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### 5.1.3 Speed of a spacetime structure falling into a singularity

Definition 1
The Zone of constant ratio of space to time density (Zcr) represents the zone of orbital frames of the space density as it is defined by equation (107), but of the time density following the course of the space density (not the course of its square root). The ratio space to time density stays constant for all Zcr frames. The significant atribute of the Zcr zone appears the fact, that the frame intrinsic speed of the object in inertial motion stays constant (the inertial motion in gravitational field exists in direction perpendicular to gravitational acceleration only), due to constant ratio of the length and time units.
Definition 2
The Zone of contemporary frames (Zct) represents the zone of orbital frames of the space density as it is defined by equation (107), but of the constant time density of the chosen frame.
Designating vox/m as the Zcr spaceflow speed through a common M frame, vzx/m as the Zct spaceflow speed through a common M frame, and vx/m as a frame intrinsic spaceflow speed, it must be:
(108)

Since
(109)

where
lm
stands for the distance passed through in a common M frame,
lo
stands for the distance passed through in a chosen M frame,
tm
stands for the time interval elapsed in a common M frame,
to
stands for the time interval elapsed in the chosen M frame,
we may declare, that the Zct speed vzx/m is defined as the speed of the spacetime structure of a common space density(in a common orbit) in its own length units within time unit of the chosen frame (the spaceflow speed contemporary with the chosen frame) and, that the Zcr speed vox/m is defined as the speed of the spacetime structure of a common space density(in a common orbit), expressed in length and time units of the chosen frame.

In accordance with equation (47a), respecting that frame M moves in a preferred frame X, and in opposite direction to the motion of the frame X with reference to frame M, we have

(110)

Thus, the equation (110) may be modified into equation (111):
(111)

Substituting for gravitational space density from equation (107), we receive:
(112)
And, since it follows from equation (106) :
(113)

we also have:
(114)
Substituting for rx from equation (107a), and, for vm/x from equation (110), we obtain:
(115)

The frame intrinsic speed vm/x - the speed of the frame M motion with respect to frame X connected with the spacetime structure, measured inside respective frame X - stays constant in all orbits. The Zct speed of a common frame M through a common frame X may be expressed similarly to the equation (108):
(116)

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