**A Theory of Gravity for the 21st Century**

**The “Central Conservative” Gravitational Force and Potential Energy – in consideration with Special Relativity and General Relativity**

The study of * Euclidean Spherical Mechanics*, is a set of conceptual and mathematical tools, used to describe the physics of a spherically symmetric system mass body, with the identical properties to a “Gravitational Vortex”, that creates its own gravitational field, while; at rest/static, in relativistic motion, spinning/rotating at rest, or spinning/rotating while in motion.

The * Euclidean Spherical Mechanics *unifies and generalizes, the theories, concepts, and mathematics of

**and**

*“Special Theory of Relativity”***into a single framework known as the**

*“General Theory of Relativity”*

*“Super Special Theory of Relativity”.*In this Gravitational Vortex Model, it is necessary to model gravity, because it is gravity that binds us to the earth, that binds the earth, and other planets to the solar system. In general, it is the “Gravitational Force” that is responsible for why all things fall down on planet earth, it is responsible for the formation of galaxies, the evolution of stars, and what keeps the bones in our bodies firm and rigid.

In this work, it will be demonstrated conceptually and mathematically that the “Potential Energy” is associated with the work done by a “central conservative force”, namely the “Gravitational Force.” Various other types of “central conservative forces” include: the *Elastic Spring Force,* the *Electrostatics Force*, and the *Magnetostatics Force*.

All “central conservative forces” can be generalized to model a system, such that there exists an associated “Potential Energy” function, where the work done by the “Central Force”, equals a decrease in the “Potential Energy” of the system. In the case of the “Gradient Gravitational Field Force”, work is done by the force of gravity, decreasing the “Potential Energy” of any mass object, located anywhere within the gradient field; and where the strength of “Gradient Gravitational Field Force”, and the “Potential Energy” decreases, with increasing distance from the center of the field.

If the only “central conservative force” acting on an isolated “Net Inertial Mass” system body is the “Gravitational Force”, then it is the force of gravity that is doing work; and according to the conservation of energy, that work is also equal to the increase in the “Kinetic Energy” of the Net Inertial Mass system body.

*The required condition for a force to be “central conservative force” is, if the total work, the force does, on any object located in its surroundings, is moved around any closed path, at any speed, and returns to its initial position, and the work done at the end of the process is equal zero (0), then the force acting on the object is considered a “central conservative force.” *

The work done by a “central conservative force” with proper mathematical formalism is denoted with a negative value; and because of conservation when the potential energy increases, the kinetic energy decreases by an equal amount; and vice versa. Therefore, the “Total Mechanical Energy” is conserved, being the sum of the “Kinetic Energy” and the “Potential Energy” which when summed together mathematically remains a constant value.

The “Total Mechanical Energy” of an isolated system is conserved, because any decrease in the potential energy is balanced by an increase in the Kinetic Energy; and vice versa; as described by the equation below.

*Total Mechanical Energy*

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**(1)**** The Conservative “Central Force” of an “Inertial Mass” Gradient Gravitational Field**

**The Conservative “Central Force” of an “Inertial Mass” Gradient Gravitational Field**

Any and every conserved and isolated “Net Inertial Mass” system body, can be modeled as a “vortex” body that is spheroid in nature, and is described by a gradient field, comprised of an infinite amount of “spherical shell potentials” relative to the center of the system. The gradient gravity field is described by concentric spherical volumetric potential shells of “Gravitational Potential Energy” and a conservative “Central Gravitational Force” at each potential.

For a general gradient gravitational field, the conservative * Gravitational Potential Energy* () of each concentric spherical shell potential, is associated with the

**(), where the source of gradient gravity field is the**

*Inertial Mass**Gravitational Force***Net Inertial Mass**().

