2009/03/31 by Philip D. Mannheim, James OʼBrien, James G. O'Brien +1 · 1 citation
Physics and Astronomy · #Astrophysics and Cosmic Phenomena #Black Holes and Theoretical Physics #Classical mechanics #Cosmology and Gravitation Theories #Covariant transformation #Exact solutions in general relativity #Geodesic #Geometry #Gravitation #Mathematical physics #Perfect fluid #Physics #Quantum field theory in curved spacetime #Quantum gravity #Quantum mechanics #Scalar (mathematics) #Spacetime #Stress–energy tensor #Tensor (intrinsic definition) #gr-qc
paper · pdf · doi:10.1007/s10714-010-0997-1
Final version to appear in General Relativity and Gravitation (the final publication is available at http://www.springerlink.com). 29 pages, 1 figure
openalex publication_date 2010/05/14 · arxiv created 2010/09/16 · arxiv updated 2015/05/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We show that the standard perfect fluid paradigm is not necessarily a valid description of a curved space steady state gravitational source. Simply by virtue of not being flat, curved space geometries have to possess intrinsic length scales, and such length scales can affect the fluid structure. For modes of wavelength of order or greater than such scales eikonalized geometrical optics cannot apply and rays are not geodesic. Covariantizing thus entails not only the replacing of flat space functions by covariant ones, but also the introduction of intrinsic scales that were absent in flat space. In principle it is thus unreliable to construct the curved space energy-momentum tensor as the covariant generalization of a geodesic-based flat spacetime energy-momentum tensor. By constructing the partition function as an incoherent average over a complete set of modes of a scalar field propagating in a curved space background, we show that for the specific case of a static, spherically symmetric geometry, the steady state energy-momentum tensor that ensues will in general be of the form Tμν=(ρ+p)UμUν+pgμν+πμν where the anisotropic πμν is a symmetric, traceless rank two tensor which obeys Uμπμν=0. Such a πμν type term is absent for an incoherently averaged steady state fluid in a spacetime where there are no intrinsic length scales, and in principle would thus be missed in a covariantizing of a flat spacetime Tμν. While the significance of such πμν type terms would need to be evaluated on a case by case basis, through the use of kinetic theory we reassuringly find that the effect of such πμν type terms is small for weak gravity stars where perfect fluid sources are commonly used.