Alfredo Macias

The Search for quantum gravity signals

We give an overview of ongoing searches for effects motivated by the study of the quantum‐gravity problem. We describe in greater detail approaches which have not been covered in recent “Quantum Gravity Phenomenology” reviews. In particular, we outline a new framework for describing Lorentz invariance violation in the Maxwell sector. We also discuss the general strategy on the experimental side as well as on the theoretical side for a search for quantum gravity effects. The role of test theories, kinematical and dymamical, in this general context is emphasized. The present status of controlled laboratory experiments is described, and we also summarize some key results obtained on the basis of astrophysical observations.

The Cotton tensor in Riemannian spacetimes

Recently, the study of three-dimensional spaces is becoming of great interest. In these dimensions the Cotton tensor is prominent as the substitute for the Weyl tensor. It is conformally invariant and its vanishing is equivalent to conformal flatness. However, the Cotton tensor arises in the context of the Bianchi identities and is present in any dimension n. We present a systematic derivation of the Cotton tensor. We perform its irreducible decomposition and determine its number of independent components as n(n2 − 4)/3 for the first time. Subsequently, we show its characteristic properties and perform a classification of the Cotton tensor in three dimensions. We investigate some solutions of Einsteins field equations in three dimensions and of the topologically massive gravity model of Deser, Jackiw and Templeton. For each class examples are given. Finally, we investigate the relation between the Cotton tensor and the energy–momentum in Einsteins theory and derive a conformally flat perfect fluid solution of Einsteins field equations in three dimensions.

Metric affine gauge theory of gravity. 2. Exact solutions

In continuing our series on metric–affine gravity (see Gronwald, Int. J. Mod. Phys.D6, 263 (1997) for Part I), we review the exact solutions of this theory.

Lorentz invariance violation and charge (non)conservation: A general theoretical frame for extensions of the Maxwell equations

All quantum gravity approaches lead to small modifications in the standard laws of physics which in most cases lead to violations of Lorentz invariance. One particular example is the extended standard model (SME). Here, a general phenomenological approach for extensions of the Maxwell equations is presented which turns out to be more general than the SME and which covers charge nonconservation (CNC), too. The new Lorentz invariance violating terms cannot be probed by optical experiments but need, instead, the exploration of the electromagnetic field created by a point charge or a magnetic dipole. Some scalar tensor theories and higher dimensional brane theories predict CNC in four dimensions and some models violating special relativity have been shown to be connected with CNC. Its relation to the Einstein Equivalence Principle has been discussed. Because of this upcoming interest, the experimental status of electric charge conservation is reviewed. Up to now there seem to exist no unique tests of charge conservation. CNC is related to the precession of polarization, to a modification of the 1/r-Coulomb potential, and to a time dependence of the fine structure constant. This gives the opportunity to describe a dedicated search for CNC.

Quantum cosmology: the supersymmetric square root

Using N=1 supergravity as the natural square root of gravity, the authors study the quantum cosmology of Bianchi type I cosmological models. This approach gives us a natural interpretation of the components of the state vector of the universe that was lacking in previous work on the square root of quantum cosmology.

On the dimensionality of space–time

Within constructive axiomatics of space–time geometry based on elements of quantum mechanics it can be shown that by means of the study of the dynamical behavior of general matter fields in a geometry‐free way one can give reasons for the dimension of space–time to be four.

Is there a stable hydrogen atom in higher dimensions

The Schrodinger equation in higher dimensions is considered. It consists of the kinetic energy part given by the corresponding Laplace operator, and a term describing the interaction with the electrostatic field of a point charge. From Rutherford-type scattering experiments one can conclude that the potential of a point charge is ∼1/r irrespective of the dimension of the space where the experiment is carried through. Also the structure of the kinetic energy is unchanged in higher dimensions so that one is lead to the result that there exist stable atoms in higher spatial dimensions d⩾4. The solutions and energy eigenvalues to this Schrodinger equation in higher dimensions are presented. As a consequence, the dimensionality of space can be read off from the spectral scheme of atoms: The three-dimensionality of space is a consequence of the existence of the Lyman series. Another consequence is that the Maxwell equations in higher dimensions must be modified in order to have the 1/r-potential as solution for...

Computer algebra in gravity: Reduce-Excalc programs for (non-) Riemannian space-times. I

Computer algebra is applied to general relativity, to electrodynamics, and to gauge theories of gravity. As mathematical formalism we use the calculus of exterior differential forms and as computer algebra system Hearn’s Reduce with Schriifer’s exterior form package Excalc. As a nontrivial example we discuss a metric of Plebaliski & Demianski (of Petrov type D) together with an electromagnetic potential and a rriplet of post-Riemanniun onelforrns. This whole geometrical construct represents an exact solution of a metric-affine gauge theory of gravity. We describe a sample session and verify by computer that this exact solution fulfills the appropriate field equations. - Computer programs are described for the irreducible decomposition of (non-Riemannian) curvature, torsion, and nonmetricity. @ 1998 Elsevier Science B.V.

Motion of test particles in a regular black hole space–time

We consider the motion of test particles in the regular black hole space-time given by Ayon-Beato and Garcia [Phys. Rev. Lett. 80, 5056 (1998)]. The complete set of orbits for neutral and weakly charged test particles is discussed, including for neutral particles the extreme and over-extreme metric. We also derive the analytical solutions for the equation of motion of neutral test particles in a parametric form and consider a post-Schwarzschild expansion of the periastron shift to second order in the charge.

Chiral fermions coupled to chiral gravity

Abstract Using a purely imaginary translational Chern-Simons term as a generating function , a chiral reformulation of gravity a la Ashtekar is achieved. It is a crucial advantage of our Clifford algebra approach that the coupling to the chiral Dirac and the Rarita-Schwinger fields arises from the same translational Chern-Simons term, now evaluated “on shell”.