A Spherical Trampoline
Is there an alternative shape to Einstein's 'flat' rubber sheet?
Is there an alternative shape to Einstein's 'flat' rubber sheet?
For his gravity wells, the model that Einstein proposed employed an infinite flat rubber sheet weighted down by spherical masses. Some have critiqued this model as being a poor representation of curved 3 dimensional space, but it is truly elegant in its simplicity. Ironically, though, for the gravitational model to work, gravity is required to pull the spherical masses downward. And the gravitational field that is required to do this is unique, in that the lines of gravitational force all have to act parallel to one another, vertically downward and perpendicular to the plane of the sheet. And although it is 'just a model', no where in the universe does gravity act in such a fashion.
Consider a positively curved universe. Under this scenario, the model's rubber sheet would have to somehow curve back on itself, for example, forming a sphere. It may help to think of a rubbery membrane surrounding the earth and 'floating' on or buoyed by the earth's atmosphere. This alternative model of gravitation still requires gravity to make it work (i.e. pull down the 'bowling balls'), however, the gravitational lines of force instead of acting parallel to one another would converge at the centre of the spherically-shaped membrane. It, therefore, employs a more traditional arrangement of gravity to pull the spherical masses into the sheet. Also a black hole, say with 2/3rds of the universe's mass, could be located close to the center of the model (pictured below) thereby pulling all other massive objects toward it without the need for the secondary mass, which is required under the flat trampoline scenario.
Interestingly, if you placed a number of bowling balls and ball bearings on this model, eventually they would all come together at one location
Interestingly, if you placed a number of bowling balls and ball bearings on this model, eventually they would all come together at one location
Now, in such a finite model of the universe, there would be a finite number of black holes. As such, the black holes could be ranked in order of their mass. Given that there could be no 'ties', one black hole would have to have a mass greater than all of the other black holes.
What would the universe look like if the most massive black hole was much much more massive than all of the other black holes combined? In the Alternatives section of this website, this mother of all black holes forms the frame of reference for the model proposed and is located, for arguments sake, at the south pole. Einstein's rubber membrane model for such a universe would be similar to a cardioid. |
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