arXiv subjects

M. Raiteri

Publications and source records attributed to M. Raiteri.

11 recordsLinked to original sources

arXiv2004

Boundary Conditions, Energies and Gravitational Heat in General Relativity (a Classical Analysis)

The variation of the energy for a gravitational system is directly defined from the Hamiltonian field equations of General Relativity. When the variation of the energy is written in a covariant form it splits into two (covariant) contributions: one of them is the Komar energy, while the other is the so-called covariant ADM correction term. When specific boundary conditions are analyzed one sees that the Komar energy is related to the gravitational heat while the ADM correction term plays the role of the Helmholtz free energy. These properties allow to establish, inside a classical geometric framework, a formal analogy between gravitation and the laws governing the evolution of a thermodynamic system. The analogy applies to stationary spacetimes admitting multiple causal horizons as well as to AdS Taub-bolt solutions.

gr-qc↗

arXiv2003

Charges and Energy in Chern-Simons Theories and Lovelock Gravity

Starting from the SO(2,2n) Chern-Simons form in (2n+1) dimensions we calculate the variation of conserved quantities in Lovelock gravity and Lovelock-Maxwell gravity through the covariant formalism developed in gr-qc/0305047. Despite the technical complexity of the Lovelock Lagrangian we obtain a remarkably simple expression for the variation of the charges ensuing from the diffeomorphism covariance of the theory. The viability of the result is tested in specific applications and the formal expression for the entropy of Lovelock black holes is recovered.

gr-qc↗

arXiv2003

Conserved Quantities from the Equations of Motion (with applications to natural and gauge natural theories of gravitation)

We present an alternative field theoretical approach to the definition of conserved quantities, based directly on the field equations content of a Lagrangian theory (in the standard framework of the Calculus of Variations in jet bundles). The contraction of the Euler-Lagrange equations with Lie derivatives of the dynamical fields allows one to derive a variational Lagrangian for any given set of Lagrangian equations. A two steps algorithmical procedure can be thence applied to the variational Lagrangian in order to produce a general expression for the variation of all quantities which are (covariantly) conserved along the given dynamics. As a concrete example we test this new formalism on Einstein's equations: well known and widely accepted formulae for the variation of the Hamiltonian and the variation of Energy for General Relativity are recovered. We also consider the Einstein-Cartan (Sciama-Kibble) theory in tetrad formalism and as a by-product we gain some new insight on the Kosmann lift in gauge natural theories, which arises when trying to restore naturality in a gauge natural variational Lagrangian.

gr-qc↗

arXiv2002

Covariant Charges in Chern-Simons AdS_3 Gravity

We try to give hereafter an answer to some open questions about the definition of conserved quantities in Chern-Simons theory, with particular reference to Chern-Simons AdS_3 Gravity. Our attention is focused on the problem of global covariance and gauge invariance of the variation of Noether charges. A theory which satisfies the principle of covariance on each step of its construction is developed, starting from a gauge invariant Chern-Simons Lagrangian and using a recipe developed in gr-qc/0110104 and gr-qc/0107074 to calculate the variation of conserved quantities. The problem to give a mathematical well-defined expression for the infinitesimal generators of symmetries is pointed out and it is shown that the generalized Kosmann lift of spacetime vector fields leads to the expected numerical values for the conserved quantities when the solution corresponds to the BTZ black hole. The fist law of black holes mechanics for the BTZ solution is then proved and the transition between the variation of conserved quantities in Chern-Simons AdS_3 Gravity theory and the variation of conserved quantities in General Relativity is analysed in detail.

gr-qc↗

arXiv2001

The First Law of Isolated Horizons via Noether Theorem

A general recipe proposed elsewhere to define, via Noether theorem, the variation of energy for a natural field theory is applied to Einstein-Maxwell theory. The electromagnetic field is analysed in the geometric framework of natural bundles. Einstein-Maxwell theory turns then out to be natural rather than gauge-natural. As a consequence of this assumption a correction term \a la Regge-Teitelboim is needed to define the variation of energy, also for the pure electromagnetic part of the Einstein-Maxwell Lagrangian. Integrability conditions for the variational equation which defines the variation of energy are analysed in relation with boundary conditions on physical data. As an application the first law of thermodynamics for rigidly rotating horizons is obtained.

gr-qc↗

arXiv2001

Hamiltonian, Energy and Entropy in General Relativity with Non-Orthogonal Boundaries

