Is Gravity Incompatible with Geodesic Motion?

Accelerating masses are repudiated to be the sources of gravitational waves just like accelerating charges in an antenna produce electromagnetic waves with the exception that the former needs a quadrupole, because masses have no charge, while the dipoles will suffice for the latter. Now, it is a matter of fact that all particles, whether they be 'test' particles or real ones, follow geodesics. Geodesics are paths of constant velocity so how can general relativity predict the existence of gravitational waves if masses don't accelerate?

Why Do Apples Fall and Non-Radiative Electric Fields Don't Aberrate?

Newton could tells us, but Einstein can't. According to his "general" theory of relativity, all particles follow what are known as 'geodesics'. These are paths of the shortest distance between any two points. In flat space, these paths are straight lines, but in non-euclidean spaces, these are curves where a point moving along such a segment moves at constant velocity with zero acceleration. How can Newton's apple be reconciled with such behavior?

Cosmic Coincidences

The critical density, as we have seen, is determined by introducing the Hubble parameter, $H$, defined from the velocity distance relation, $v=HR$. Rather than being a 'receding speed', $v$, and $R$ the distance the galaxy and the observer, the former appears as a revolving speed, so that $H$ is an angular speed of rotation, and the latter the radius measuring the distance between the galaxy and the cosmic center.

What's Wrong With The Robertson-Walker Metric, and Why a Critical Mass Has No Meaning

The Robertson-Walker metric supposedly describes a homogeneous and isotropic universe.It supposedly gives the criterion of a critical mass of the universe whose deficiency has led to the supposition of "dark matter." It is commendable that the same criterion also follows from an elementary, nonrelativistic, derivation where the total kinetic and gravitational energies of the universe are conserved at two different times $$\frac{1}{2}v^2-\frac{GM}{R}=\frac{1}{2}v_0^2-\frac{GM}{R_0},$$ where the subscript "0" refers to here and now, $t_0$, and the unsubscripted sy

Beyond the Confines of Relativity: The Breakdown of Symmetry in Past and Future

There is a deep connection between the formula for aberration,

$$\cos\omega=\frac{\cos\omega'-\beta}{1-\beta\cos\omega'},$$

and the Mobius automorphism that swaps the relative state of motion, $\beta$, with one at rest, $0$,

$$\mathcal{M}(\cos\omega')=\frac{\cos\omega'-\beta}{\beta\cos\omega'-1},$$

except for the negative sign. If $\cos\omega'=\beta$, then $\mathcal{M}(\beta)=0$, while if $\omega'$ is a right-angle, then $\mathcal{M}(0)=\beta$. But, there is more to this than what meets the eye.

The Limited Scope of Special Relativity

In his first paper on special relativity, Einstein wrote (in our notation)

$$\cos\omega=\frac{\cos\omega'-\beta}{1-\beta\cos\omega'},$$

for "the law of aberration in its most general form. If $\omega'=\pi/2$, the equation takes the simple form

$$\cos\omega=-\beta$$. In the annotated version of this paper, the angle $\omega$ is formed from "light source-observer" was changed to "direction of motion."