive. But while positive charges attract in gravity, positive momenta repell. So you have as matter gets tinier and tinier in a black hole, the momenta repell perpendicular to the circle they are spinning in: ie polar plumes on pulsars, and the fermi spheres of the galaxy.

Theiry deMeers has demonstrated that galaxies take their shape and constant speed because of the operation of co-gravitation.