Abstract

This paper formulates additional General Relativistic [G.R.] equations.  They do not contradict General Relativity.  They examine the deductions of Dr. Einstein from a relativistically distorted perspective.  The equations examine the distorted escape velocity of a G.R. object, determining its true – not relativistically distorted – escape velocity.  The values of non-Relativistic velocity and the apparent escape velocity relativistic deformation puts on are it equally true.  In contrast to the variables in the Classical equations of Relativity, they are more specific in their aspect, and in their relationship to escape velocity, not simply the time distortion.  The values for the quantities of rate (the Time and the Velocity) are the quantities for zero escape velocity||zero deformation – the non-Relativistic aspects.

Because there are fewer seconds for a Relativistic Perspective that has distortion, the perspective equations have a different relation.  They calculate higher velocity perceived by the observers in a General relativistically distorted body.  The escape velocity would appear to increase in exactly same proportion as time – but the energy needed for that escape velocity would decrease because of the slowing of all Bosons – including the Graviton.

The development of the equations is done more completely in the paper, but two examples show the principle.  The equations show the relation of two points of view: the independent variables had non-deformation and the depending variable would be the value observed because of the deformation.  The equation reasoned to show to this relationship is: 

       Time’ = Time/(1 – 2GM/rc²)^½

Because escape velocity [Velocity_Escape = (2GM/r)^½], then [Velocity_Escape² = 2GM/r)].  So the above |Time| equation could also be expressed as:

       Time’ = Time/(1 – Velocity_Escape²/c²)^½ 

– that could be reasoned to mean that Escape velocity is limited to light speed, just as Real||non-Relativistic velocity is limited to “c”.  Less time will go by when there is a relativistic deformation so all Bosons (including the Graviton) would lose their velocity/mass/energy.  The inverse relation would be where the independent variables were the observed velocity from the Relativistic or distorted view.  The dependent variable would be the True||non-relativistic||non-distorted Time||Escape_Velocity.  The parallel equation for that Relativistic Perspective is: 

       Time = Time’/(1 + Relativistic_{Escape-Velocity}²/c²)^½ 

This relationship allows the additional development of 2 formula/equations for the Escape velocity.  There are a number of other equations for Mass and Radius that will be proposed in a following paper.  These equations are all of the two Perspectives. 

All the equations are confirmed to two to thousand figures for 35 different values to have a range of 1.0E-500 m/s to c-(1.0E-500) m/s without the significant error.  The tables are available on request.