Abstract
Presented herein is a new and independent derivation of equation for the radius of Black Holes, i.e. the event horizon of black holes. The equation has been derived by formulating the relativistic equation of escape velocity derived from the relativistic equations for gravitational potential and kinetic energy. Based upon that, it is now shown that the actual size of a black hole, as determined by its event horizon, is exactly half the value predicted by the escape velocity equation used in the Newtonian mechanics. It proves that the actual radius of a black hole is exactly one half of the Schwarzschild radius.
Highlights
This work shows that the principles introduced by Einstein in his paper published in 1911 on the influence of gravitation on light propagation [1], when properly interpreted lead to a relativistic form of the escape velocity equation in addition to a relativistic form of the gravitational potential energy equation
It is shown in this present work that the relativistic form of the escape velocity equation leads to a relativistic value for the event horizon of black holes that is exactly half the distance determined by using the Newtonian form of the escape velocity equation
The standard Newtonian derivation of the escape velocity equation is as follows: First we are given the equation for the potential energy of a mass m at any radius R from the centre of a celestial body of mass M as stated by Gravitational Potential Energy, where PE is the gravitational potential energy [2]
Summary
This work shows that the principles introduced by Einstein in his paper published in 1911 on the influence of gravitation on light propagation [1], when properly interpreted lead to a relativistic form of the escape velocity equation in addition to a relativistic form of the gravitational potential energy equation. It is shown in this present work that the relativistic form of the escape velocity equation leads to a relativistic value for the event horizon of black holes that is exactly half the distance determined by using the Newtonian form of the escape velocity equation. As stated in the abstract, this means that the actual radius of a black hole is exactly one half of the Newtonian based Schwarzschild radius
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