5.1.3 Speed of a spacetime structure falling into a singularity

Definition 1

The Zone of constant ratio of space to time density (Z_{cr}) 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 Z_{cr} frames. The significant atribute of the Z_{cr} 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 (Z_{ct}) 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 v_{ox/m} as the Z_{cr} spaceflow speed through a common
M frame, v_{zx/m} as the Z_{ct} spaceflow speed through a common
M frame, and v_{x/m} as a frame intrinsic spaceflow speed, it must be:

(108)

Since

(109)

where

l_{m}

stands for the distance passed through in a common M frame,

l_{o}

stands for the distance passed through in a chosen M frame,

t_{m}

stands for the time interval elapsed in a common M frame,

t_{o}

stands for the time interval elapsed in the chosen M frame,

we may declare, that the Z_{ct} speed v_{zx/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 Z_{cr} speed
v_{ox/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:

Substituting for r_{x} from equation (107a), and, for
v_{m/x} from equation (110), we obtain:

(115)

The frame intrinsic speed v_{m/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 Z_{ct} speed of a common frame M
through a common frame X may be expressed similarly to the equation (108):