The Duality of Time Theory, that results from the Single Monad Model of the Cosmos, explains how physical multiplicity is emerging from absolute (metaphysical) Oneness, at every instance of our normal time! This leads to the Ultimate Symmetry of space and its dynamic formation and breaking into the physical and psychical (supersymmetrical) creations, in orthogonal time directions. General Relativity and Quantum Mechanics are complementary consequences of the Duality of Time Theory, and all the fundamental interactions become properties of the new granular complex-time geometry, at diifferent dimensions. - => Conference Talk [Detailed Presentation]
of the gravitating mass
, is much larger than its Schwarzschild radius
. For example, the radius of the Sun is approximately 700,000 km, while its Schwarzschild radius is only 3 km. The radius of the Earth is 6,371 km, while its Schwarzschild radius is only 8.9 mm. This means that if the mass of the Earth is compressed to a sphere with 8.9 mm radius, it becomes a black hole with a singularity at
.
divides the Schwarzschild coordinates in two disconnected patches with two different solutions. The exterior solution with
is the one that is related to the gravitational fields of stars and planets, while the interior solution with
, which contains the singularity at
, is completely separated from the outer patch.
arises from a bad choice of coordinates or coordinate conditions. Using a different coordinate transformation, such as: Lemaitre coordinates, Eddington-Finkelstein coordinates, Kruskal-Szekeres coordinates, Novikov coordinates, or Gullstrand-Painleve coordinates, one can then relate the extended external patch to the inner patch.
is a true physical singularity at the origin. To see that this is a true singularity one must look at quantities that are independent of the choice of coordinates. One such important quantity is the Kretschmann invariant, which is given by:
(3.14)
the curvature becomes infinite, indicating the presence of a singularity. At this point, the metric, and space-time itself, is no longer well-defined. For a long time it was thought that such a solution was non-physical. However, a greater understanding of General Relativity led to the realization that such singularities were a generic feature of the theory and not just an exotic special case.
, is called a Schwarzschild black hole. It is a perfectly valid solution of the Einstein field equations, although it has some rather bizarre properties. For
the Schwarzschild radial coordinate
becomes time-like and the time coordinate
becomes space-like. A curve at constant
is no longer a possible world-line of a particle or observer, not even if a force is exerted to try to keep it there; this occurs because space-time has been curved so much that the direction of cause and effect points into the singularity.
demarcates the event horizon of the black hole, which represents the point past which light can no longer escape the gravitational field. Any physical object whose radius becomes less than or equal to the Schwarzschild radius will undergo gravitational collapse and become a black hole.
The science of Time is a noble science, that reveals the secret of Eternity. Only the Elites of Sages may ever come to know this secret. It is called the First Age, or the Age of ages, from which time is emerging.
