A detailed analysis of the BF formulation for general relativity given by Capovilla, Montesinos, Prieto, and Rojas is performed. The action principle of this formulation is written in an equivalent form by doing a transformation of the fields of which the action depends functionally on. The transformed action principle involves two BF terms and the two Lorentz invariants that appear in the original action principle generically. As an application of this formalism, the action principle used by Engle, Pereira, and Rovelli in their spin foam model for gravity is recovered and the coupling of the cosmological constant in such a formulation is obtained.
This paper investigates the implications from area quantization in Loop Quantum Gravity, particularly focusing on the application of the Landauer principle -- a fundamental thermodynamic concept establishing a connection between information theory and thermodynamics. By leveraging the Landauer principle in conjunction with the Bekenstein-Hawking entropy law, we derive the usual value for the Immirzi parameter precisely, $γ= \ln2/(π\sqrt{3})$, without using the typical procedure that involves the Boltzmann-Gibbs entropy. Furthermore, following an analogous procedure, we derive a modified expres…
The action principle of the BF type introduced by Capovilla, Montesinos, Prieto, and Rojas (CMPR) which describes general relativity with Immirzi parameter is modified in order to allow the inclusion of the cosmological constant. The resulting action principle is on the same footing as the original Plebanski action in the sense that the equations of motion coming from the new action principle are equivalent to the Holst action principle plus a cosmological constant without the need of imposing additional restrictions on the fields. We consider this result a relevant step towards the coupling o…
Conformal loop quantum gravity provides an approach to loop quantization through an underlying conformal structure i.e. conformally equivalent class of metrics. The property that general relativity itself has no conformal invariance is reinstated with a constrained scalar field setting the physical scale. Conformally equivalent metrics have recently been shown to be amenable to loop quantization including matter coupling. It has been suggested that conformal geometry may provide an extended symmetry to allow a reformulated Immirzi parameter necessary for loop quantization to behave like an arb…
We embed the Loop Quantum Gravity Barbero-Immirzi parameter and field within an action describing 4D, $\cal N$ = 1 supergravity and thus within a Low Energy Effective Action of Superstring/M-Theory. We use the fully gauge-covariant description of supergravity in (curved) superspace. The gravitational constant is replaced with the vacuum expectation value of a scalar field, which in local supersymmetry is promoted to a complex, covariantly chiral scalar superfield. The imaginary part of this superfield couples to a supersymmetric Holst term. The Holst term also serves as a starting point in the…
Working in the first order formalism of gravity, we propose an action that combines the self and anti-self-dual parts of the curvature and comprises all the diffeomorphism invariant Lagrangians that one can consider in this formalism. The action that we propose is motivated by (A)dS gauge theories of gravity. We use this action to derive the (2+1)-dimensional version of the Immirzi parameter. Our derivation relates explicitly the Immirzi parameter to the existence of two classically equivalent actions for the description of gravity in (2+1) dimensions, namely the standard and exotic actions in…
We consider cosmological solution for Einstein gravity with massive fermions with a four-fermion coupling, which emerges from the Holst action and is related to the Barbero-Immirzi (BI) parameter. This gravitational action is an important object of investigation in a non-perturbative formalism of quantum gravity. We study the equation of motion for for the Dirac field within the standard Friedman-Robertson-Walker (FRW) metric. Finally, we show the theory with BI parameter and minimally coupling Dirac field, in the zero mass limit, is equivalent to an additional term which looks like a perfect …
We consider a loop-quantum gravity inspired modification of general relativity, where the Holst action is generalized by making the Barbero-Immirzi (BI) parameter a scalar field, whose value could be dynamically determined. The modified theory leads to a non-zero torsion tensor that corrects the field equations through quadratic first-derivatives of the BI field. Such a correction is equivalent to general relativity in the presence of a scalar field with non-trivial kinetic energy. This stress-energy of this field is automatically covariantly conserved by its own dynamical equations of motion,…
One of the virtues of the Ashtekar variables is the simplification of the initial value constraints for gravity. In the case of self-dual variables this entails a complexification of the phase space which comes at the expense of having to implement reality conditions in the Lorentzian signature case. A reformulation of the theory in terms of real variables eliminates this difficulty, albeit at the expense of having to deal with a more complicated Hamiltonian constraint. The set of available gravitational theories classically equivalent to Einstein's is parametrized by a parameter $β$, known as…
{\it If} the total number of punctures($N$) of a quantum isolated horizon is considered to be a macroscopic parameter alongside the Chern-Simons level($k$) or equivalently classical area$(A_{cl})$ a strict analysis of the {\it microcanonical} ensemble reveals that the {\it microcanonical} entropy has the form $S_{MC}=A_{cl}/4\ell_p^2+Nσ(γ)$, only for values of the Barbero-Immirzi(BI) parameter$(γ)$ greater than a certain number. It is argued that the term $Nσ(γ)$ must be negative definite, which leads to the bound on the BI parameter.
