This equation has been previously parameterised to account for space,
and matter radius reductions in the form of dynamic gravity [3].
Space Radius (R’) and Matter Radius (r’) Reduction
R’ =
R
,
(1 + 3GM/Rc
2
)
(3)
r’ =
r
,
(1 + GM/3rc
2
)
(4)
where
M
is the gravitational mass,
c
is the speed of light and
G
the gravitational constant,
R is the radius for space.
It has previously been shown that
R’
gives answers that are technically in
exact agreement in the advance in the perihelia of Mercury, and the other
planets in the solar system. We have also used data for the binary pulsar
PSR B 1534+12 from Straumann to verify the results [6]. Using Eqs. (3, 4)
we compared this with the DD model (for Damour and Deruelle) [7, 8], and
other classical models [9]. The models in general, gave results that were
largely indistinguishable from that of observation for binary pulsars [6, 10,
11].
4

The subject of time dilation has not previously been addressed,
using the model introduced here. Extrapolating from the above principles,
in this paper we further develop an adaptation for gravitational time
dilation. Here, we introduce equations which are shown to account very
accurately for the gravitational time dilation seen in GPS data (see Results
3.1), and in the extreme gravitation of black holes (see Results 3.2).
Equally, these equations also resolve the problems associated with infinite
time dilation and the formation of black hole singularities. Importantly
these gravitational equations offer readily testable predictions for gravity,
particularly in the vicinity of black holes.
5

2. Methods
:
All mathematical calculations follow strict standard algebraic and standard
mathematical rules.
The principal physics proofs are based upon standard
physical formulae. The worked example is technically in exact agreement
with observation of time dilation as seen in satellite navigation systems.
This is also in agreement with data from black holes (see Results 3.1 &
3.2). The paper also proposes observational experimental methods for
further verification, based upon an analysis of the data from black holes,
as listed in the conclusions.
6

3. 1 Results: Gravitational time dilation in satellite navigation
systems.
Here we explore the technique of translating the equations for gravity
from describing curved space-time, to describing a separate parameter for
the equations of gravitational time dilation.
Straumann’s calculations showed that an algebraic equation [Eq.
(2)], was a very accurate representation of gravitational experiment, when
applied to solar system and even using binary pulsar data [6]. Thus by
using these principles it has also been possible to reformulate the
equations for gravitational time dilation.
Here we introduce the generic equations for gravitational time dilation.

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- Spring '14
- DanielKevles
- General Relativity, Time Dilation, dilation.