In this *“Gravitational Vortex”* model, at the origin of every “Net Inertial Mass Gradient Gravity Field’ there is a “Schwarzschild Radius Black Hole Event Horizon.” The most minimum spatial distance of the gradient gravitational field is the ** Schwarzschild Radius** ()

**Black Hole Event Horizon**.

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**The Conservative “Central Force” of an “Inertial Mass” Gradient Gravitational Field**

**The Conservative “Central Force” of an “Inertial Mass” Gradient Gravitational Field**

The ** Inertial Mass Gravitational Force** () is a measure of the force of attraction and interaction, of

*and is a conservative central force, exerted by the*

**“mass towards mass”**,**() on any other**

*Net Inertial Mass***() body, of the “collective” net mass system body; which includes its “Self” attraction and interaction force.**

*“test” mass*The strength of the ** Inertial Mass Gravitational Force** () varies inversely with the square of the

**() distance, relative to the center of the Gradient Gravitational Field.**

*Semi-Major radius*Also, the ** Inertial Mass Gravitational Force** () is a conservative central force that comes in two forms, the

**(), and the**

*“Newtonian” Gravitational Force***().**

*“Self” Gravitational Force***************************************************************

**Recording Playback**

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### Video of Newton & Self Gravitational Force (Self Gravity) Lecture

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The ** Inertial Mass Gravitational Force** () which is described mathematically below, is an “inflow” radial vector, given by the following equations.

**Aphorism:**

The strength of the

() is a measure of the force of attraction and interaction of“Newtonian” Gravitational Force“mass towards mass”,and varies in direct proportion to the product of the() multiplied by theNet Inertial Mass(), and varies inversely with the square of theorbiting “test” mass() distance, relative to the center of the Gradient Gravitational Field.Semi-Major radius

*Inertial Mass “Newtonian” Gravitational Force*

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**Aphorism:**

The strength of the

() is a measure of the force of attraction and interaction of“Self” Gravitational Force“mass towards mass”, and varies directly with the square of the(); and likewise varies in direct proportion to the square of theLinear Mass Density(), and varies inversely with the square of theNet Inertial Mass() distance, relative to the center of the Gradient Gravitational Field.Semi-Major radius

*Inertial Mass “Self” Gravitational Force*

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**Black Hole Event Horizon – Inertial Mass “Self” Gravitational Force**

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**(2)**** ****The “Gravitational Acceleration” of an “Inertial Mass” Gradient Gravitational Field**

**The “Gravitational Acceleration” of an “Inertial Mass” Gradient Gravitational Field**

The ** Inertial Mass Gradient Gravitational Field Acceleration** () describes the acceleration of mass and energy, towards the center of the gradient gravity field, and towards ever decreasing and smaller volumes of spherical gradient shell potentials.

The ** Inertial Mass Gradient Gravitational Field Acceleration** () varies in each spherical volume potential of the gravity field, such that the larger the volume potential, the slower the acceleration towards the center of the gradient gravity field; and the smaller the volume potential, the faster the acceleration towards the center of the gradient gravity field.

The ** Inertial Mass Gradient Gravitational Field Acceleration** () is defined as the ratio of the

**() divided by the**

*Inertial Mass Gravitational Force***() of the system; and likewise the Gravitational Field Acceleration () diminishes as the square of the**

*Mass***() distance from the center of the Gradient Gravitational Field increases.**

*Semi-Major radius***Aphorism:**

The motion of the

()Gradient Gravitational Fieldis a measure of the acceleration of the attraction and interaction ofAcceleration“mass towards mass”, and varies directly proportional to the()Net InertialMass, and varies inversely with the square of the() distance, relative to the center of the Gradient Gravitational Field.Semi-Major radius

*Inertial Mass – Gradient Gravitational Field Acceleration*

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**Black Hole Event Horizon – Gradient Gravitational Field Acceleration**

The ** Black Hole Event Horizon – Gradient Gravitational Field **()

*can be thought of as the measure of the amount of curvature, and the measure of the acceleration that any observer standing at the surface of the “Black Hole Event Horizon”, would feel being pulled towards the center of the black hole.*

**Acceleration** The ** Black Hole Event Horizon – Gradient Gravitational Field **()

*is the “Quantized” and maximum amount of acceleration of a gradient gravitational field system, where the measure of the “Black Hole Acceleration” is inversly proportional to the*

**Acceleration****() of the system.**

*Net Inertial Mass*Such that the ** larger** the

**() of the gradient gravitational field the**

*Net Inertial Mass***the**

*slower**(), rate relative to the “Black Hole Event Horizon – Potential” and towards the center of the gradient field.*

