132 research outputs found
Green functions of higher-order differential operators
The Green functions of the partial differential operators of even order
acting on smooth sections of a vector bundle over a Riemannian manifold are
investigated via the heat kernel methods. We study the resolvent of a special
class of higher-order operators formed by the products of second-order
operators of Laplace type defined with the help of a unique Riemannian metric
but with different bundle connections and potential terms. The asymptotic
expansion of the Green functions near the diagonal is studied in detail in any
dimension. As a by-product a simple criterion for the validity of the Huygens
principle is obtained. It is shown that all the singularities as well as the
non-analytic regular parts of the Green functions of such high-order operators
are expressed in terms of the usual heat kernel coefficients for a
special Laplace type second-order operator.Comment: 26 pages, LaTeX, 65 KB, no figures, some misprints and small mistakes
are fixed, final version to appear in J. Math. Phys. (May, 1998
Lukewarm black holes in quadratic gravity
Perturbative solutions to the fourth-order gravity describing
spherically-symmetric, static and electrically charged black hole in an
asymptotically de Sitter universe is constructed and discussed. Special
emphasis is put on the lukewarm configurations, in which the temperature of the
event horizon equals the temperature of the cosmological horizon
Uniqueness of de Sitter space
All inextendible null geodesics in four dimensional de Sitter space dS^4 are
complete and globally achronal. This achronality is related to the fact that
all observer horizons in dS^4 are eternal, i.e. extend from future infinity
scri^+ all the way back to past infinity scri^-. We show that the property of
having a null line (inextendible achronal null geodesic) that extends from
scri^- to scri^+ characterizes dS^4 among all globally hyperbolic and
asymptotically de Sitter spacetimes satisfying the vacuum Einstein equations
with positive cosmological constant. This result is then further extended to
allow for a class of matter models that includes perfect fluids.Comment: 22 pages, 2 figure
Quasi-classical Lie algebras and their contractions
After classifying indecomposable quasi-classical Lie algebras in low
dimension, and showing the existence of non-reductive stable quasi-classical
Lie algebras, we focus on the problem of obtaining sufficient conditions for a
quasi-classical Lie algebras to be the contraction of another quasi-classical
algebra. It is illustrated how this allows to recover the Yang-Mills equations
of a contraction by a limiting process, and how the contractions of an algebra
may generate a parameterized families of Lagrangians for pairwise
non-isomorphic Lie algebras.Comment: 17 pages, 2 Table
Inflation and Transition to a Slowly Accelerating Phase from S.S.B. of Scale Invariance
We consider the effects of adding a scale invariant term to the
action of the scale invariant model (SIM) studied previously by one of us
(E.I.G., Mod. Phys. Lett. A14, 1043 (1999)). The SIM belongs to the general
class of theories, where an integration measure independent of the metric is
introduced. To implement scale invariance (S.I.), a dilaton field is
introduced. The integration of the equations of motion associated with the new
measure gives rise to the spontaneous symmetry breaking (S.S.B) of S.I.. After
S.S.B. of S.I. in the model with the term, it is found that a non
trivial potential for the dilaton is generated. This potential contains two
flat regions: one associated with the Planck scale and with an inflationary
phase, while the other flat region is associated to a very small vacuum energy
(V.E.) and is associated to the present slowly accelerated phase of the
universe (S.A.PH). The smallness of the V.E. in the S.A.PH. is understood
through the see saw mechanism introduced in S.I.M.Comment: 22 pages, latex, three figures now in separate file
A Unified Approach to Variational Derivatives of Modified Gravitational Actions
Our main aim in this paper is to promote the coframe variational method as a
unified approach to derive field equations for any given gravitational action
containing the algebraic functions of the scalars constructed from the Riemann
curvature tensor and its contractions. We are able to derive a master equation
which expresses the variational derivatives of the generalized gravitational
actions in terms of the variational derivatives of its constituent curvature
scalars. Using the Lagrange multiplier method relative to an orthonormal
coframe, we investigate the variational procedures for modified gravitational
Lagrangian densities in spacetime dimensions . We study
well-known gravitational actions such as those involving the Gauss-Bonnet and
Ricci-squared, Kretchmann scalar, Weyl-squared terms and their algebraic
generalizations similar to generic theories and the algebraic
generalization of sixth order gravitational Lagrangians. We put forth a new
model involving the gravitational Chern-Simons term and also give three
dimensional New massive gravity equations in a new form in terms of the Cotton
2-form
Regular black holes in quadratic gravity
The first-order correction of the perturbative solution of the coupled
equations of the quadratic gravity and nonlinear electrodynamics is
constructed, with the zeroth-order solution coinciding with the ones given by
Ay\'on-Beato and Garc{\'\i}a and by Bronnikov. It is shown that a simple
generalization of the Bronnikov's electromagnetic Lagrangian leads to the
solution expressible in terms of the polylogarithm functions. The solution is
parametrized by two integration constants and depends on two free parameters.
By the boundary conditions the integration constants are related to the charge
and total mass of the system as seen by a distant observer, whereas the free
parameters are adjusted to make the resultant line element regular at the
center. It is argued that various curvature invariants are also regular there
that strongly suggests the regularity of the spacetime. Despite the complexity
of the problem the obtained solution can be studied analytically. The location
of the event horizon of the black hole, its asymptotics and temperature are
calculated. Special emphasis is put on the extremal configuration
Ambient metrics for -dimensional -waves
We provide an explicit formula for the Fefferman-Graham-ambient metric of an
-dimensional conformal -wave in those cases where it exists. In even
dimensions we calculate the obstruction explicitly. Furthermore, we describe
all 4-dimensional -waves that are Bach-flat, and give a large class of
Bach-flat examples which are conformally Cotton-flat, but not conformally
Einstein. Finally, as an application, we use the obtained ambient metric to
show that even-dimensional -waves have vanishing critical -curvature.Comment: 17 pages, in v2 footnote and references added and typos corrected, in
v3 remark in the Introduction about Brinkmann's results corrected and
footnote adde
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