Legendre transformation and dynamical structure of higher-derivative gravity

Magnano, Guido; Ferraris, Maurizio; Francaviglia, M.

doi:10.1088/0264-9381/7/4/007

Cited by 73 publications

(95 citation statements)

References 13 publications

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“…[16] (b) A large class of higher order theories of gravitation are equivalent to general relativity plus additional matter fields with a new metric (often referred to as "dynamical universality" of Einstein's gravity, see, for example, Ref. [17] and references therein).…”

Section: Discussionmentioning

confidence: 99%

Classical Trace Anomaly

Farhoudi

2005

Int. J. Mod. Phys. D

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We seek an analogy of the mathematical form of the alternative form of Einstein's field equations for Lovelock's field equations. We find that the price for this analogy is to accept the existence of the trace anomaly of the energy-momentum tensor even in classical treatments. As an example, we take this analogy to any generic second order Lagrangian and exactly derive the trace anomaly relation suggested by Duff. This indicates that an intrinsic reason for the existence of such a relation should perhaps be, classically, somehow related to the covariance of the form of Einstein's equations.

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Section: Discussionmentioning

confidence: 99%

Classical Trace Anomaly

Farhoudi

2005

Int. J. Mod. Phys. D

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“…The generalization into the theories whose Lagrangian includes the Weyl tensor and the derivatives of the Riemann tensor also seems to be interesting. While a "Legendre" transformation in such cases is discussed by Magnano et al [21], however, the action is not transformed into the Einstein frame in those cases. Therefore, the possibility of such generalization is not clear at present.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

Equivalence of black hole thermodynamics between a generalized theory of gravity and the Einstein theory

Koga

Maeda

1998

Phys. Rev. D

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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.

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“…Let us here briefly consider the class of Extended Theories of Gravitation (ETG); see [23][24][25]. This class of theories is used in Cosmology and Astrophysics in order to model phenomena and observations that are usually related to dark matter and dark energy; [26].…”

Section: Extended Theories Of Gravitationmentioning

confidence: 99%

Noether Symmetries and Covariant Conservation Laws in Classical, Relativistic and Quantum Physics

2010

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Abstract:We review the Lagrangian formulation of (generalised) Noether symmetries in the framework of Calculus of Variations in Jet Bundles, with a special attention to so-called "Natural Theories" and "Gauge-Natural Theories" that include all relevant Field Theories and physical applications (from Mechanics to General Relativity, to Gauge Theories, Supersymmetric Theories, Spinors, etc.). It is discussed how the use of Poincaré-Cartan forms and decompositions of natural (or gauge-natural) variational operators give rise to notions such as "generators of Noether symmetries", energy and reduced energy flow, Bianchi identities, weak and strong conservation laws, covariant conservation laws, Hamiltonian-like conservation laws (such as, e.g., so-called ADM laws in General Relativity) with emphasis on the physical interpretation of the quantities calculated in specific cases (energy, angular momentum, entropy, etc.). A few substantially new and very recent applications/examples are presented to better show the power of the methods introduced: one in Classical Mechanics (definition of strong conservation laws in a frame-independent setting and a discussion on the way in which conserved quantities depend on the choice of an observer); one in Classical Field Theories (energy and entropy in General Relativity, in its standard formulation, in its spin-frame formulation, in its first order formulation "à la Palatini" and in its extensions to Non-Linear Gravity Theories); one in Quantum Field Theories (applications to conservation laws in Loop Quantum Gravity via spin connections and Barbero-Immirzi connections).

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Legendre transformation and dynamical structure of higher-derivative gravity

Cited by 73 publications

References 13 publications

Classical Trace Anomaly

Classical Trace Anomaly

Equivalence of black hole thermodynamics between a generalized theory of gravity and the Einstein theory

Noether Symmetries and Covariant Conservation Laws in Classical, Relativistic and Quantum Physics

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