**Black Hole Acceleration**Likewise, such that the ** smaller** the

**() of the gradient gravitational field the**

*Net Inertial Mass***the**

*faster**(), rate relative to the “Black Hole Event Horizon – Potential” and towards the center of the gradient field.*

**Black Hole Acceleration** The ** Black Hole Event Horizon – Gradient Gravitational Field **()

*can also be thought of as the measure of the “Quantized” amount warping, or curvature, in the form of the*

**Acceleration***acceleration*of a “Spherical” disturbance, in the “Vacuum of Space-time” and in the local vicinity, of the Net Inertial Mass; the source of the gradient gravitational field system body.

**Aphorism:**

The motion of the

()Black Hole Event Horizon – Gradient Gravitational Fieldis equal to the measure of the acceleration of the attraction and interaction ofAcceleration“mass towards mass”, at the “Black Hole Potential”, and isidependentof the “distance” or “radius” of the “Black Hole” and isdependent, and varies inversely proportional to the()Net InertialMass, of the Gradient Gravitational Field, system body.

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For example: ** Electrons** have faster or larger

*() towards their Black Hole centers than do*

**Black Hole Acceleration****,**

*Protons***and**

*Plantets***.**

*Suns*** Protons** have faster or larger

*() towards their Black Hole centers than do*

**Black Hole Acceleration****.**

*Neutrons*And the ** Earth**, has a faster or larger

*(), towards its Black Hole center, than the*

**Black Hole Acceleration****does.**

*Sun*Furthermore the ** Sun**, has a faster or larger

*(), towards its Black Hole center, than the*

**Black Hole Acceleration****does.**

*Galaxy*This means that, an object with the right amount of force and acceleration, that being larger than the Black Hole event Horizon acceleration, should be able to escape the death grips of the **Black Hole! **

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**(3)**** The “Potential Energy” of an “Inertial Mass” Gradient Gravitational Field**

**The “Potential Energy” of an “Inertial Mass” Gradient Gravitational Field**

For a general gradient gravitational field, the conservative * Gravitational Potential Energy* () of each concentric spherical shell potential, is associated with the

**(), where the source of gradient gravity field is the**

*Inertial Mass**Gravitational Force***Net Inertial Mass**(), and manifests, when a “Gravity Force” acts upon a “mass” object within the gradient field, that tends to move it to a lower energy location within the field.

The * Gravitational Potential Energy* () is a measure of the “work energy”, of the relative spatial separation, of the attraction and interaction of

**“mass towards mass”**.

*The*is the work done in the gravity field, by the

*()***Gravitational Potential Energy****Net Inertial Mass**() of the system body, moving

**“mass towards mass”**from infinite places in the universe!

The change in the * Gravitational Potential Energy* () is the measure of the work done by the

**() of a general gradient gravitational field; and the work done by the force, is integrated over changes in the**

*Inertial Mass**Gravitational Force***distance (), relative to the center of the gradient gravity field.**

*Semi-Major radius*The * Gravitational Potential Energy* () can be described physically as the energy associated with each “surface potential” of the infinite concentric “thin” spherical shells, that make up the gradient gravity field, and is the potential energy difference between the energy of a “mass” object in a given gradient field position, and its energy at some other reference position within the field; given by the following equations.

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**Aphorism:**

The energy content of the

() is a measure of the energy potential, of the relative spatial separation, of the attraction and interaction ofGradient Gravitational Field “Newtonian” Potential Energy“mass towards mass”,and varies in direct proportion to the product of the() multiplied by theNet Inertial Mass(), and varies inversely with thetest mass() distance, relative to the center of the Gradient Gravitational Field.Semi-Major radius

**Gradient Gravitational Field “Newtonian” Potential Energy**

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**Aphorism:**

The energy content of the

() is a measure of the energy potential, of the relative spatial separation, of the attraction and interaction ofGradient Gravitational Field “Self” Potential Energy“mass towards mass”, and varies directly proportional to the square of the(), and varies inversely with the linear,Net Inertial Mass() distance, relative to the center of the Gradient Gravitational Field.Semi-Major radius

