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I'm looking to establish a simple explanation of coordinate acceleration-
Basically, as GR established, gravity is the curvature of space. If we use the ball on a trampoline analogy (which is a 2 dimensional representation of what is happening in 3 dimensions), we have a sphere creating a well in the fabric and a marble rolls down the well which is represented by Gm/r^2, the Newtonian equation for gravity. Now say the sphere is very heavy and represents a neutron star, now not only does the sphere create a well in the fabric but is pulling on the fabric causing it to stretch, so not only is the marble rolling down the sides of the well but it's also accelerating at the same rate the fabric is stretching which is represented (in Schwarzschild coordinates) by (1-2GM/rc^2)^-1/2 which gravity is multiplied by. Not only is the marbles acceleration increasing with the increase in curvature, but it's increasing due to the stretching of the fabric also. This rate of stretching also explains gravitational redshift as the wavelength is stretched as it travels out of the well. It also explains why the Newtonian gravity gradient equation, 2GM/r^3, remains unaffected by Schwarzschild coordinates as it only applies to the increase in acceleration of gravity, not the increase in acceleration due to curvature stretching.
I also understand that Schwarzschild coordinates model this phenomena well but 'behave badly' at the event horizon of a black hole where they diverge. There have been various attempts by other physicists to modify or evolve Schwarzschild metric in order to apply up to and beyond the event horizon.
If anything appears incorrect, let me know.
Steve
Basically, as GR established, gravity is the curvature of space. If we use the ball on a trampoline analogy (which is a 2 dimensional representation of what is happening in 3 dimensions), we have a sphere creating a well in the fabric and a marble rolls down the well which is represented by Gm/r^2, the Newtonian equation for gravity. Now say the sphere is very heavy and represents a neutron star, now not only does the sphere create a well in the fabric but is pulling on the fabric causing it to stretch, so not only is the marble rolling down the sides of the well but it's also accelerating at the same rate the fabric is stretching which is represented (in Schwarzschild coordinates) by (1-2GM/rc^2)^-1/2 which gravity is multiplied by. Not only is the marbles acceleration increasing with the increase in curvature, but it's increasing due to the stretching of the fabric also. This rate of stretching also explains gravitational redshift as the wavelength is stretched as it travels out of the well. It also explains why the Newtonian gravity gradient equation, 2GM/r^3, remains unaffected by Schwarzschild coordinates as it only applies to the increase in acceleration of gravity, not the increase in acceleration due to curvature stretching.
I also understand that Schwarzschild coordinates model this phenomena well but 'behave badly' at the event horizon of a black hole where they diverge. There have been various attempts by other physicists to modify or evolve Schwarzschild metric in order to apply up to and beyond the event horizon.
If anything appears incorrect, let me know.
Steve
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