Historical research guide · 1071 · 2009
On the gravitational radiation of gravitating objects
Arbab I. Arbab
In one minute
Every physics student learns the Larmor formula: shake an electric charge and it radiates light, at a power set by how hard you shake it. Arbab I. Arbab asks the question the site’s thirteenth chapter keeps circling — what if gravity works the same way? Writing inside a framework that treats gravity and electromagnetism as two faces of one thing, he argues that an accelerating mass radiates gravitational waves by a formula of exactly the Larmor form, and from that he derives new expressions for the power a spinning object and an orbiting object each pour into gravitational radiation. The result he singles out is a limit rather than a rate: for a body of mass m and radius R there is a shortest gravitational wavelength it can emit, fixed by nothing but its mass, its size and the constants G and c. Compact, heavy objects radiate short; big, light ones cannot.
Connection
Chapter 13 is the unified picture — the claim that electromagnetism and gravitation are one subject written twice — and this is that claim carried all the way to a working formula, published in a mainstream astrophysics journal. Chapter 11 needs exactly this bridge: if a gravitational Larmor formula holds, then whatever you can do to an accelerating charge you can in principle do to an accelerating mass, and gravitational radiation becomes something to engineer rather than only to detect.
From the source
Working in a framework that unifies gravity and electromagnetism, Arbab argues that accelerating objects emit gravitational waves according to a formula of the same form as the Larmor formula for an accelerating charged particle — that is, the radiated power is set by the acceleration in the same way for mass as for charge.Abstract, first sentence
From that starting point the paper derives a new formula for the power of the gravitational waves radiated by a spinning object.Abstract, second sentence
The paper also derives a new formula for the power of the gravitational waves radiated by an orbiting object, so the same treatment covers both rotation about an axis and revolution about a partner.Abstract, second sentence
The result the abstract states in full is a limit on wavelength rather than a rate: the minimum wavelength of the gravitational wave emitted by an object of mass m and radius R is the fourth root of thirty-two thirds, multiplied by the square root of pi squared times the gravitational constant times m times R, divided by the speed of light squared — a shortest emitted wavelength fixed by the object’s mass and size alone.Abstract, third sentence and the displayed formula
What would settle it is a measurement rather than an argument: because the minimum-wavelength relation contains only the mass, the radius and the constants G and c, it predicts a definite shortest wavelength for any named body, so a gravitational-wave observation of a spinning or orbiting source, compared against that prediction, is the test this formula invites.Abstract, third sentence and the displayed formula
The way in
https://doi.org/10.1007/s10509-009-0058-yHow to cite it
Arbab I. Arbab (2009) On the gravitational radiation of gravitating objects doi:10.1007/s10509-009-0058-y