**Gradient Gravitational Field “Self” Potential Energy**

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**Black Hole Event Horizon – Gradient Gravitational Field “Self” Potential Energy**

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**(4)**** The “Inertia Potential” of an “Inertial Mass” Gradient Gravitational Field**

**The “Inertia Potential” of an “Inertial Mass” Gradient Gravitational Field**

The ** Inertial Mass Gradient Gravitational Field “Inertia” Potential** () is a measure of the square of the orbiting/spin/rotation squared tangential velocity of each potential of the gradient gravity field; and describes the squared velocity “inertia” potential, of the relative spatial separation, of the attraction and interaction of

**“mass towards mass”**; and towards the center of the gradient gravity field, and towards ever decreasing and smaller volumes, of spherical gradient shell potentials.

The ** Inertial Mass Gradient Gravitational Field “Inertia” Potential** () varies in each spherical volume potential of the gravity field, such that the larger the volume potential, the slower the squared velocity “inertia” towards the center of the gradient gravity field; and the smaller the volume potential, the faster the squared velocity “inertia” towards the center of the gradient gravity field.

The ** Inertial Mass Gradient Gravitational Field “Inertia” Potential** () is a measure of the inertia of motion in gravity field, and is defined as the ratio of the

**() divided by the**

*Gravitational Potential Energy***() of the system; and likewise the**

*Mass***() diminishes as the linear**

*Gravitational Field Potential***() distance from the center of the Gradient Gravitational Field increases.**

*Semi-Major radius***Aphorism:**

The inertia motion of the

() is a measure of the orbiting/spin/rotation squared velocity potential, of the relative spatial separation, of the attraction and interaction ofGradient Gravitational Field “Inertia” Potential“mass towards mass”, and varies in direct proportion to the(); and likewise varies in direct proportion to theLinear Mass Density(), and varies inversely with the linearNet Inertial Mass() distance, relative to the center of the Gradient Gravitational Field.Semi-Major radius

*Inertial Mass – Gradient Gravitational Field “Inertia” Potential*

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**Black Hole Event Horizon – Gradient Gravitational Field “Inertia” Potential**

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**(5)**** The “Inertial” Linear Mass Density Gradient Gravitational Field Potentials**

**The “Inertial” Linear Mass Density Gradient Gravitational Field Potentials**

For a general gradient gravitational field, the conservative the * “Self” Gravitational Potential Energy* (), and the

**() of each concentric spherical shell potential of the gradient gravity field, varies in direct proportion to the**

*Inertial Mass “Self” Gravitational Force***Net Inertial Linear Mass Density**() of the the gradient field, dependent only on the inverse distance from the center of the field.

This model predicts that, while considering the **Net Inertial Mass** () of the gradient gravity field constant, the **Net Inertial Linear Mass Density** (), of the field varies from place to place or location to location within the gravity field.

The **Net Inertial Linear Mass Density** (), measures a “greater” or “condensed” linear density, the closer the **Semi-Major Radius** () distance is to the “mean center” and **Schwarzschild Radius** () Black Hole Event Horizon of the system.

The **Net Inertial Linear Mass Density** (), measures a “smaller” or “rarer” linear density, the further away the **Semi-Major Radius** () distance is from the “mean center” and the **Schwarzschild Radius** () Black Hole Event Horizon of the gradient gravity field system.

The **Net Inertial Linear Mass Density** (), is actually the result of the * “Linear Mass Density”* “potential” difference between the

*maximum*

**“Black Hole” Net Inertial Linear Mass Density**() constant, at the core of the gradient field, and its

**Net Inertial Linear Mass Density**() at some other reference position within the field.

The **Net Inertial Linear Mass Density** (), measures a “maximum” linear density, when the **Semi-Major Radius** () distance is equal to the **Schwarzschild Radius** () of the gradient gravity field system; and measures zero (0) when the **Semi-Major Radius** () distance is equal to infinity, or an infinite distance away from the “mean center” of the gradient gravity field system body.

