20 research outputs found
On the Domain of Applicability of General Relativity
We consider the domain of applicability of general relativity (GR), as a
classical theory of gravity, by considering its applications to a variety of
settings of physical interest as well as its relationship with real
observations. We argue that, as it stands, GR is deficient whether it is
treated as a microscopic or a macroscopic theory of gravity. We briefly discuss
some recent attempts at removing this shortcoming through the construction of a
macroscopic theory of gravity. We point out that such macroscopic extensions of
GR are likely to be non-unique and involve non-Riemannian geometrical
frameworks.Comment: 19 pages, LaTeX, submitted to Found. Phy
The Averaging Problem in Cosmology and Macroscopic Gravity
The averaging problem in cosmology and the approach of macroscopic gravity to
resolve the problem is discussed. The averaged Einstein equations of
macroscopic gravity are modified on cosmological scales by the macroscopic
gravitational correlation tensor terms as compared with the Einstein equations
of general relativity. This correlation tensor satisfies a system of structure
and field equations. An exact cosmological solution to the macroscopic gravity
equations for a constant macroscopic gravitational connection correlation
tensor for a flat spatially homogeneous, isotropic macroscopic space-time is
presented. The correlation tensor term in the macroscopic Einstein equations
has been found to take the form of either a negative or positive spatial
curvature term. Thus, macroscopic gravity provides a cosmological model for a
flat spatially homogeneous, isotropic Universe which obeys the dynamical law
for either an open or closed Universe.Comment: 8 pages, LaTeX, ws-ijmpa.cls, few style and typo corrections. Based
on the plenary talk given at the Second Stueckelberg Workshop, ICRANet
Coordinating Center, Pescara, Italy, September 3-7, 2007. To appear in
International Journal of Modern Physics A (2008
The Gravitational Polarization in General Relativity: Solution to Szekeres' Model of Quadrupole Polarization
A model for the static weak-field macroscopic medium is analyzed and the
equation for the macroscopic gravitational potential is derived. This is a
biharmonic equation which is a non-trivial generalization of the Poisson
equation of Newtonian gravity. In case of the strong gravitational quadrupole
polarization it essentially holds inside a macroscopic matter source. Outside
the source the gravitational potential fades away exponentially. The equation
is equivalent to a system of the Poisson equation and the nonhomogeneous
modified Helmholtz equations. The general solution to this system is obtained
by using Green's function method and it does not have a limit to Newtonian
gravity. In case of the insignificant gravitational quadrupole polarization the
equation for macroscopic gravitational potential becomes the Poisson equation
with the matter density renormalized by the factor including the value of the
quadrupole gravitational polarization of the source. The general solution to
this equation obtained by using Green's function method has a limit to
Newtonian gravity.Comment: 22 pages, no figures, to appear on Class. Quantum Gra