On a Dark-Matter-Free Theory of Gravity

It is well known that there is a conflict between Newton's and Einstein's theories of gravity and the behavior of distant galaxies. Either there is more mass in these galaxies than we see, or the pull of gravity is in these conditions stronger than expected. Rather than second-guess Newton, physicists have invented a thing they called 'dark matter', non-luminous matter. Not everyone believes in dark matter, and according to MOND (Modified Newtonian Dynamics), the gravitational attraction between the center and the outside of certain galaxies is stronger than that between the center and outside of the solar system, and closer to 1/r rather than 1/r^2. But MOND is unable to explain the central piece of evidence for the existence of dark matter, a colliding cluster of galaxies known as a "bullet cluster". A bullet cluster poses a problem for MOND because, while the majority of the mass of the colliding galaxies lies between them in the form of gas, gravitational lensing shows that gravity is in the galaxies themselves. No mere modification of the strength of gravity will be sufficient to account for this situation, because no such modification can explain why the gravity is in the galaxies rather than the gas. In order to solve this problem without recourse to dark matter, a deeper modification than that offered by MOND required. This note outlines the mathematical principles underlying a theory of gravity that can account for the behavior of galaxies without the need for dark matter.