We are told to imagine that within the Schwarzschild radius, a particle will spiral in to its doom hitting the singularity in an undetermined amount of time. All this comes from extrapolating the Schwarzschild metric beyond its domain of validity, $r<2GM/c^2$. This is undoubtedly why Karl Schwarzschild did not find any such sucking in of material, and why he went beyond his outer solution to create an inner solution for $r<\surd(G\varrho)/c$, where $\varrho$ is the density and $1/\surd(G\varrho)$ is the Newtonian free-fall time.

There are more parallels between Newton's force and the Weberian force of electrodynamics than meets the eye. Newton derived his inverse square law from the centrifugal force

$$F_c=F_s\sin\alpha=\frac{v^2}{\varrho},$$

where $F_s$ is the force directed at the source, $v$ the velocity and $\varrho$, the radius of curvature. Newton then introduced Kepler's II,

$$rv\sin\alpha=L,$$

to obtain

$$F_s=\frac{L^2}{r^2\sin^3\alpha}.$$

We all know what sound waves are. A mechanical wave, which a sound wave is, vibrates in the medium by causing compression and rarefactions, as in the diagram below.

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LIGO chose to measure the strength of gravitational waves by using a Michelson type interferometer while recognizing that the "ripples in the fabric of spacetime cause the frequency of the laser light to fluctuate "ever so slightly" as well as admitting to the fact that "a gravitational wave does stretch and squeeze the wavelengths of light in the arms." However, LIGO adds that "it turns out that it doesn't matter. What matters is how long the laser beam spends traveling in each arm.

Brown, in his Reflections on Relativity attempts "to give a very plausible (if not entirely rigorous) derivation of Schwarzschild's metric purely from [a] knowledge of the inverse square characteristic of gravity, Kepler's third law for circular orbit, and the null intervals of light paths."

Brown bases his derivation on the space-time metric

$$d\tau^2=g_{tt}dt^2-r^2d\phi^2,$$

We will show that Kepler's III destroys the independence of the frequency $\omega$ and its rate of change in time, $\dot{\omega}$ so that they cannot be varied independently to determine the 'chirp' mass $\eta^{3/5}M$ from

$$ G(\eta N)^{3/5}M=c^3\left(\frac{\dot{\omega}}{3\omega^{11/3}}\right)^{3/5}.$$

where $N$ is a numerical factor, $32/5$ for linear GR, and $N=2/5$ for the EM-like model discussed by Hilborn. For equal masses $\eta^{3/5}M=M/\sqrt[5]{2}$ so that Kepler's third law

$$GM=a^3\omega^2,$$

$\ldots$ so say LIGO [Abbott et al, "Observation of gravitational waves from a binary black hole merger", (Hulse) Taylor and Weisberg, "The relativistic binary pulsar B1913+16: thirty years of observation and analysis", and Peters and Mathews, "Gravitational radiation from point masses in a Keplerian orbit".

In a tutorial Hilborn, in his tutorial on the derivation of gravity waves without general relativity, asks if the luminosity of gravitational waves,

$$L=\frac{2}{5}\frac{\mu}{c^5}a^4\omega^6$$

The best way to show how ridiculous is the theory of gravitational waves is to present the arguments used by Hilbron in a tutorial on gravitational waves that does not use general relativity. Although his expressions for the  polarization, angular distributions, and overall power results differ from those of GR, waveforms that are very similar to the pre-binary-merger portions of the signals observed by the Laser Interferometer Gravitational-Wave Observatory (LIGO-VIRGO) collaboration.

In our last blog we derived the speed of gravity from the observational period and variation in the period of the binary pulsar PSR 1913+16 that was discovered by Taylor and Hulse. The luminosity spectrum they used went back to a 1963 paper of Peter and Mathews who took the rate of energy emission of Einstein's rotating dumbbell,

$$L=\frac{G}{5c^5}\left(\frac{d^3Q_{ij}}{dt^3}\frac{d^3Q_{ij}}{dt^3}-\frac{1}{3}\frac{d^3Q_{ii}}{dt^3}\frac{d^3Q_{jj}}{dt^3}\right),$$

and evaluated the quadrupole moments using a Keplerian ellipse

 Derivations of Laplace's formula for the change in period of the moon, that yielded a formula for the speed of gravity, has been derived by a number of authors. The key point is to consider the tangential force acting on the moon due to aberration due to the finite speed at which (supposedly) gravity propagates. To the central force, $\mu/a^2$,  where $\mu$ is the gravitational parameter containing the mass of the earth, $GM$, and $a$ the semi-major axis, the aberration term $v/v_G$ is appended where $v_G$ is the speed at which gravity supposedly propagates.