3,740 research outputs found
Hamilton-Jacobi formalism for Linearized Gravity
In this work we study the theory of linearized gravity via the
Hamilton-Jacobi formalism. We make a brief review of this theory and its
Lagrangian description, as well as a review of the Hamilton-Jacobi approach for
singular systems. Then we apply this formalism to analyze the constraint
structure of the linearized gravity in instant and front-form dynamics.Comment: To be published in Classical and Quantum Gravit
Bopp-Podolsky black holes and the no-hair theorem
Bopp-Podolsky electrodynamics is generalized to curved space-times. The
equations of motion are written for the case of static spherically symmetric
black holes and their exterior solutions are analyzed using Bekenstein's
method. It is shown the solutions split-up into two parts, namely a
non-homogeneous (asymptotically massless) regime and a homogeneous
(asymptotically massive) sector which is null outside the event horizon. In
addition, in the simplest approach to Bopp-Podolsky black holes, the
non-homogeneous solutions are found to be Maxwell's solutions leading to a
Reissner-Nordstr\"om black hole. It is also demonstrated that the only exterior
solution consistent with the weak and null energy conditions is the Maxwell's
one. Thus, in light of energy conditions, it is concluded that only Maxwell
modes propagate outside the horizon and, therefore, the no-hair theorem is
satisfied in the case of Bopp-Podolsky fields in spherically symmetric
space-times.Comment: 9 pages, updated to match published versio
Cosmic String in Scalar-Tensor Gravity
The gravitational properties of a local cosmic string in the framework of
scalar-tensor gravity are examined. We find the metric in the weak-field
approximation and we show that, contrary to the General Relativity case, the
cosmic string in scalar-tensor gravitation exerces a force on non-relativistic,
neutral test particle. This force is proportional to the derivative of the
conformal factor and it is always attractive. Moreover, this
force could have played an important role at the Early Universe, although
nowadays it can be neglegible. It is also shown that the angular separation
remains unaltered for scalar-tensor cosmic strings.Comment: 15 pages, LATEX, no figure
The canonical structure of Podolsky's generalized electrodynamics on the Null-Plane
In this work we will develop the canonical structure of Podolsky's
generalized electrodynamics on the null-plane. This theory has second-order
derivatives in the Lagrangian function and requires a closer study for the
definition of the momenta and canonical Hamiltonian of the system. On the
null-plane the field equations also demand a different analysis of the
initial-boundary value problem and proper conditions must be chosen on the
null-planes. We will show that the constraint structure, based on Dirac
formalism, presents a set of second-class constraints, which are exclusive of
the analysis on the null-plane, and an expected set of first-class constraints
that are generators of a U(1) group of gauge transformations. An inspection on
the field equations will lead us to the generalized radiation gauge on the
null-plane, and Dirac Brackets will be introduced considering the problem of
uniqueness of these brackets under the chosen initial-boundary condition of the
theory
An analysis of cosmological perturbations in hydrodynamical and field representations
Density fluctuations of fluids with negative pressure exhibit decreasing time
behaviour in the long wavelength limit, but are strongly unstable in the small
wavelength limit when a hydrodynamical approach is used. On the other hand, the
corresponding gravitational waves are well behaved. We verify that the
instabilities present in density fluctuations are due essentially to the
hydrodynamical representation; if we turn to a field representation that lead
to the same background behaviour, the instabilities are no more present. In the
long wavelength limit, both approachs give the same results. We show also that
this inequivalence between background and perturbative level is a feature of
negative pressure fluid. When the fluid has positive pressure, the
hydrodynamical representation leads to the same behaviour as the field
representation both at the background and perturbative levels.Comment: Latex file, 18 page
How can one probe Podolsky Electrodynamics?
We investigate the possibility of detecting the Podolsky generalized
electrodynamics constant . First we analyze an ion interferometry apparatus
proposed by B. Neyenhuis, et al (Phys. Rev. Lett. 99, (2007) 200401) who looked
for deviations from Coulomb's inverse-square law in the context of Proca model.
Our results show that this experiment has not enough precision for measurements
of . In order to set up bounds for we investigate the influence of
Podolsky's electrostatic potential on the ground state of the Hydrogen atom.
The value of the ground state energy of the Hydrogen atom requires Podolsky's
constant to be smaller than 5.6 fm, or in energy scales larger than 35.51 MeV.Comment: 12 pages, 2 figure
Essential self-adjointness in one-loop quantum cosmology
The quantization of closed cosmologies makes it necessary to study squared
Dirac operators on closed intervals and the corresponding quantum amplitudes.
This paper proves self-adjointness of these second-order elliptic operators.Comment: 14 pages, plain Tex. An Erratum has been added to the end, which
corrects section
First Order Actions: a New View
We analyse systems described by first order actions using the Hamilton-Jacobi
(HJ) formalism for singular systems. In this study we verify that generalized
brackets appear in a natural way in HJ approach, showing us the existence of a
symplectic structure in the phase spaces of this formalism
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