Mach's Principle and Spatial ScaleInvariance of Gravity
Abstract
Gravity does not provide any scale for matter properties. We argue that this is also the implication of Mach's hypothesis of the relativity of inertia. The most general spacetime compatible with this property of gravity is that admitting three, independent spatial homothetic Killing vectors generating an arbitrary function of each one of the three spatial coordinates. The matter properties for such a spacetime are (spatially) arbitrary and the matter generating the spacetime admits {\it any} equation of state. This is also the most general spacetime containing the weak gravity physics in its entirety. This spacetime is machian in that it is {\em globally} degenerate for antimachian situations such as vacuum, a single matter particle etc. and, hence, has no meaning in the absence of matter.
 Publication:

arXiv eprints
 Pub Date:
 February 2002
 arXiv:
 arXiv:grqc/0202005
 Bibcode:
 2002gr.qc.....2005W
 Keywords:

 General Relativity and Quantum Cosmology
 EPrint:
 Revtex4, No figures