2,577 research outputs found
Local and global gravity
Our long experience with Newtonian potentials has inured us to the view that
gravity only produces local effects. In this paper we challenge this quite
deeply ingrained notion and explicitly identify some intrinsically global
gravitational effects. In particular we show that the global cosmological
Hubble flow can actually modify the motions of stars and gas within individual
galaxies, and even do so in a way which can apparently eliminate the need for
galactic dark matter. Also we show that a classical light wave acquires an
observable, global, path dependent phase in traversing a gravitational field.
Both of these effects serve to underscore the intrinsic difference between
non-relativistic and relativistic gravity.Comment: LaTeX, 20 pages plus three figures in two postscript files. To appear
in a special issue of Foundations of Physics honoring Professor Lawrence
Horwitz on the occasion of his 65th birthday; A. van der Merwe and S. Raby,
Editors, Plenum Publishing Company, N.Y., 199
Newtonian Limit of Conformal Gravity
We study the weak-field limit of the static spherically symmetric solution of
the locally conformally invariant theory advocated in the recent past by
Mannheim and Kazanas as an alternative to Einstein's General Relativity. In
contrast with the previous works, we consider the physically relevant case
where the scalar field that breaks conformal symmetry and generates fermion
masses is nonzero. In the physical gauge, in which this scalar field is
constant in space-time, the solution reproduces the weak-field limit of the
Schwarzschild--(anti)DeSitter solution modified by an additional term that,
depending on the sign of the Weyl term in the action, is either oscillatory or
exponential as a function of the radial distance. Such behavior reflects the
presence of, correspondingly, either a tachion or a massive ghost in the
spectrum, which is a serious drawback of the theory under discussion.Comment: 9 pages, comments and references added; the version to be published
in Phys. Rev.
Completeness of non-normalizable modes
We establish the completeness of some characteristic sets of non-normalizable
modes by constructing fully localized square steps out of them, with each such
construction expressly displaying the Gibbs phenomenon associated with trying
to use a complete basis of modes to fit functions with discontinuous edges. As
well as being of interest in and of itself, our study is also of interest to
the recently introduced large extra dimension brane-localized gravity program
of Randall and Sundrum, since the particular non-normalizable mode bases that
we consider (specifically the irregular Bessel functions and the associated
Legendre functions of the second kind) are associated with the tensor
gravitational fluctuations which occur in those specific brane worlds in which
the embedding of a maximally four-symmetric brane in a five-dimensional anti-de
Sitter bulk leads to a warp factor which is divergent. Since the brane-world
massless four-dimensional graviton has a divergent wave function in these
particular cases, its resulting lack of normalizability is thus not seen to be
any impediment to its belonging to a complete basis of modes, and consequently
its lack of normalizability should not be seen as a criterion for not including
it in the spectrum of observable modes. Moreover, because the divergent modes
we consider form complete bases, we can even construct propagators out of them
in which these modes appear as poles with residues which are expressly finite.
Thus even though normalizable modes appear in propagators with residues which
are given as their finite normalization constants, non-normalizable modes can
just as equally appear in propagators with finite residues too -- it is just
that such residues will not be associated with bilinear integrals of the modes.Comment: 34 pages, 6 figures. Revte
Implications of Cosmic Repulsion for Gravitational Theory
In this paper we present a general, model independent analysis of a recently
detected apparent cosmic repulsion, and discuss its potential implications for
gravitational theory. In particular, we show that a negatively spatially curved
universe acts like a diverging refractive medium, to thus naturally cause
galaxies to accelerate away from each other. Additionally, we show that it is
possible for a cosmic acceleration to only be temporary, with some accelerating
universes actually being able to subsequently recontract.Comment: RevTeX, 13 page
Gauge Invariant Treatment of the Energy Carried by a Gravitational Wave
Even though the energy carried by a gravitational wave is not itself gauge
invariant, the interaction with a gravitational antenna of the gravitational
wave which carries that energy is. It therefore has to be possible to make some
statements which involve the energy which are in fact gauge invariant, and it
is the objective of this paper to provide them. In order to develop a gauge
invariant treatment of the issues involved, we construct a specific action for
gravitational fluctuations which is gauge invariant to second perturbative
order. Then, via variation of this action, we obtain an energy-momentum tensor
for perturbative gravitational fluctuations around a general curved background
whose covariant conservation condition is also fully gauge invariant to second
order. Contraction of this energy-momentum tensor with a Killing vector of the
background conveniently allows us to convert this covariant conservation
condition into an ordinary conservation condition which is also gauge invariant
through second order. Then, via spatial integration we are able to obtain a
relation involving the time derivative of the total energy of the fluctuation
and its asymptotic spatial momentum flux which is also completely gauge
invariant through second order. It is only in making the simplification of
setting the asymptotic momentum flux to zero that one would actually lose
manifest gauge invariance, with only invariance under those particular gauge
transformations which leave the asymptotic momentum flux zero then remaining.
However, if one works in an arbitrary gauge where the asymptotic momentum flux
is non-zero, the gravitational wave will then deliver both energy and momentum
to a gravitational antenna in a completely gauge invariant manner, no matter
how badly behaved at infinity the gauge function might be.Comment: 13 pages, revtex4. Final version. To appear in Phys. Rev.
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