#
Spacetime
Curvature, The Schwarzschild Radius, and the Quantity C

The

**Schwarzschild radius**(*r*_{s}) represents the ability of mass to cause curvature in space and time. The**Schwarzschild radius**(sometimes historically referred to as the**gravitational radius**) is the radius of a sphere such that, if all the mass of an object is compressed within that sphere, the escape speed from the surface of the sphere would equal the speed of light.###
Clearly,
the Radius of Curvature of all Natural Law offers far clearer, and simpler, explanations
to the natural laws of space time mass matter energy gravity, permitting
application.

###
The
stumbling blocks in Physics’ Standard Model lie in the mis-interpretations
resulting from non-recognition of the anomalous effects that occur when an
energy differential approaches, equals, and exceeds QC (speed of light energy differential) between
any two or more given reference points, ......due to the fact that
QC differential also represents the exact kinetic energy equivalent of the mass
energy of matter.

###
Compare the explanations using the standard
model of relativity and quantum against the Radius of Curvature of all Natural Law (links below), and note the conflict always arises at scale
variances approaching the QC energy differential across the natural laws of
space time mass matter energy gravity….recalling also the natural laws are
relative, not absolute, i.e., change to one causes change to the others.

#
Radius of Curvature of all Natural Law:

#
Schwarzschild radius

From Wikipedia,
the free encyclopedia http://en.wikipedia.org/wiki/Schwarzschild_radius

##
Formula for the Schwarzschild radius[edit]

The Schwarzschild
radius is proportional to the mass with a proportionality constant involving
the gravitational constant and the speed of light: The Schwarzschild
radius marks the point where the event horizon forms, below this radius no
light escapes. The visual image of a black hole is one of a dark spot in space
with no radiation emitted. Any radiation falling on the black hole is not
reflected but rather absorbed, and starlight from behind the black hole is
lensed. Even though a black hole is
invisible, it has properties and structure. The boundary surrounding the black
hole at the Schwarzschild radius is called the event horizon, events below this
limit are not observed. Since the forces of matter can not overcome the force
of gravity, all the mass of a black hole compresses to infinity at the very
center, called the singularity.

###
http://www.einsteins-theory-of-relativity-4engineers.com/what-is-gravity.html
It is now known that
Newton's universal gravitation does not fully describe the effects of gravity
when the gravitational field is very strong, or when objects move at very high
speed in the field. This is where Einstein's general theory of relativity
rules.

**Einstein's Gravity (1916)**

In his monumental 1916 work 'The Foundation of the
General Theory of Relativity', Albert Einstein unified his own Special
relativity, Newton's law of universal gravitation, and the crucial insight that
the effects of gravity can be described by the curvature of space and time,
usually just called 'space-time' curvature.

It is now known that Newton's universal gravitation
does not fully describe the effects of gravity when the gravitational field is
very strong, or when objects move at very high speed in the field. This is
where Einstein's general theory of relativity rules.

The above holds well for weak gravity fields and low
speed movement, i.e., the Newtonian limit of general relativity. In strong
gravity fields, the curvature of spacetime and the effect of velocity must be
catered for. They both have the effect of lengthening the radius of curvature
of the path of the particle. The diagram below illustrates this shift in the position
of the center of curvature in an exaggerated fashion.

Spacetime curvature can be a little bewildering for most of us. It is an intimidating subject and just when we had a good look at the "rubber sheet analogy" and start thinking, "OK, I get it", someone tells us that it's less than half the story.

The Einstein tcnsor describes the
curvature of space-time; the stress-energy tensor describes the density of
mass-energy. This equation therefore concisely describes the curvature of
space-time that results from the presence of mass-energy. This curvature in turn
determines the motion of freely falling objects.

The math
involved in using this equation to its fullest is a textbook-length subject.
This equation can only be explicitly solved for limited situations, one of
which is described by Schwarzschild.

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