Applying the gravitational wave energy density hypothesis:

Using the gravitational wave energy density hypothesis, relative motion in a given direction changes the gravitational wave energy density influence on an object moving in that direction, relative to the gravitational wave energy density in the rest frame.

Given the premise that gravitational waves always travel at the speed of light in the local frame, and that the speed of light varies relative to the motion between a stationary frame and a moving frame, the speed of gravitational waves also varies relative to the motion between a stationary frame and a moving frame, as well.

Therefore, the equation for calculating the difference in the gravitational wave energy density encountered in the rest frame vs. in the moving frame would be an inverse relationship. It is inverse because as you increase the relative velocity between the frames, the increased gravitational wave energy density causes the speed of gravity to slow down in the moving frame. Either frame can be deemed to be the moving frame.

The change in gravitational wave energy density between a rest frame and a moving frame is a factor that you would multiply the gravitational wave energy density in the rest frame by, to calculate the higher value of gravitational wave energy density in the moving frame. The factor is always greater than 1 since gravitational wave energy density always increases relative to the gravitational wave energy density in the rest frame.

To get the factor to apply, you take the inverse relationship using a calculation that invokes the relative velocity between frames divided by the speed of gravity. With the numerator of the factor equal to one, the denominator will always be less than one, making the factor always greater than one. Further, dealing with the speed of gravitational waves just like we deal with the speed of light in time dilation calculations, the equation factor is $$\frac{1}{\sqrt{ 1- (v/c)^2}} $$

or $$ \frac{1}{\sqrt{ 1- (v/c)^2}} $$

Using the gravitational wave energy density hypothesis, relative motion in a given direction changes the gravitational wave energy density influence on an object moving in that direction, relative to the gravitational wave energy density in the rest frame.

Given the premise that gravitational waves always travel at the speed of light in the local frame, and that the speed of light varies relative to the motion between a stationary frame and a moving frame, the speed of gravitational waves also varies relative to the motion between a stationary frame and a moving frame, as well.

Therefore, the equation for calculating the difference in the gravitational wave energy density encountered in the rest frame vs. in the moving frame would be an inverse relationship. It is inverse because as you increase the relative velocity between the frames, the increased gravitational wave energy density causes the speed of gravity to slow down in the moving frame. Either frame can be deemed to be the moving frame.

The change in gravitational wave energy density between a rest frame and a moving frame is a factor that you would multiply the gravitational wave energy density in the rest frame by, to calculate the higher value of gravitational wave energy density in the moving frame. The factor is always greater than 1 since gravitational wave energy density always increases relative to the gravitational wave energy density in the rest frame.

To get the factor to apply, you take the inverse relationship using a calculation that invokes the relative velocity between frames divided by the speed of gravity. With the numerator of the factor equal to one, the denominator will always be less than one, making the factor always greater than one. Further, dealing with the speed of gravitational waves just like we deal with the speed of light in time dilation calculations, the equation factor is $$\frac{1}{\sqrt{ 1- (v/c)^2}} $$

or $$ \frac{1}{\sqrt{ 1- (v/c)^2}} $$

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