Bounds on the masstoradius ratio for noncompact field configurations
Abstract
It is well known that a spherically symmetric compact star whose energy density decreases monotonically possesses an upper bound on its masstoradius ratio, 2M/R <= 8/9. However, field configurations typically will not be compact. Here we investigate noncompact static configurations whose matter fields have a slow global spatial decay, bounded by a power law behavior. These matter distributions have no sharp boundaries. We derive an upper bound on the fundamental ratio max_{r}{2m(r)/r} which is valid throughout the bulk. In its simplest form, the bound implies that in any region of spacetime in which the radial pressure increases, or alternatively decreases no faster than some power law r^{(γ+4)}, one has 2m(r)/r <= (2 + 2γ)/(3 + 2γ). (For γ <= 0 the bound degenerates to 2m(r)/r <= 2/3.) In its general version, the bound is expressed in terms of two physical parameters: the spatial decaying rate of the matter fields, and the highest occurring ratio of the trace of the pressure tensor to the local energy density.
 Publication:

Classical and Quantum Gravity
 Pub Date:
 December 2007
 DOI:
 10.1088/02649381/24/23/021
 arXiv:
 arXiv:0712.1988
 Bibcode:
 2007CQGra..24.6019H
 Keywords:

 General Relativity and Quantum Cosmology
 EPrint:
 4 pages