Abstract
Einstein’s equivalence principle allows one to compare the magnitudes of a gravitational acceleration field with the magnitudes of a field of Unruh acceleration temperatures. The validity of such a comparison is demonstrated by using it to derive the effective Hawking black body radiation at a Schwarzschild black hole horizon. One can then extend the black hole thought experiment to a Hawking-Unruh temperature equation expressed in terms of the Schwarzschild radius. This follows an inverse radius law rather than an inverse radius-squared law. Following a brief discussion of current theoretical failures to explain galactic rotation curves, the Unruh acceleration temperature equations are brought together to show how a rotating supermassive black hole galactic system should follow an inverse radius rule of centripetal gravitational force and centripetal acceleration. This result appears to indicate that galactic observations currently attributed to dark matter may in part be attributed to classical Newtonian dynamics superimposed on a relativistic rotating system powered by a supermassive black hole.
Highlights
Introduction and BackgroundIt is well-known that an inertial reference frame within a gravity field can be treated as equivalent to an accelerating reference frame (Einstein’s equivalence principle)
One can extend the black hole thought experiment to a Hawking-Unruh temperature equation expressed in terms of the Schwarzschild radius
Following a brief discussion of current theoretical failures to explain galactic rotation curves, the Unruh acceleration temperature equations are brought together to show how a rotating supermassive black hole galactic system should follow an inverse radius rule of centripetal gravitational force and centripetal acceleration. This result appears to indicate that galactic observations currently attributed to dark matter may in part be attributed to classical Newtonian dynamics superimposed on a relativistic rotating system powered by a supermassive black hole
Summary
It is well-known that an inertial reference frame within a gravity field can be treated as equivalent to an accelerating reference frame (Einstein’s equivalence principle) This is why a gravity field can be represented entirely by gamma acceleration vectors. Seshavatharam in a vacuum field will observe a black body radiation spectrum appearing to originate in-line with the direction of acceleration. Unruh acceleration temperatures around an isolated gravitating body, with its relative magnitudes corresponding in direct proportion to the gamma field magnitudes. By Equation (1) we can imagine a proportional equivalency between the magnitudes of an Unruh acceleration temperature field and the gamma magnitudes of a gravitational field. In Equation (3) we see indirect proportionality between the magnitude of the Unruh acceleration temperature field at a black hole’s horizon and the magnitude of its Schwarzschild radius R. Of particular note is that these relationships can only be true if the gravitational field around a black hole of any size does not follow an inverse R-squared law but rather an inverse R law!
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