5.1.5 Acceleration of the spacetime structure falling into a singularity

Again, standing in a common frame (in a distance r_lmx from singularity), and observing the spacetime structure flowing through our own frame, we could detect (if, for example, the quantum of the spacetime structure was dyed) by the length instrument calibrated on our frame (frame of the observer), and the clock calibrated on the chosen frame (frame corresponding to the distance r_lm from the singularity point), that the spacetime structure is falling into a singularity at a speed v_zx/m, following the equation (114),or, (115) different than the frame intrinsic speed according to equation (110). This speed may be considered as a real con-spacetime speed of the spacetime structure through a common orbital frame (in its own units), respecting changes of the space and time densities relating to a chosen reference frame.

	(127)

g_zx/m

stands for the Z_ct spaceflow acceleration.

• in case of a constant speed of light c_g:

  	(128)

• in case the speed of light c_g varies along with a radius (space density):

  	(129)

	(130)

in case of a constant speed of light c_g:

	(131)

in case the speed of light c_g varies along with a radius (space density):

	(132)

galilean projection of the time interval t_m into Z_ct frame, giving time interval

for the speed v_zx/m,

frame intrinsic time interval

t_m
for the speed v_x/m,

galilean projection of the time interval t_m into Z_cr frame, giving time interval

for the speed v_ox/m

	(133)

• g_x/m
  as the frame M intrinsic spaceflow acceleration, and,
• g_ox/m
  as the Z_cr spaceflow acceleration (the acceleration of the space flow, expressed in length and time units of a chosen frame).

• the frame M intrinsic space flow gravitational acceleration in case of a constant speed of light will be:

  	(133a)

• the frame M intrinsic space flow gravitational acceleration, in case the speed of light varies with the radius,
  will depend on the derivation dc_g/dr_lmx

	(134)

	(135)

	(136)

	(137)

1. Measuring the acceleration of the space flow by means of the meter calibrated on the spacetime structure belonging to a respective point (radius), and by means of the clock calibrated on a spacetime structure of the chosen frame (like of the frame on Earth surface), we obtain the results corresponding to equation (131) or (132). This acceleration acts in direction of the space flow (accelerating it).
2. Measuring the acceleration of the space flow by means of both, the meter and clock, calibrated on spacetime structure belonging to a respective point (radius), we would come to conclusion, that the space flow moves without acceleration, or, with acceleration (if any) due to change of the speed of light with the radius.
   Note: The spaceflow acceleration due to change of the speed of light might become significant in gravitational fields of the big cosmic bodies (like stars) or in gravitational fields of the bodies of a very high mass density (like nucleons).
3. Measuring the acceleration of the space flow by means both meter and clock calibrated on the chosen frame, we would find out that the acceleration is constant (acc. to equation (137)), but acting in opposite to the direction of the space flow (slowing down the spaceflow speed).