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

The Schwarzschild radius (rs) 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.

# Radius of Curvature of all Natural Law:

## Formula for the Schwarzschild radius[]

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.