219 research outputs found
Causal Structure of Vacuum Solutions to Conformal(Weyl) Gravity
Using Penrose diagrams the causal structure of the static spherically
symmetric vacuum solution to conformal (Weyl) gravity is investigated. A
striking aspect of the solution is an unexpected physical singularity at
caused by a linear term in the metric. We explain how to calculate the
deflection of light in coordinates where the metric is manifestly conformal to
flat i.e. in coordinates where light moves in straight lines.Comment: 18 pages, 2 figures, title and abstract changed, contents essentially
unaltered accepted for publication in General Relativity and Gravitatio
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.
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
Quantum Diffeomorphisms and Conformal Symmetry
We analyze the constraints of general coordinate invariance for quantum
theories possessing conformal symmetry in four dimensions. The character of
these constraints simplifies enormously on the Einstein universe . The global conformal symmetry algebra of this space determines
uniquely a finite shift in the Hamiltonian constraint from its classical value.
In other words, the global Wheeler-De Witt equation is {\it modified} at the
quantum level in a well-defined way in this case. We argue that the higher
moments of should not be imposed on the physical states {\it a priori}
either, but only the weaker condition . We
present an explicit example of the quantization and diffeomorphism constraints
on for a free conformal scalar field.Comment: PlainTeX File, 37 page
Conformal Anomaly in 4D Gravity-Matter Theories Non-minimally Coupled with Dilaton
The conformal anomaly for 4D gravity-matter theories, which are non-minimally
coupled with the dilaton, is systematically studied. Special care is taken for:
rescaling of fields, treatment of total derivatives, hermiticity of the system
operator and choice of measure. Scalar, spinor and vector fields are taken as
the matter quantum fields and their explicit conformal anomalies in the
gravity-dilaton background are found. The cohomology analysis is done and some
new conformal invariants and trivial terms, involving the dilaton, are
obtained. The symmetry of the constant shift of the dilaton field plays an
important role. The general structure of the conformal anomaly is examined. It
is shown that the dilaton affects the conformal anomaly characteristically for
each case: 1)[Scalar] The dilaton changes the conformal anomaly only by a new
conformal invariant, ; 2)[Spinor] The dilaton does {\it not} change the
conformal anomaly; 3)[Vector] The dilaton changes the conformal anomaly by
three new (generalized) conformal invariants, . We present some
new anomaly formulae which are useful for practical calculations. Finally, the
anomaly induced action is calculated for the dilatonic Wess-Zumino model. We
point out that the coefficient of the total derivative term in the conformal
anomaly for the 2D scalar coupled to a dilaton is ambiguous. This resolves the
disagreement between calculations in refs.\cite{ENO,NO,SI97,KLV} and the result
of Hawking-Bousso\cite{BH}.Comment: 37 pages, Latex, No figur
Effective actions with fixed points, (error in derivation of coefficient corrected)
The specific form of the constant term in the asymptotic expansion of the
heat-kernel on an axially-symmetric space with a codimension two fixed-point
set of conical singularities is used to determine the associated conformal
change of the effective action in four dimensions. Another derivation of the
relevant coefficient is presented.Comment: 10p,uses JyTeX,MUTP/94/1
Thermodynamics of Quantum Fields in Black Hole Backgrounds
We discuss the relation between the micro-canonical and the canonical
ensemble for black holes, and highlight some problems associated with extreme
black holes already at the classical level. Then we discuss the contribution of
quantum fields and demonstrate that the partition functions for scalar and
Dirac (Majorana) fields in static space-time backgrounds, can be expressed as
functional integrals in the corresponding optical space, and point out that the
difference between this and the functional integrals in the original metric is
a Liouville-type action. The optical method gives both the correction to the
black hole entropy and the bulk contribution to the entropy due to the
radiation, while (if the Liouville term is ignored) the conical singularity
method just gives the divergent contribution to the black hole entropy. A
simple derivation of a general formula for the free energy in the
high-temperature approximation is given and applied to various cases. We
conclude with a discussion of the second law.Comment: 26 pages, latex, no figures. References added, minor error correcte
A Field-theoretical Interpretation of the Holographic Renormalization Group
A quantum-field theoretical interpretation is given to the holographic RG
equation by relating it to a field-theoretical local RG equation which
determines how Weyl invariance is broken in a quantized field theory. Using
this approach we determine the relation between the holographic C theorem and
the C theorem in two-dimensional quantum field theory which relies on the
Zamolodchikov metric. Similarly we discuss how in four dimensions the
holographic C function is related to a conjectured field-theoretical C
function. The scheme dependence of the holographic RG due to the possible
presence of finite local counterterms is discussed in detail, as well as its
implications for the holographic C function. We also discuss issues special to
the situation when mass deformations are present. Furthermore we suggest that
the holographic RG equation may also be obtained from a bulk diffeomorphism
which reduces to a Weyl transformation on the boundary.Comment: 24 pages, LaTeX, no figures; references added, typos corrected,
paragraph added to section
Vertex Operators in 4D Quantum Gravity Formulated as CFT
We study vertex operators in 4D conformal field theory derived from quantized
gravity, whose dynamics is governed by the Wess-Zumino action by Riegert and
the Weyl action. Conformal symmetry is equal to diffeomorphism symmetry in the
ultraviolet limit, which mixes positive-metric and negative-metric modes of the
gravitational field and thus these modes cannot be treated separately in
physical operators. In this paper, we construct gravitational vertex operators
such as the Ricci scalar, defined as space-time volume integrals of them are
invariant under conformal transformations. Short distance singularities of
these operator products are computed and it is shown that their coefficients
have physically correct sign. Furthermore, we show that conformal algebra holds
even in the system perturbed by the cosmological constant vertex operator as in
the case of the Liouville theory shown by Curtright and Thorn.Comment: 26 pages, rewrote review part concisely, added explanation
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