In order to understand how an object behaves as it attempts to leave a massive gravitational body (neuron star, black hole) it is necessary to work out the form of the formula for escape velocity under the condition of extreme velocity that such an object would have to travel in order to have any chance of escaping such a gravitational field.  Since such an extreme velocity would have to be near that of the speed of light the formula for escape velocity must take into account the effects of special relativity.  Now, in order to solve for this formula of relativistic escape velocity we must first look at the classical formula for escape velocity for a gravitational field,

This formula comes from the energy formula

where  is the distance of the object from the center of the gravitational mass M where the object has ½mv² of kinetic energy, sufficient energy for the object to reach a distance of  at which the object’s kinetic energy, and hence velocity become zero.  Now, what this formula shows is that escape velocity is ultimately derived from a comparison of the amount of potential energy that must be overcome to escape a gravitational field with the kinetic energy an object would possess if it were given a velocity upwards in an attempt to escape that gravitational field.  If the kinetic energy equals or is greater than the potential energy then the object escapes, if the kinetic energy cannot exceed the potential energy then it is impossible for the object to attain enough energy to escape and the gravitational body is a black hole.  Now, in the case of the classical escape velocity formula the potential energy can go to infinity, however the kinetic energy is restricted to ½mc² by the restriction that the velocity v cannot exceed the speed of light c.  However the classical kinetic energy formula only applies to velocities significantly less than the velocity of light, for velocities near the speed of light the relativistic energy formula

,

must be used.  This formula, unlike the classical formula for kinetic energy, goes to infinity as the velocity v goes to the speed of light c.  Now, the other side of the classical formula for escape velocity, the potential energy, is unchanged under relativistically significant velocities.  This is the case do to the law of conservation of energy.  If the law of conservation of energy is to be maintained then it is necessary that the potential energy be the same regardless of the path an object takes through a gravitational field.  If the energy a gravitational field imparted to an object were to increase or decrease as a result of an object travelling through the field at near the speed of light then it would be possible to send an object into a gravitational field at non-relativistically significant velocity and then send the object out at relativistically significant velocity.  In this way, by the two paths, the low velocity inbound path and the high velocity outbound path, having different potential energies, energy could be created or destroyed simply by sending particles around such a path, thereby breaking the law of conservation of energy.  So, replacing the classical kinetic energy formula with the relativistic kinetic energy formula within the classical formula for evaluating escape velocity gives the relativistic formula

Unlike the classical formula, both sides of this equation are capable of reaching infinite energy.  Reordering in terms of velocity gives

When we take  to infinity, which is the condition of full escape from a gravitational field we get the relativistic escape velocity

For this formula, as the mass of the gravitational body approaches infinity, and/or an objects proximity to the body approaches zero the escape velocity approaches c, the speed of light.  However, for black hole theory to be valid the escape velocity must exceed the speed of light as the mass approaches infinity and/or the distance approaches zero.  Therefore, relativistic escape velocity proves that no gravitational body can ever reach sufficient mass to form a black hole.

            Now, this result is not unexpected.  Rather it reflects the dissymmetry of the idea of black holes, the idea of a gravitational body existing into which an object could enter but not escape.  By symmetry, any path by which an object enters a gravitational field, if reversed, is a path by which the object could exit that field.  And so, if a gravitational body existed that would require more than an infinite amount of energy to escape then that body would impart an equal, greater than infinity energy on any object entering that body.  As such, since such a gravitational body would require greater than an infinity of energy to escape, since escaping it would require more than an infinity of energy it would impart more than an infinity of energy to any object that was to enter its field and so would give any such object the energy to escape its field.  And so, in order for a gravitational body to exist from which nothing could escape, that body would have to impart less energy to objects entering its field than it draws from objects that attempt to leave its field.  If gravitational fields were to behave in this way then energy could be created from nothing and the law of conservation of energy would be invalid.  Since the law of conservation of energy is valid, black holes are not.

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