Mach Principle and a new theory of gravitation
  Einstein was highly fascinated by Ernest Mach's work and by formulating the
general theory of relativity (GR) he tried to provide a mathematical
description to the Mach's principle. However, soon after its formulation, it
was realized that GR does not follow Mach's principle. As it accurately
explained many observational results, Einstein did not make any farther attempt
to reformulate the theory to explain Mach's principle. Later on, several
attempts were made by different researchers to formulate a theory of gravity
based on Mach's principle. However, all these theories have their own merits
and drawbacks. In this paper a new theory of gravity is proposed that is
completely based on the Mach's principle. It is a metric theory and can be
derived from action principle, which guarantees to follow all the conservation
laws.
  We present few examples to show that the theory can explain the galactic
rotation curves very accurately. It also explains the discrepancy between
dynamic mass and the photo-metric mass of the galaxy clusters without any
exotic dark matter. The bullet cluster weak lensing phenomenon that is
considered to be a strong evidence for dark matter can also be explained using
this new gravitational theory. Hence, the theory provides a viable alternative
to standard gravity theory.
