14983134
Spin foam diagrammatics and topological invariance
We provide a simple proof of the topological invariance of the Turaev–Viro model (corresponding to simplicial 3D pure Euclidean gravity with cosmological constant) by means of a novel diagrammatic formulation of the state sum models for quantum BF theories. Moreover, we prove the invariance under more general conditions allowing the state sum to be defined on arbitrary cellular decompositions of the underlying manifold. Invariance is governed by a set of identities corresponding to local gluing and rearrangement of cells in the complex. Due to the fully algebraic nature of these identities our results extend to a vast class of quantum groups. The techniques introduced here could be relevant for investigating the scaling properties of non-topological state sums, proposed as models of quantum gravity in 4D, under refinement of the cellular decomposition.
15415939
Perturbations with angular momentum of Robinson-Trautman spacetimes
We study the possible asymptotically flat perturbations of Robinson-Trautman spacetimes. We differentiate between algebraically special perturbations and general perturbations. The equations that determine physically realistic spacetimes with angular momentum are presented.
732756
On the quantum origin of the seeds of cosmic structure
The current understanding of the quantum origin of cosmic structure is discussed critically. We point out that in the existing treatments a transition from a symmetric quantum state to an (essentially classical) non-symmetric state is implicitly assumed, but not specified or analysed in any detail. In facing this issue, we are led to conclude that new physics is required to explain the apparent predictive power of the usual schemes. Furthermore, we show that the novel way of looking at the relevant issues opens new windows from where relevant information might be extracted regarding cosmological issues and perhaps even clues about aspects of quantum gravity.
9066120
Introduction to loop quantum gravity and spin foams
These notes are a didactic overview of the non perturbative and background independent approach to a quantum theory of gravity known as loop quantum gravity. The definition of real connection variables for general relativity, used as a starting point in the program, is described in a simple manner. The main ideas leading to the definition of the quantum theory are naturally introduced and the basic mathematics involved is described. The main predictions of the theory such as the discovery of Planck scale discreteness of geometry and the computation of black hole entropy are reviewed. The quantization and solution of the constraints is explained by drawing analogies with simpler systems. Difficulties associated with the quantization of the scalar constraint are discussed.In a second part of the notes, the basic ideas behind the spin foam approach are presented in detail for the simple solvable case of 2+1 gravity. Some results and ideas for four dimensional spin foams are reviewed.
18617564
Iterative approach to gravitational lensing theory
We develop an iterative approach to gravitational lensing theory based on approximate solutions of the null geodesic equations. The approach can be employed in any space-time which is ``close'' to a space-time in which the null geodesic equations can be completely integrated, such as Minkowski space-time, Robertson-Walker cosmologies, or Schwarzschild-Kerr geometries. To illustrate the method, we construct the iterative gravitational lens equations and time of arrival equation for a single Schwarzschild lens. This example motivates a discussion of the relationship between the iterative approach, the standard thin lens formulation, and an exact formulation of gravitational lensing.
208165775
The spin-foam-representation of LQG
The problem of background independent quantum gravity is the problem of defining a quantum field theory of matter and gravity in the absence of an underlying background geometry. Loop quantum gravity (LQG) is a promising proposal for addressing this difficult task. Despite the steady progress of the field, dynamics remains to a large extend an open issue in LQG. Here we present the main ideas behind a series of proposals for addressing the issue of dynamics. We refer to these constructions as the spin foam representation of LQG. This set of ideas can be viewed as a systematic attempt at the construction of the path integral representation of LQG. The spin foam representation is mathematically precise in 2+1 dimensions, so we will start this chapter by showing how it arises in the canonical quantization of this simple theory. This toy model will be used to precisely describe the true geometric meaning of the histories that are summed over in the path integral of generally covariant theories. In four dimensions similar structures appear. We call these constructions spin foam models as their definition is incomplete in the sence that at least one of the following issues remains unclear: 1) the connection to a canonical formulation, and 2) regularization independence (renormalizability). In the second part of this chapter we will describe the definition of these models emphasizing the importance of these open issues.
16895941
Relativistic direct Urca processes in cooling neutron stars
Abstract We derive a relativistic expression for neutrino energy losses caused by the direct Urca processes in degenerate baryon matter of neutron stars. We use two different ways to calculate the emissivity caused by the reactions to our interest. First we perform a standard calculation by Fermi's “golden” rule. The second calculation, resulting in the same expression, is performed with the aid of polarization functions of the medium. Our result for neutrino energy losses strongly differs from previous nonrelativistic results. We also discuss nonconservation of the baryon vector current in reactions through weak charged currents in the medium, when the asymmetry between protons and neutrons is considered. The above effects, not discussed in the literature before, substantially modify the polarization functions responsible for the induced weak charged currents in baryon matter.
122905847
Topological gravity from a transgression gauge field theory
Abstract It is shown that a topological action for gravity in even dimensions can be obtained from a gravity theory whose Lagrangian is given by a transgression form invariant under the Poincare group. The field ϕ a , which is necessary to construct this type of topological gravity in even dimensions, is identified with the coset field associated with the non-linear realizations of the Poincare group ISO ( d − 1 , 1 ) .
14359365
Random phase approximation to neutrino energy losses from a relativistic electron-positron plasma
The process of $\nu \bar{\nu}$ radiation from a relativistic plasma of electrons and positrons is studied within the Random Phase Approximation.
14718218
Nucleon–nucleon effective potential in dense matter including rho-meson exchange
Abstract We obtain the RPA summed one-meson exchange potential between nucleons in symmetric nuclear matter at zero temperature, from a model which includes ρ , σ , ω and π mesons. The behavior of rho mesons inside the medium is first discussed using different schemes to extract a finite contribution from the vacuum polarization. These schemes give qualitatively different results for the in-medium rho mass. The results are discussed in connection with the nonrenormalizability of the model. We next study the modified potential as density increases. In the intermediate-distance range, it is qualitatively modified by matter and vacuum effects. In the long-distance range ( r >2 fm), one observes the presence of oscillations, which are not present in free space. Features on this distance range are insensitive to the renormalization scheme.
124142447
Higher Spin Black Holes
We review some relevant results in the context of higher spin black holes in three-dimensional spacetimes, focusing on their asymptotic behaviour and thermodynamic properties. For simplicity, we mainly discuss the case of gravity nonminimally coupled to spin-three fields, being nonperturbatively described by a Chern–Simons theory of two independent \(\mathit{sl}\left (3, \mathbb{R}\right )\) gauge fields. Since the analysis is particularly transparent in the Hamiltonian formalism, we provide a concise discussion of their basic aspects in this context; and as a warming up exercise, we briefly analyze the asymptotic behaviour of pure gravity, as well as the BTZ black hole and its thermodynamics, exclusively in terms of gauge fields. The discussion is then extended to the case of black holes endowed with higher spin fields, briefly signaling the agreements and discrepancies found through different approaches. We conclude explaining how the puzzles become resolved once the fall off of the fields is precisely specified and extended to include chemical potentials, in a way that it is compatible with the asymptotic symmetries. Hence, the global charges become completely identified in an unambiguous way, so that different sets of asymptotic conditions turn out to contain inequivalent classes of black hole solutions being characterized by a different set of global charges.