Volume 22: Pages 179-189, 2009

New space-time metrics for symmetric spaces

Jaroslav Hynecek ¹

¹Isetex, Inc., 905 Pampa Drive, Allen, Texas 75013, USA

In this article, it is shown that the new space-time metrics can be easily derived for the spaces possessing certain symmetries such as the space-time of the centrally gravitating body, the axially symmetric space-time, and the space-time of uniform gravity. The method of deriving these metrics is general and expandable to more complex orthogonal spaces. It is based on the previously introduced concept of the physical Minkowski space-time that remains flat and undistorted when the gravitational field is added. In this concept, the gravitational field only affects mapping from the physical space-time into the curved coordinate space-time that we are living in and are conducting measurements or observations. Since the coordinate mapping is from the flat space-time into the curved space-time, it is necessary that the metric line element ds, which is the hallmark of the Riemannian geometry, is not a coordinate transformation invariant. This is the main departure from the conventional approach of finding metrics for the above mentioned space-times that is based on finding the solutions of Einstein field equations in a particular coordinate system with the mass-energy tensor set to zero.

Keywords: Physical Space-Time, Spherically Symmetric Space-Time Metric, Axially Symmetric Space-Time Metric, Uniform Gravity Space-Time Metric, Ehrenfest Paradox, Sagnac Effect, Coordinate Transform without ds Being Invariant, Generalized Lorentz Coordinate Transform, Graviton Trajectory in Uniform Field, Speed of Gravitons

Received: June 23, 2008; Accepted: April 3, 2009; Published Online: April 30, 2009