**Aphorism:**

The dense intensity of

Net Inertial Linear Mass Density() is a measure of the linear density of the gradient potentials of the gravity field, and varies in direct proportion to the ratio of the(), and inversely with increases or decreases in the linearNet Inertial Mass() distance, relative to the center of the Gradient Gravitational Field. And likewise varies in direct proportion to the theSemi-Major radius(); and further varies in direct proportion to the square root of theGravitational Field Potential() of each concentric spherical shell potential of the gradient gravity field.“Self” Gravitational Force

The **Net Inertial Linear Mass Density** ()

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**(6)**** The “Maximum – Black Hole – Event Horizon” Linear Mass Density Gradient Gravitational Field Potential Constant**

**The “Maximum – Black Hole – Event Horizon” Linear Mass Density Gradient Gravitational Field Potential Constant**

### The* “Maximum – Black Hole – Event Horizon” Net Inertial Linear Mass Density** *()

*“Maximum – Black Hole – Event Horizon” Net Inertial Linear Mass Density*

The **“Maximum”****Net Inertial Linear Mass Density** (), measures a “maximum” linear density, when the **Semi-Major Radius** () distance is equal to the **Schwarzschild Radius** () Black Hole Event Horizon, and represents the * “lowest potential”* or the

**of the gradient gravity field system mass body.**

*“smallest volume”*In this Gravitational Vortex Model, the **“Maximum”****Net Inertial Linear Mass Density** (), which is located in the * “lowest potential”* of the gradient field, is also known as the

**; an it measures a**

*“Black Hole”*Net Inertial Linear Mass Density*“constant”*value.

The **“Maximum”****Net Inertial Linear Mass Density** (), exists at the core center, of every * Net Inertial Mass* (), and is the core of every gradient gravitational field; and represents the:

*smallest*volume,

*greatest*

**Gravitational Force**,

*largest*

**Inertia Potential**,

*greatest*

**Potential Energy**,

*largest*

**Gravitational Acceleration**,

*fastest*

**Orbiting Velocity**, and the

*shortest*

**Orbital Period**, of the gradient gravity field.

In this “Gradient Vortex Gravitational Field” model, the **“Black Hole”****Net Inertial Linear Mass Density** ()” is a constant value, that is spatially located at the Black Hole Event Horizon” origin source, of the gravitational gradient field; and is the “vacuum energy” binding proportionality between “Matter/Mass” and the “Space” of the “Vacuum of Space-time”; and can be modeled as a “fabric continuum” or “vacuum energy” that permeates throughout the entire universe.

*There is no place in the cosmos of the universe that is void of vacuum energy.*

The **“Black Hole”****Net Inertial Linear Mass Density** ()” is a direct measure of the vacuum of space-time continuum, where the **Net Inertial Mass** – () or “matter” of the gravitational field system body, is directly proportional to the “space” distance of the “source of the” gravity field; and where the minimum distance, and the lowest energy potential, is given by the **Schwarzschild Radius** () Black Hole Event Horizon, of the gradient gravity field, described by the following relation, and equation.

The **“Black Hole”****Net Inertial Linear Mass Density** () is a gravitational field parameter where the ratio of the **Net Inertial Mass** – () divided by the **Schwarzschild Radius** () Black Hole Event Horizon, is a constant of nature.

**“Black Hole”****Net Inertial Linear Mass Density** ()

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In this “Gravitational Vortex” model, the **“Black Hole”****Net Inertial Linear Mass Density** ()” is a gravitational field parameter, such that at the location of the “Black Hole Event Horizon”, all the “central conservative forces” of the system become equal.

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**(7)**** The “General Relativistic” Linear Mass Density Gradient Gravitational Field Potentials**

**The “General Relativistic” Linear Mass Density Gradient Gravitational Field Potentials**

Where the **Net Inertial Mass** – () – in the * Proper Observer* “center of mass” frame of reference is given by the following.

And, the **Relativistic Net Inertial Mass** – () – in the * External Observer* frame of reference is given by the following.

