1,311 research outputs found
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.Comment: PlainTEX, 16 pages. Revised version 1.
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.Comment: PlainTEX, 20 page
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.Comment: 29 pages with 1 figur
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.Comment: Latex file, 31 page
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.Comment: Latex file, 31 pages; one reference and two comments added, misprints
correcte
The present universe in the Einstein frame, metric-affine R+1/R gravity
We study the present, flat isotropic universe in 1/R-modified gravity. We use
the Palatini (metric-affine) variational principle and the Einstein
(metric-compatible connected) conformal frame. We show that the energy density
scaling deviates from the usual scaling for nonrelativistic matter, and the
largest deviation occurs in the present epoch. We find that the current
deceleration parameter derived from the apparent matter density parameter is
consistent with observations. There is also a small overlap between the
predicted and observed values for the redshift derivative of the deceleration
parameter. The predicted redshift of the deceleration-to-acceleration
transition agrees with that in the \Lambda-CDM model but it is larger than the
value estimated from SNIa observations.Comment: 11 pages; published versio
Two-spinor Formulation of First Order Gravity coupled to Dirac Fields
Two-spinor formalism for Einstein Lagrangian is developed. The gravitational
field is regarded as a composite object derived from soldering forms. Our
formalism is geometrically and globally well-defined and may be used in
virtually any 4m-dimensional manifold with arbitrary signature as well as
without any stringent topological requirement on space-time, such as
parallelizability. Interactions and feedbacks between gravity and spinor fields
are considered. As is well known, the Hilbert-Einstein Lagrangian is second
order also when expressed in terms of soldering forms. A covariant splitting is
then analysed leading to a first order Lagrangian which is recognized to play a
fundamental role in the theory of conserved quantities. The splitting and
thence the first order Lagrangian depend on a reference spin connection which
is physically interpreted as setting the zero level for conserved quantities. A
complete and detailed treatment of conserved quantities is then presented.Comment: 16 pages, Plain TE
Universal field equations for metric-affine theories of gravity
We show that almost all metric--affine theories of gravity yield Einstein
equations with a non--null cosmological constant . Under certain
circumstances and for any dimension, it is also possible to incorporate a Weyl
vector field and therefore the presence of an anisotropy. The viability
of these field equations is discussed in view of recent astrophysical
observations.Comment: 13 pages. This is a copy of the published paper. We are posting it
here because of the increasing interest in f(R) theories of gravit
On the energy-momentum tensor
We clarify the relation among canonical, metric and Belinfante's
energy-momentum tensors for general tensor field theories. For any tensor field
T, we define a new tensor field \til {\bm T}, in terms of which the
Belinfante tensor is readily computed. We show that the latter is the one that
arises naturally from Noether Theorem for an arbitrary spacetime and it
coincides on-shell with the metric one.Comment: 11 pages, 1 figur
Equilibrium hydrostatic equation and Newtonian limit of the singular f(R) gravity
We derive the equilibrium hydrostatic equation of a spherical star for any
gravitational Lagrangian density of the form . The Palatini
variational principle for the Helmholtz Lagrangian in the Einstein gauge is
used to obtain the field equations in this gauge. The equilibrium hydrostatic
equation is obtained and is used to study the Newtonian limit for
. The same procedure is carried out for the more
generally case giving a good
Newtonian limit.Comment: Revised version, to appear in Classical and Quantum Gravity
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