Covariant approach of perturbations in Lovelock type brane gravity

Bagatella-Flores, N.; Campuzano, Cuauhtemoc; Cruz, Miguel; Rojas, Efraín

doi:10.1088/0264-9381/33/24/245012

Cited by 9 publications

(19 citation statements)

References 51 publications

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“…This equation is clearly in accord with the results found in Ref. [23] for the case of an action functional depending linearly of the trace of the extrinsic cur-vature which corresponds to the so-called second Lovelock type brane invariant. In another fashion, Eq.…”

Section: Second Variation and The Linearized Equations Of Motionsupporting

confidence: 91%

“…Concerning the hypersurface embedding case, i = 1, the action (1) specializes to a functional depending linearly of the mean extrinsic curvature which has been discussed extensively in the relativistic context in the framework of the Lovelock type branes [22,23] whereas in the Euclidean context such functional has attracted lot of attention as being part of the geometrical prescription to study biological lipid membranes [25][26][27][28]. In such a case, R ij specializes to R so that, K (1) = 1 and the equations of motion (12) reduce to a single equation of second order in the derivatives of the fields, E (1) = R = 0.…”

Section: First Variation and The Equations Of Motionmentioning

confidence: 99%

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Covariant perturbations in the gonihedric string model

Rojas

2017

Int. J. Mod. Phys. A

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We provide a covariant framework to study classically the stability of small perturbations on the so-called gonihedric string model by making precise use of variational techniques. The local action depends of the square root of the quadratic mean extrinsic curvature of the worldsheet swept out by the string, and is reparametrization invariant. A general expression for the worldsheet perturbations, guided by Jacobi equations without any early gauge fixing, is obtained. This is manifested through a set of highly coupled nonlinear differential partial equations where the perturbations are described by scalar fields, Φ i , living in the worldsheet. This model contains, as a special limit, to the linear model in the mean extrinsic curvature. In such a case the Jacobi equations specialize to a single wave-like equation for Φ.

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Section: Second Variation and The Linearized Equations Of Motionsupporting

confidence: 91%

Section: First Variation and The Equations Of Motionmentioning

confidence: 99%

Covariant perturbations in the gonihedric string model

Rojas

2017

Int. J. Mod. Phys. A

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“…where the Hamiltonians ( 22) have been introduced. This expression is in agreement with (25). On the other hand, bearing in mind the nature of the matrix (4), we must recall that the only independent parameter is t 0 so that…”

Section: B Characteristic Equationssupporting

confidence: 77%

Hamilton-Jacobi approach for linearly acceleration-dependent Lagrangians

Aguilar-Salas,

Rojas

2021

Preprint

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We develop a constructive procedure for arriving at the Hamilton-Jacobi framework for the socalled affine in acceleration theories by analysing the canonical constraint structure. We find two scenarios in dependence of the order of the emerging equations of motion. By properly defining generalized brackets, the non-involutive constraints that originally arose, in both scenarios, may be removed so that the resulting involutive Hamiltonian constraints ensure integrability of the theories and, at the same time, lead to the right dynamics in the reduced phase space. In particular, when we have second-order in derivatives equations of motion we are able to detect the gauge invariant sector of the theory by using a suitable approach based on the projection of the Hamiltonians onto the tangential and normal directions of the congruence of curves in the configuration space. Regarding this, we also explore the generators of canonical and gauge transformations of these theories. Further, we briefly outline how to determine the Hamilton principal function S for some particular setups. We apply our findings to some representative theories: a Chern-Simons-like theory in (2 + 1)-dim, an harmonic oscillator in 2D and, the geodetic brane cosmology emerging in the context of extra dimensions.

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“…As shown, this is a consequence of the invariance under reparametrizations of the action functional in this type of gravity. In each surface governed by this action, there is only one degree of freedom, corresponding to the breathing mode of the worldvolume so its nature is only geometric [14]. In this sense, it is expected that the Lagrangians, either L bulk or L surf reflect this fact, thereby encoding the same amount of dynamical content by describing the same degree of freedom.…”

Section: Discussionmentioning

confidence: 99%

Holographic relationships in Lovelock type brane gravity

Rojas

2019

Class. Quantum Grav.

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We show that the Lovelock type brane gravity is naturally holographic by providing a correspondence between bulk and surface terms that appear in the Lovelock-type brane gravity action functional. We prove the existence of relationships between the L bulk and L surf allowing L surf to be determined completely by L bulk . In the same spirit, we provide relationships among the various conserved tensors that this theory possesses. We further comment briefly on the correspondence between geometric degrees of freedom in both bulk and surface space.

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Covariant approach of perturbations in Lovelock type brane gravity

Cited by 9 publications

References 51 publications

Covariant perturbations in the gonihedric string model

Covariant perturbations in the gonihedric string model

Hamilton-Jacobi approach for linearly acceleration-dependent Lagrangians

Holographic relationships in Lovelock type brane gravity

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