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Next, employing the – ** Map/Patch/Manifold – “Geodesic” Arc Length** – () – which is a “geodesic arc-length” spatial component, on the surface of the sphere, and changes as a function of the “Radius” (), and changes as a function of the “Euclidean Radius” () of a symmetric sphere, as derived in

**Section 3**, of the work:

Euclidean Spherical Mechanics – Euclidean/Minkowski Space-time Metrics

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The **Map/Patch/Manifold – “Geodesic” Arc Length** – ()

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Where the **Net Inertial Linear Mass Density** () – in the * Proper Observer* “center of mass” frame of reference, is given by the following.

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Where the **Map/Patch/Manifold – **“**Geodesic Arc-Length” Net Inertial Linear Mass Density** () – in the * Proper Observer* “center of mass” frame of reference, is given by the following.

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Where the **Net Inertial Linear Mass Density** () – in the * External Observer* frame of reference, is given by the following.

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Where the **Map/Patch/Manifold – **“**Geodesic Arc-Length” Net Inertial Linear Mass Density** () – in the * External Observer* frame of reference, is given by the following.

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**(8)**** The “Inertia Potential” of an “Inertial Mass” Gradient Gravitational Field – in consideration for Special Relativity & General Relativity**

**The “Inertia Potential” of an “Inertial Mass” Gradient Gravitational Field – in consideration for Special Relativity & General Relativity**

The ** Inertial Mass Gradient Gravitational Field “Inertia” Potential** () is a measure of the square of the orbiting/spin/rotation squared tangential velocity of each potential of the gradient gravity field; and describes the squared velocity “inertia” potential, of the relative spatial separation, of the attraction and interaction of

**“mass towards mass”**; and towards the center of the gradient gravity field, and towards ever decreasing and smaller volumes, of spherical gradient shell potentials.

The **Inertial Mass Gradient Gravitational Field “Inertia” Potential** () is a gravitational field parameter that varies, in direct proportion to the **Net Inertial Linear Mass Density** (); and is described mathematically in terms of “Relativistic” frames of reference, observers, and their respective motions, below.

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Where the **Gradient Gravitational Field “Inertia” Potential** () – in the * Proper Observer* “center of mass” frame of reference, is given by the following.

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Where the “**Geodesic Arc-Length” Gradient Gravitational Field “Inertia” Potential **() – in the

*“center of mass” frame of reference, is given by the following.*

**Proper Observer****************************************************************

Where the **Gradient Gravitational Field “Inertia” Potential** () – in the * External Observer* frame of reference, is given by the following.

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Where the **Map/Patch/Manifold – **“**Geodesic Arc-Length” Gradient Gravitational Field “Inertia” Potential **() – in the

*frame of reference, is given by the following.*

**External Observer****************************************************************

**(9)**** The Conservative “Self Gravitational Force” of an “Inertial Mass” Gradient Gravitational Field – in consideration for Special Relativity & General Relativity**

**The Conservative “Self Gravitational Force” of an “Inertial Mass” Gradient Gravitational Field – in consideration for Special Relativity & General Relativity**

Any and every conserved and isolated *“Net Inertial Mass”* system body, can be modeled as a *“vortex”* system body, that is spheroid in nature, and is described by a gradient field, comprised of an infinite amount of “spherical shell potentials” relative to the center of the system. The gradient gravity field is described by concentric spherical volumetric potential shells of *“Gravitational Potential Energy”* and a conservative *“Self Gravitational Force”* at each potential.

For a general gradient gravitational field, the conservative * “Self” Gravitational Potential Energy* () of each concentric spherical shell potential, is associated with the

**(), where the source of gradient gravity field is the**

*Inertial Mass*“Self “*Gravitational Force***Net Inertial Mass**().

The **Inertial Mass “Self” Gravitational Force** () is a gravitational field parameter that varies, in direct proportion to the square of the **Net Inertial Linear Mass Density** (); and is described mathematically in terms of “Relativistic” frames of reference, observers, and their respective motions, below.

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Where the **Inertial Mass “Self” Gravitational Force** () – in the * Proper Observer* “center of mass” frame of reference, is given by the following.

