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Why is there an inherent presumption imbedded in the field of physics that gravitational force is exempt from the rules of relativity?

The presumption is based on the non-relativistic expression for escape velocity:

v=(2MG/r)^.5

Thus, with a very large mass or a very small radius velocity can exceed the speed of light.

This expression is, of course. derived by setting the expression for kinetic energy equal to gravitational potential as follows:

(mv^2)/2=mMG/r

Our physics textbooks, however, define relativistic potential kinetic energy as:

mc^2(γ-1) where γ=(1-v^2/c^2)^-.5

If, however, you set the relativistic version of potential kinetic energy equal to gravitational potential, after a little algebra you find that:

v=c(1-((rc^2)/(MG+rc^2))^2)^.5

This expression yields nearly equivalent results to the non-relativistic version for observed planets and stars. For example the non-relativistic expression predicts the escape velocity at the surface of the earth is 1.1178839 X 10^4 m/s whereas the relativistic expression predicts 1.1178840 X 10^4 m/s.

For theoretical planets and stars however, the difference between the non-relativistic prediction and the relativistic prediction can be significant. If for example the earth's mass were 5.97 X 10^36 kg versus 5.97 X 10^24 kg the non-relativistic prediction is 1.1178839 X 10^10 m/s (or approximately 37 times the speed of light) whereas the relativistic prediction is 2.9979215 X 10^8 m/s (or just under the speed of light). In fact, no matter how large the mass or how tiny the radius, the relativistic version will never predict a velocity that exceeds the speed of light.

The equation for relativistic escape velocity described above seems to be a very reasonable and natural extension of relativity theory.

Escape velocity predicts the speed that objects and particles must achieve in order to escape the force of gravity. On the other side, however, it also predicts the speed that an object or particle achieves as it is attracted by gravitational force. Since the relativistic form of the equation predicts that gravity cannot accelerate an object or particle to a speed equal to or greater than the speed of light, it also casts a shadow on theories which depend on speeds reaching the speed of light such as black hole theory.

I would be interested in input from anybody on the above analysis.

The presumption is based on the non-relativistic expression for escape velocity:

v=(2MG/r)^.5

Thus, with a very large mass or a very small radius velocity can exceed the speed of light.

This expression is, of course. derived by setting the expression for kinetic energy equal to gravitational potential as follows:

(mv^2)/2=mMG/r

Our physics textbooks, however, define relativistic potential kinetic energy as:

mc^2(γ-1) where γ=(1-v^2/c^2)^-.5

If, however, you set the relativistic version of potential kinetic energy equal to gravitational potential, after a little algebra you find that:

v=c(1-((rc^2)/(MG+rc^2))^2)^.5

This expression yields nearly equivalent results to the non-relativistic version for observed planets and stars. For example the non-relativistic expression predicts the escape velocity at the surface of the earth is 1.1178839 X 10^4 m/s whereas the relativistic expression predicts 1.1178840 X 10^4 m/s.

For theoretical planets and stars however, the difference between the non-relativistic prediction and the relativistic prediction can be significant. If for example the earth's mass were 5.97 X 10^36 kg versus 5.97 X 10^24 kg the non-relativistic prediction is 1.1178839 X 10^10 m/s (or approximately 37 times the speed of light) whereas the relativistic prediction is 2.9979215 X 10^8 m/s (or just under the speed of light). In fact, no matter how large the mass or how tiny the radius, the relativistic version will never predict a velocity that exceeds the speed of light.

The equation for relativistic escape velocity described above seems to be a very reasonable and natural extension of relativity theory.

Escape velocity predicts the speed that objects and particles must achieve in order to escape the force of gravity. On the other side, however, it also predicts the speed that an object or particle achieves as it is attracted by gravitational force. Since the relativistic form of the equation predicts that gravity cannot accelerate an object or particle to a speed equal to or greater than the speed of light, it also casts a shadow on theories which depend on speeds reaching the speed of light such as black hole theory.

I would be interested in input from anybody on the above analysis.

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