The Immirzi ambiguity arises in loop quantum gravity when geometric operators are represented in terms of different connections that are related by means of an extended Wick transform. We analyze the action of this transform in gravity coupled with matter fields and discuss its analogy with the Wick rotation on which the Thiemann transform between Euclidean and Lorentzian gravity is based. In addition, we prove that the effect of this extended Wick transform is equivalent to a constant scale transformation as far as the symplectic structure and kinematical constraints are concerned. This equiv…
We discuss the issue of parity violation in quantum gravity. In particular, we study the coupling of fermionic degrees of freedom in the presence of torsion and the physical meaning of the Immirzi parameter from the viewpoint of effective field theory. We derive the low-energy effective lagrangian which turns out to involve two parameters, one measuring the non-minimal coupling of fermions in the presence of torsion, the other being the Immirzi parameter. In the case of non-minimal coupling the effective lagrangian contains an axial-vector interaction leading to parity violation. Alternatively…
We carry out the complete variational analysis of the Barbero--Immirzi--Holst Lagrangian, which is the Holst Lagrangian expressed in terms of the triad of fields $(θ, A, κ)$, where $θ$ is the solder form/spin frame, $A$ is the spacetime Barbero--Immirzi connection, and $κ$ is the extrinsic spacetime field. The Holst Lagrangian depends on the choice of a real, non zero Holst parameter $γ\neq 0$ and constitutes the classical field theory which is then quantized in Loop Quantum Gravity. The choice of a real Immirzi parameter $β$ sets up a one-to-one correspondence between pairs $(A, κ)$ and spin …
We revisit a propagating torsion gravity theory obtained by introducing a field coupled to the Holst term in the first-order Einstein-Cartan action. The resulting theory has second order field equations, no adjustable coupling constants, and one more propagating degree of freedom as compared to general relativity. When no fermions are present the theory is known to be equivalent to that of a single massless scalar field canonically coupled to gravity. We extend this result to the case with fermions and obtain an effective interaction between the scalar field and the fermionic currents. We also…
It was showed by Perez and Rovelli in 2006 that the Holst action in gravity with torsion with massless and minimally coupling Dirac fermions gives rise to the four-fermion coupling term, whose coefficient is a function of the Barbero-Immirzi (BI) parameter. This parameter is present in the Holst action, which is an object of investigation in a non-perturbative formalism of quantum gravity. The key feature is the torsion because its absence implies no effect from Holst term in dynamical equations. In this paper we consider a spin fluid (also called Weyssenhoff fluid), which is a perfect fluid t…
We give a unified description of all recent spin foam models introduced by Engle, Livine, Pereira and Rovelli (ELPR) and by Freidel and Krasnov (FK). We show that the FK models are, for all values of the Immirzi parameter, equivalent to path integrals of a discrete theory and we provide an explicit formula for the associated actions. We discuss the relation between the FK and ELPR models and also study the corresponding boundary states. For general Immirzi parameter, these are given by Alexandrov's and Livine's SO(4) projected states. For 0 <= gamma < 1, the states can be restricted to SU(2) s…
We consider the background-independent quantization of a general scale-invariant theory of gravity with matter, which supports a conserved Weyl current recently suggested as a natural flow of time. For scalar-metric systems, a conformal class of Ashtekar-Barbero connection variables is constructed, which can be quantized using spin networks. Crucially, the quantum states become separable into the eigen states of the generator of the scale transformation and spin-network states in the Einstein frame. The eigen values consist of additional quantum numbers including a new type of fundamental freq…
