65 research outputs found
Charged Black Holes In Quadratic Theories
We point out that in general the Reissner-Nordstr\"om (RN) charged black
holes of general relativity are not solutions of the four dimensional quadratic
gravitational theories. They are, e.g., exact solutions of the
quadratic theory but not of a theory where a term is present in
the gravitational Lagrangian. In the case where such a non linear curvature
term is present with sufficiently small coupling, we obtain an approximate
solution for a charged black hole of charge and mass . For the
validity of this solution extends down to the horizon. This allows us to
explore the thermodynamic properties of the quadratic charged black hole and we
find that, to our approximation, its thermodynamics is identical to that of a
RN black hole. However our black hole's entropy is not equal to the one fourth
of the horizon area. Finally we extend our analysis to the rotating charged
black hole and qualitatively similar results are obtained.Comment: 11 pages, LaTeX/RevTeX3.
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
Gravitation, electromagnetism and cosmological constant in purely affine gravity
The Ferraris-Kijowski purely affine Lagrangian for the electromagnetic field,
that has the form of the Maxwell Lagrangian with the metric tensor replaced by
the symmetrized Ricci tensor, is dynamically equivalent to the metric
Einstein-Maxwell Lagrangian, except the zero-field limit, for which the metric
tensor is not well-defined. This feature indicates that, for the
Ferraris-Kijowski model to be physical, there must exist a background field
that depends on the Ricci tensor. The simplest possibility, supported by recent
astronomical observations, is the cosmological constant, generated in the
purely affine formulation of gravity by the Eddington Lagrangian. In this paper
we combine the electromagnetic field and the cosmological constant in the
purely affine formulation. We show that the sum of the two affine (Eddington
and Ferraris-Kijowski) Lagrangians is dynamically inequivalent to the sum of
the analogous (CDM and Einstein-Maxwell) Lagrangians in the
metric-affine/metric formulation. We also show that such a construction is
valid, like the affine Einstein-Born-Infeld formulation, only for weak
electromagnetic fields, on the order of the magnetic field in outer space of
the Solar System. Therefore the purely affine formulation that combines
gravity, electromagnetism and cosmological constant cannot be a simple sum of
affine terms corresponding separately to these fields. A quite complicated form
of the affine equivalent of the metric Einstein-Maxwell- Lagrangian
suggests that Nature can be described by a simpler affine Lagrangian, leading
to modifications of the Einstein-Maxwell-CDM theory for
electromagnetic fields that contribute to the spacetime curvature on the same
order as the cosmological constant.Comment: 17 pages, extended and combined with gr-qc/0612193; published versio
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
Topological Defects in Gravitational Theories with Non Linear Lagrangians
The gravitational field of monopoles, cosmic strings and domain walls is
studied in the quadratic gravitational theory with , and is compared with the result in Einstein's theory. The metric
aquires modifications which correspond to a short range `Newtonian' potential
for gauge cosmic strings, gauge monopoles and domain walls and to a long range
one for global monopoles and global cosmic strings. In this theory the
corrections turn out to be attractive for all the defects. We explain, however,
that the sign of these corrections in general depends on the particular higher
order derivative theory and topological defect under consideration. The
possible relevance of our results to the study of the evolution of topological
defects in the early universe is pointed out.Comment: LaTeX (uses revrex macros), 13 page
On Physical Equivalence between Nonlinear Gravity Theories
We argue that in a nonlinear gravity theory, which according to well-known
results is dynamically equivalent to a self-gravitating scalar field in General
Relativity, the true physical variables are exactly those which describe the
equivalent general-relativistic model (these variables are known as Einstein
frame). Whenever such variables cannot be defined, there are strong indications
that the original theory is unphysical. We explicitly show how to map, in the
presence of matter, the Jordan frame to the Einstein one and backwards. We
study energetics for asymptotically flat solutions. This is based on the
second-order dynamics obtained, without changing the metric, by the use of a
Helmholtz Lagrangian. We prove for a large class of these Lagrangians that the
ADM energy is positive for solutions close to flat space. The proof of this
Positive Energy Theorem relies on the existence of the Einstein frame, since in
the (Helmholtz--)Jordan frame the Dominant Energy Condition does not hold and
the field variables are unrelated to the total energy of the system.Comment: 37 pp., TO-JLL-P 3/93 Dec 199
Quadratic Curvature Gravity with Second Order Trace and Massive Gravity Models in Three Dimensions
The quadratic curvature lagrangians having metric field equations with second
order trace are constructed relative to an orthonormal coframe. In
dimensions, pure quadratic curvature lagrangian having second order trace
constructed contains three free parameters in the most general case. The fourth
order field equations of some of these models, in arbitrary dimensions, are
cast in a particular form using the Schouten tensor. As a consequence, the
field equations for the New massive gravity theory are related to those of the
Topologically massive gravity. In particular, the conditions under which the
latter is "square root" of the former are presented.Comment: 24 pages, to appear in GR
Resonant particle production with non-minimally coupled scalar fields in preheating after inflation
We investigate a resonant particle production of a scalar field
coupled non-minimally to a spacetime curvature () as well as
to an inflaton field (). In the case of , effect assists -resonance in certain parameter regimes.
However, for , -resonance is not enhanced by
effect because of suppression effect as well as a back reaction effect.
If , the maximal fluctuation of produced -particle is
GeV for , which is larger than the minimally coupled case with .Comment: 33pages, 12figures. to appear in Physical Review
New constraints on multi-field inflation with nonminimal coupling
We study the dynamics and perturbations during inflation and reheating in a
multi-field model where a second scalar field is nonminimally coupled to
the scalar curvature ). When is positive, the usual
inflationary prediction for large-scale anisotropies is hardly altered while
the fluctuation in sub-Hubble modes can be amplified during preheating
for large . For negative values of , however, long-wave modes of the
fluctuation exhibit exponential increase during inflation, leading to
the strong enhancement of super-Hubble metric perturbations even when
is less than unity. This is because the effective mass becomes negative
during inflation. We constrain the strength of and the initial by
the amplitude of produced density perturbations. One way to avoid nonadiabatic
growth of super-Hubble curvature perturbations is to stabilize the mass
through a coupling to the inflaton. Preheating may thus be necessary in these
models to protect the stability of the inflationary phase.Comment: 20 pages, 8 figures, submitted to Physical Review
Local inhibition of nitrergic activity in tenotomized rats accelerates muscle regeneration by increasing fiber area and decreasing central core lesions
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