510 research outputs found
A new duality transformation for fourth-order gravity
We prove that for non-linear L = L(R), the Lagrangians L and \hat L give
conformally equivalent fourth-order field equations being dual to each other.
The proof represents a new application of the fact that the operator
is conformally invariant.Comment: 11 pages, LaTeX, no figures. Gen. Relat. Grav. in prin
Non-Trivial Vacua in Higher-Derivative Gravitation
A discussion of an extended class of higher-derivative classical theories of
gravity is presented. A procedure is given for exhibiting the new propagating
degrees of freedom, at the full non-linear level, by transforming the
higher-derivative action to a canonical second-order form. For general
fourth-order theories, described by actions which are general functions of the
scalar curvature, the Ricci tensor and the full Riemann tensor, it is shown
that the higher-derivative theories may have multiple stable vacua. The vacua
are shown to be, in general, non-trivial, corresponding to deSitter or
anti-deSitter solutions of the original theory. It is also shown that around
any vacuum the elementary excitations remain the massless graviton, a massive
scalar field and a massive ghost-like spin-two field. The analysis is extended
to actions which are arbitrary functions of terms of the form ,
and it is shown that such theories also have a non-trivial vacuum structure.Comment: 25 pages, LaTeX2e with AMS-LaTeX 1.2, 7 eps figure
Ostrogradski Formalism for Higher-Derivative Scalar Field Theories
We carry out the extension of the Ostrogradski method to relativistic field
theories. Higher-derivative Lagrangians reduce to second differential-order
with one explicit independent field for each degree of freedom. We consider a
higher-derivative relativistic theory of a scalar field and validate a powerful
order-reducing covariant procedure by a rigorous phase-space analysis. The
physical and ghost fields appear explicitly. Our results strongly support the
formal covariant methods used in higher-derivative gravity.Comment: 22 page
Gauge Fixing in Higher Derivative Gravity
Linearized four-derivative gravity with a general gauge fixing term is
considered. By a Legendre transform and a suitable diagonalization procedure it
is cast into a second-order equivalent form where the nature of the physical
degrees of freedom, the gauge ghosts, the Weyl ghosts, and the intriguing
"third ghosts", characteristic to higher-derivative theories, is made explicit.
The symmetries of the theory and the structure of the compensating
Faddeev-Popov ghost sector exhibit non-trivial peculiarities.Comment: 21 pages, LaTe
Equivalence of black hole thermodynamics between a generalized theory of gravity and the Einstein theory
We analyze black hole thermodynamics in a generalized theory of gravity whose
Lagrangian is an arbitrary function of the metric, the Ricci tensor and a
scalar field. We can convert the theory into the Einstein frame via a
"Legendre" transformation or a conformal transformation. We calculate
thermodynamical variables both in the original frame and in the Einstein frame,
following the Iyer--Wald definition which satisfies the first law of
thermodynamics. We show that all thermodynamical variables defined in the
original frame are the same as those in the Einstein frame, if the spacetimes
in both frames are asymptotically flat, regular and possess event horizons with
non-zero temperatures. This result may be useful to study whether the second
law is still valid in the generalized theory of gravity.Comment: 14 pages, no figure
The dynamical equivalence of modified gravity revisited
We revisit the dynamical equivalence between different representations of
vacuum modified gravity models in view of Legendre transformations. The
equivalence is discussed for both bulk and boundary space, by including in our
analysis the relevant Gibbons-Hawking terms. In the f(R) case, the Legendre
transformed action coincides with the usual Einstein frame one. We then
re-express the R+f(G) action, where G is the Gauss-Bonnet term, as a second
order theory with a new set of field variables, four tensor fields and one
scalar and study its dynamics. For completeness, we also calculate the
conformal transformation of the full Jordan frame R+f(G) action. All the
appropriate Gibbons-Hawking terms are calculated explicitly.Comment: 17 pages; v3: Revised version. New comments added in Sections 3 & 5.
New results added in Section 6. Version to appear in Class. Quantum Gravit
The Universality of Einstein Equations
It is shown that for a wide class of analytic Lagrangians which depend only
on the scalar curvature of a metric and a connection, the application of the
so--called ``Palatini formalism'', i.e., treating the metric and the connection
as independent variables, leads to ``universal'' equations. If the dimension
of space--time is greater than two these universal equations are Einstein
equations for a generic Lagrangian and are suitably replaced by other universal
equations at bifurcation points. We show that bifurcations take place in
particular for conformally invariant Lagrangians and prove
that their solutions are conformally equivalent to solutions of Einstein
equations. For 2--dimensional space--time we find instead that the universal
equation is always the equation of constant scalar curvature; the connection in
this case is a Weyl connection, containing the Levi--Civita connection of the
metric and an additional vectorfield ensuing from conformal invariance. As an
example, we investigate in detail some polynomial Lagrangians and discuss their
bifurcations.Comment: 15 pages, LaTeX, (Extended Version), TO-JLL-P1/9
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