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Where the **Map/Patch/Manifold – **“**Geodesic Arc-Length”**** Inertial Mass “Self” Gravitational Force **() – in the

*“center of mass” frame of reference, is given by the following.*

**Proper Observer****************************************************************

Where the **Inertial Mass “Self” Gravitational Force** () – in the * External Observer* frame of reference, is given by the following.

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Where the **Map/Patch/Manifold – **“**Geodesic Arc-Length” Inertial Mass “Self” Gravitational Force **() – in the

*frame of reference, is given by the following.*

**External Observer****************************************************************

**(10)**** The Gradient Gravitational “Acceleration” described in the form of a “Elastic Wave Equation” – in consideration for Special Relativity & General Relativity**

**The Gradient Gravitational “Acceleration” described in the form of a “Elastic Wave Equation” – in consideration for Special Relativity & General Relativity**

The ** Inertial Mass Gradient Gravitational Field Acceleration** () varies as a function of

**and**

*“space”***in each spherical volume potential of the gravity field, such that the larger the volume potential, the slower the acceleration towards the center of the gradient gravity field; and the smaller the volume potential, the faster the acceleration towards the center of the gradient gravity field; and can be described in the form of the second order partial differential**

*“time”*

*“Elastic Wave Equation.”*In a consideration for General Relativity, we will need to obtain the equations for the *Gradient Gravitational Field Acceleration*** **() as a function of the “Space-Time Metrics”, which were derived in **Section 4**, of the work:

Euclidean Spherical Mechanics – Euclidean/Minkowski Space-time Metrics

Only the “Proper Observer” center of mass frame of reference, *“Elastic Wave”,* ** Gravitational Field Acceleration – **() will be described below. Limiting, the discussion to the

**center of mass frame of reference is done for the main reason, that is the frame that the mechanics and mathematics, of the classical discussions of gravity, are most commonly discussed.**

*“Proper Observer”*************************************************************

** Proper Observer – Gradient Gravitational Field Acceleration – **()

**second order partial differential**

*–***function of**

*“Elastic Wave Equation”***()**

*Radius of Sphere***and in the**

*Space & Time Metric**frame of reference.*

**“Proper Observer”****************************************************************

** Proper Observer – Gradient Gravitational Field Acceleration – **()

**second order partial differential**

*–***function of**

*“Elastic Wave Equation”***()**

*Map/Patch/Manifold – “Geodesic”***and in the**

*“Equal Observer (Co-Variant)” Space & Time Metric**frame of reference.*

**“Proper Observer”**************************************************************

**Proper Observer – Gradient Gravitational Field Acceleration – **()

**– second order partial differential**

**function of**

*“Elastic Wave Equation”***()**

*Euclidean**Radius of Sphere***and in the**

*Space & Time Metric***frame of reference.**

*“External Observer”***************************************************************

**Proper Observer – Gradient Gravitational Field Acceleration – **()

**second order partial differential**

*–***function of**

*“Elastic Wave Equation”***(**

*Map/Patch/Manifold – “Geodesic”**and in the*

**Space & Time Metric****frame of reference.**

*“External Observer”*************************************************************

**General Constants**

**Gravitational Constant**

**Speed of Light** in vacuum constant

**“Black Hole”****Net Inertial Linear Mass Density Constant**

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**Citation**

Cite this article as:

Robert Louis Kemp; The Super Principia Mathematica – The Rage to Master Conceptual & Mathematical Physics – The General Theory of Relativity – “**The “Central Conservative” Gravitational Force and Potential Energy – in consideration with Special Relativity and General Relativity****” – Online Volume – ISBN 978-0-9841518-2-0, Volume 3; July 2010**

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The above work completes a *new* theory of Gravity for the 21st Century; and produces a complete conceptual and mathematical model of matter, space, and time. The above work opens the door to discuss *new* concepts and mathematics of gravity, in consideration for *Special Relativity* and *General Relativity*; the *Super Special Theory of Relativity*.

Best,

Author: Robert Louis Kemp

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Doctor Who Matt Smith,

Thanks for your comment, I think. So how can I get an “A” in your book. What do you mean by this statememt “I am not necessarily sure of just how you seem to connect the details which produce your conclusion”?

Best

Kemp