The "Universality Theorem" for gravity shows that f(R) theories (in their metric-affine formulation) in vacuum are dynamically equivalent to vacuum Einstein equations with suitable cosmological constants. This holds true for a generic (i.e. except sporadic degenerate cases) analytic function f(R) and standard gravity without cosmological constant is reproduced if f is the identity function (i.e. f(R)=R). The theorem is here extended introducing in dimension 4 a 1-parameter family of invariants R' inspired by the Barbero-Immirzi formulation of GR (which in the Euclidean sector includes also sel…
We study a parity violating Metric-Affine gravitational theory given by the Einstein-Hilbert action plus the so-called Holst term in vacuum. We find out that for a certain value of the Barbero-Immirzi parameter the total action possesses a remarkable invariance under particular transformations of the affine connection. We prove that in all cases, with appropriate gauge choices, the connection reduces to the Levi-Civita one and that the theory turns out to be equivalent to general relativity in vacuum. Subsequently, we generalize our discussion and analyze the case of Metric-Affine $f(R)$ gravi…
We investigate the canonical aspects of the algebraic first order formulation of strings introduced two decades ago by Balachandran and collaborators. We slightly enlarge the Lagrangian framework and show the existence of a self-dual formulation and of an Immirzi-type parameter reminiscent of four-dimensional first order gravity. We perform a full Hamiltonian analysis of the self-dual case: we extract the first class constraints and construct the Dirac bracket associated to the second class constraints. The first class constraints contain the diffeomorphisms algebra on the world-sheet, and the…
Spaniol and Andrade introduced grvitoelectromagnetism in TEGR by considering superpotentials, times the determinant of tetrads, as the gravitoelectromagnetic fields. However, since this defined gravitoelectromagnetic field strength does not give rise to a complete set of Maxwell-like equations, we propose an alternative definition of the gravitoelectromagnetic field strength: instead of superpotentials, torsions are taken as the gravitoelectromagnetic field strengths. Based on this new proposal we are able to derive a complete set of Maxwell-like equations. We then apply them to obtain explici…
A review of the teleparallel equivalent of general relativity is presented. It is emphasized that general relativity may be formulated in terms of the tetrad fields and of the torsion tensor, and that this geometrical formulation leads to alternative insights into the theory. The equivalence with the standard formulation in terms of the metric and curvature tensors takes place at the level of field equations. The review starts with a brief account of the history of teleparallel theories of gravity. Then the ordinary interpretation of the tetrad fields as reference frames adapted to arbitrary o…
The equations for gravitational plane waves produced by a typical binary system as a solution of linear approximation of Einstein equations is derived. The dynamics of the corresponding gravitational field is analyzed in a 4-dimensional space-time manifold, endowed with a metric and taking into account the torsion. In this context, the geometrical reason of the existence of torsion due to the presence of gravitational waves, as an asymmetry of connection coefficients with respect of the swapping of indices's is highlighted. In a laser interferometer gravitational detector The delay time betwee…
Feynman's sum-over-histories formulation of quantum mechanics is reviewed as an independent statement of quantum theory in spacetime form. It is different from the usual Schrödinger-Heisenberg formulation that utilizes states on spacelike surfaces because it assigns probabilities to different sets of alternatives. Sum-over-histories quantum mechanics can be generalized to deal with spacetime alternatives that are not "at definite moments of time". An example in field theory is the set of alternative ranges of values of a field averaged over a spacetime region. An example in particle mechanics …
A variational principle was recently suggested by Goenner, where an independent metric generates the spacetime connection. It is pointed out here that the resulting theory is equivalent to the usual Palatini theory. However, a bimetric reformulation of the variational principle leads to theories which are physically distinct from both the metric and the metric-affine ones, even for the Einstein-Hilbert action. They are obtained at a decoupling limit of C-theories, which contain also other viable generalizations of the Palatini theories.