A general recipe to define, via Noether theorem, the Hamiltonian in any natural field theory is suggested. It is based on a Regge-Teitelboim-like approach applied to the variation of Noether conserved quantities. The Hamiltonian for General Relativity in presence of non-orthogonal boundaries is analysed and the energy is defined as the on-shell value of the Hamiltonian. The role played by boundary conditions in the formalism is outlined and the quasilocal internal energy is defined by imposing metric Dirichlet boundary conditions. A (conditioned) agreement with previous definitions is proved. A correspondence with Brown-York original formulation of the first principle of black hole thermodynamics is finally established.

gr-qc↗

arXiv2000

Energy for N-Body Motion in Two Dimensional Gravity

A general definition of energy is given, via the Nöther theorem, for the N-body problem in (1+1) dimensional gravity. Within a first-order Lagrangian framework, the density of energy of a solution relative to a background is identified with the superpotential of the theory. For specific applications we reproduce the expected Hamiltonian for the motion of N particles in a curved spacetime. This Hamiltonian agrees with that found through an ADM-like prescription for the energy when the latter is applicable but it also extends to a wider class of solutions provided a suitable background is chosen.

gr-qc↗

arXiv2000

Noether Charges, Brown-York Quasilocal Energy and Related Topics

The Lagrangian proposed by York et al. and the covariant first order Lagrangian for General Relativity are introduced to deal with the (vacuum) gravitational field on a reference background. The two Lagrangians are compared and we show that the first one can be obtained from the latter under suitable hypotheses. The induced variational principles are also compared and discussed. A conditioned correspondence among Noether conserved quantities, quasilocal energy and the standard Hamiltonian obtained by 3+1 decomposition is also established. As a result, it turns out that the covariant first order Lagrangian is better suited whenever a reference background field has to be taken into account, as it is commonly accepted when dealing with conserved quantities in non-asymptotically flat spacetimes. As a further advantage of the use of a covariant first order Lagrangian, we show that all the quantities computed are manifestly covariant, as it is appropriate in General Relativity.

gr-qc↗

arXiv1999

The Entropy of Taub-Bolt Solution

A geometrical framework for the definition of entropy in General Relativity via Noether theorem is briefly recalled and the entropy of Taub-Bolt Euclidean solutions of Einstein equations is then obtained as an application. The computed entropy agrees with previously known results, obtained by statistical methods. It was generally believed that the entropy of Taub-Bolt solution could not be computed via Noether theorem, due to the particular structure of singularities of this solution. We show here that this is not true. The Misner string singularity is, in fact, considered and its contribution to the entropy is analyzed. As a result, in our framework entropy does not obey the "one-quarter area law" and it is not directly related to horizons, as sometimes erroneously suggested in current literature on the subject.

gr-qc↗

arXiv1999

Remarks on Conserved Quantities and Entropy of BTZ Black Hole Solutions. Part I: the General Setting

The BTZ stationary black hole solution is considered and its mass and angular momentum are calculated by means of Noether theorem. In particular, relative conserved quantities with respect to a suitably fixed background are discussed. Entropy is then computed in a geometric and macroscopic framework, so that it satisfies the first principle of thermodynamics. In order to compare this more general framework to the prescription by Wald et al. we construct the maximal extension of the BTZ horizon by means of Kruskal-like coordinates. A discussion about the different features of the two methods for computing entropy is finally developed.

gr-qc↗

arXiv1999

Remarks on Conserved Quantities and Entropy of BTZ Black Hole Solutions. Part II: BCEA Theory

The BTZ black hole solution for (2+1)-spacetime is considered as a solution of a triad-affine theory (BCEA) in which topological matter is introduced to replace the cosmological constant in the model. Conserved quantities and entropy are calculated via Noether theorem, reproducing in a geometrical and global framework earlier results found in the literature using local formalisms. Ambiguities in global definitions of conserved quantities are considered in detail. A dual and covariant Legendre transformation is performed to re-formulate BCEA theory as a purely metric (natural) theory (BCG) coupled to topological matter. No ambiguities in the definition of mass and angular momentum arise in BCG theory. Moreover, gravitational and matter contributions to conserved quantities and entropy are isolated. Finally, a comparison of BCEA and BCG theories is carried out by relying on the results obtained in both theories.

gr-qc↗