43 research outputs found
On Dual Formulation of Gravity
In this paper we consider a possibility to construct dual formulation of
gravity where the main dynamical field is the Lorentz connection
\omega_\mu^{ab} and not that of tetrad e_\mu^a or metric g_\mu\nu. Our approach
is based on the usual dualization procedure which uses first order parent
Lagrangians but in (Anti) de Sitter space and not in the flat Minkowski one. It
turns out that in d=3 dimensions such dual formulation is related with the so
called exotic parity-violating interactions for massless spin-2 particles.Comment: 7 pages, plain LaTe
Darboux coordinates for (first order) tetrad gravity
The Hamiltonian form of the Hilbert action in the first order tetrad
formalism is examined. We perform a non-linear field redefinition of the
canonical variables isolating the part of the spin connection which is
canonically conjugate to the tetrad. The geometrical meaning of the constraints
written in these new variables is examined.Comment: 12 pages, Latex. Minor presentation changes and some references
added. Version to appear in Classical and Quantum Gravit
Selfdual 2-form formulation of gravity and classification of energy-momentum tensors
It is shown how the different irreducibility classes of the energy-momentum
tensor allow for a Lagrangian formulation of the gravity-matter system using a
selfdual 2-form as a basic variable. It is pointed out what kind of
difficulties arise when attempting to construct a pure spin-connection
formulation of the gravity-matter system. Ambiguities in the formulation
especially concerning the need for constraints are clarified.Comment: title changed, extended versio
SU(2)-invariant reduction of the 3+1 dimensional Ashtekar's gravity
We consider a space-time with spatial sections isomorphic to the group
manifold of SU(2). Triad and connection fluctuations are assumed to be
SU(2)-invariant. Thus, they form a finite dimensional phase space. We perform
non-perturbative path integral quantization of the model. Contarary to previous
claims the path integral measure appeared to be non-singular near
configurations admitting additional Killing vectors. In this model we are able
to calculate the generating functional of Green functions of the reduced phase
space variables exactly.Comment: 12 page
Non-Metric Gravity I: Field Equations
We describe and study a certain class of modified gravity theories. Our
starting point is Plebanski formulation of gravity in terms of a triple B^i of
2-forms, a connection A^i and a ``Lagrange multiplier'' field Psi^ij. The
generalization we consider stems from presence in the action of an extra term
proportional to a scalar function of Psi^ij. As in the usual Plebanski general
relativity (GR) case, a certain metric can be constructed from B^i. However,
unlike in GR, the connection A^i no longer coincides with the self-dual part of
the metric-compatible spin-connection. Field equations of the theory are shown
to be relations between derivatives of the metric and components of field Psi,
as well as its derivatives, the later being in contrast to the GR case. The
equations are of second order in derivatives. An analog of the Bianchi identity
is still present in the theory, as well as its contracted version tantamount to
energy conservation equation.Comment: 21 pages, no figures (v2) energy conservation equation simplified,
note on reality conditions added (v3) minor change
New Variables for Classical and Quantum Gravity in all Dimensions II. Lagrangian Analysis
We rederive the results of our companion paper, for matching spacetime and
internal signature, by applying in detail the Dirac algorithm to the Palatini
action. While the constraint set of the Palatini action contains second class
constraints, by an appeal to the method of gauge unfixing, we map the second
class system to an equivalent first class system which turns out to be
identical to the first class constraint system obtained via the extension of
the ADM phase space performed in our companion paper. Central to our analysis
is again the appropriate treatment of the simplicity constraint. Remarkably,
the simplicity constraint invariant extension of the Hamiltonian constraint,
that is a necessary step in the gauge unfixing procedure, involves a correction
term which is precisely the one found in the companion paper and which makes
sure that the Hamiltonian constraint derived from the Palatini Lagrangian
coincides with the ADM Hamiltonian constraint when Gauss and simplicity
constraints are satisfied. We therefore have rederived our new connection
formulation of General Relativity from an independent starting point, thus