It has been shown recently that within the framework of the teleparallel equivalent of general relativity (TEGR) it is possible to define the energy density of the gravitational field. The TEGR amounts to an alternative formulation of Einstein's general relativity, not to an alternative gravity theory. The localizability of the gravitational energy has been investigated in a number of space-times with distinct topologies, and the outcome of these analises agree with previously known results regarding the exact expression of the gravitational energy, and/or with the specific properties of the s…
A modified Newton's gravity is obtained as the weak field approximation of the Einstein's equation in Finsler space. It is found that a specified Finsler structure makes the modified Newton's gravity equivalent to the modified Newtonian dynamics (MOND). In the framework of Finsler geometry, the flat rotation curves of spiral galaxies can be deduced naturally without invoking dark matter.
We develop an alternative Ashtekar formalism in eight dimensions. In fact, using a MacDowell-Mansouri physical framework and a self-dual curvature symmetry we propose an action in eight dimensions in which the Levi-Civita tenor with eight indices plays a key role. We explicitly show that such an action contains number of linear, quadratic and cubic terms in the Riemann tensor, Ricci tensor and scalar curvature. In particular, the linear term is reduced to the Einstein-Hilbert action with cosmological constant in eight dimensions. We prove that such a reduced action is equivalent to the Loveloc…
In the frameworks of the effective field theory of metric supplemented by some distinct dynamical coordinates parametrized, in turn, by a scalar quartet -- the so-called quartet-metric gravity -- the extension of tensor gravity through a massive scalar graviton in addition to the massless tensor one is consistently exposed. The field equations for the two realizations of such an extension originating from the classically equivalent prototype theories - General Relativity (GR) and its Weyl transverse (WTDiff) alternative - are derived and argued to be, generally, non-equivalent, with the pure-g…
The general covariance principle, seen as an active version of the principle of equivalence, is used to study the gravitational coupling prescription in the presence of curvature and torsion. It is concluded that the coupling prescription determined by this principle is always equivalent with the corresponding prescription of general relativity. An application to the case of a Dirac spinor is made.
We study new Legendre transforms in classical mechanics and investigate some of their general properties. The behaviour of the new functions is analyzed under coordinate transformations.When invariance under different kinds of transformations are considered, the new formulation is found to be completly equivalent to the usual Lagrangian formulation, recovering well established results like the conservation of the angular momentum. Furthermore, a natural generalization of the Poisson Bracket is found to be inherent to the formalism introduced. On the other hand, we find that with a convenient r…
Motivated by the study of physical models associated with General Relativity, we review some finite-dimensional, geometric and covariant formulations that allow us to characterize in a simple manner the symmetries for classical field theory by implementing an appropriate fibre-bundle structure, either at the Lagrangian, the multisymplectic or the polysymplectic levels. In particular, we are able to formulate Noether's theorems by means of the covariant momentum maps and to systematically introduce a covariant Poisson-Hamiltonian framework. Also, by focusing on the space plus time decomposition…
In this note we propose the use of an alternate action for the open string tachyon on a non-BPS $D3$-brane. At the classical level this action is precisely equivalent to the more commonly used DBI action, but involves an additional coupling to dynamical world-volume gravity. We find that, for a FRW metric, exponential expansion occurs provided that the cosmological constant is positive. For anti de-Sitter solutions we find a periodically bouncing universe, and there are no accelerating trajectories for a theory with no cosmological constant. In specific cases the acceleration is terminated by …
We propose a new approach to test possible corrections to Newtonian gravity using solar physics. The high accuracy of current solar models and new precise observations allow one to constrain corrections to standard gravity at unprecedented levels. Our case study is Eddington-inspired gravity, an attractive modified theory of gravity which results in non-singular cosmology and collapse. The theory is equivalent to standard gravity in vacuum, but it sensibly differs from it within matter, for instance it affects the evolution and the equilibrium structure of the Sun, giving different core temper…