confirming the consistency of this framework.Comment: 42 pages. v2: Journal version. Some nonessential sign errors in
section 2 corrected. Minor clarification
6D interpretation of 3D gravity
We show that 3D gravity, in its pure connection formulation, admits a natural 6D interpretation. The 3D field equations for the connection are equivalent to 6D Hitchin equations for the Chern–Simons 3-form in the total space of the principal bundle over the 3-dimensional base. Turning this construction around one gets an explanation of why the pure connection formulation of 3D gravity exists. More generally, we interpret 3D gravity as the dimensional reduction of the 6D Hitchin theory. To this end, we show that any invariant closed 3-form in the total space of the principal bundle can be parametrised by a connection together with a 2-form field on the base. The dimensional reduction of the 6D Hitchin theory then gives rise to 3D gravity coupled to a topological 2-form field
Spherically symmetric black holes in minimally modified self-dual gravity
We discuss spherically symmetric black holes in the modified self-dual theory
of gravity recently studied by Krasnov, obtained adding a Weyl-curvature
dependent `cosmological term' to the Plebanski lagrangian for general
relativity. This type of modified gravity admits two different types of
singularities: one is a true singularity for the theory where the fundamental
fields of the theory, as well as the (auxiliary) spacetime metric, become
singular, and the other one is a milder "non-metric singularity" where the
metric description of the spacetime breaks down but the fundamental fields
themselves are regular. We first generalise this modified self-dual gravity to
include Maxwell's field and then study basic features of spherically symmetric,
charged black holes, with particular focus on whether these two types of
singularities are hidden or naked. We restrict our attention to minimal forms
of the modification, and find that the theory exhibits `screening' effects of
the electric charge (or `anti-screening', depending upon the sign of the
modification term), in the sense that it leads to the possibility of charging
the black hole more (or less) than it would be possible in general relativity
without exposing a naked singularity. We also find that for any (even
arbitrarily large) value of charge, true singularities of the theory appear to
be either achronal (non-timelike) covered by the hypersurface of a harmless
non-metric singularity, or simply hidden inside at least one Killing horizon.Comment: 42 pages, many colour figures. v2: discussion of the conformal
ambiguity improved, references added. v3: amended to match published versio
Anisotropic singularities in chiral modified gravity
In four space-time dimensions, there exists a special infinite-parameter
family of chiral modified gravity theories. All these theories describe just
two propagating polarizations of the graviton. General Relativity with an
arbitrary cosmological constant is the only parity-invariant member of this
family. We review how these modified gravity theories arise within the
framework of pure-connection formulation. We introduce a new convenient
parametrisation of this family of theories by using certain set of auxiliary
fields. Modifications of General Relativity can be arranged so as to become
important in regions with large Weyl curvature, while the behaviour is
indistinguishable from GR where Weyl curvature is small. We show how the Kasner
singularity of General Relativity is resolved in a particular class of modified
gravity theories of this type, leading to solutions in which the fundamental
connection field is regular all through the space-time. There arises a new
asymptotically De Sitter region `behind' the would-be singularity, the complete
solution thus being of a bounce type.Comment: v2: published version, 42 pages, 4 figure
On a partially reduced phase space quantisation of general relativity conformally coupled to a scalar field
The purpose of this paper is twofold: On the one hand, after a thorough
review of the matter free case, we supplement the derivations in our companion
paper on 'loop quantum gravity without the Hamiltonian constraint' with
calculational details and extend the results to standard model matter, a
cosmological constant, and non-compact spatial slices. On the other hand, we
provide a discussion on the role of observables, focussed on the situation of a
symmetry exchange, which is key to our derivation. Furthermore, we comment on
the relation of our model to reduced phase space quantisations based on
deparametrisation.Comment: 51 pages, 5 figures. v2: Gauge condition used shown to coincide with
CMC gauge. Minor clarifications and correction