Alternative symplectic structures for SO(3,1) and SO(4) four-dimensional BF theories

The most general action, quadratic in the B fields as well as in the curvature F, having SO(3,1) or SO(4) as the internal gauge group for a four-dimensional BF theory is presented and its symplectic geometry is displayed. It is shown that the space of solutions to the equations of motion for the BF theory can be endowed with symplectic structures alternative to the usual one. The analysis also includes topological terms and cosmological constant. The implications of this fact for gravity are briefly discussed.Comment: 13 pages, LaTeX file, no figure

Feedback-limited Accretion: Luminous Signatures from Growing Planets

Planets form in discs of gas and dust around stars, and keep growing by accretion of disc material while available. Massive planets clear a gap in that protoplanetary disc, but still accrete through spiral wakes. On its way to the planet, the gas will settle on a \emph{circumplanetary} disc around the planet and slowly accrete on to it. The energy of the accreted gas will be released, heating the planet surroundings in a feedback process. For high enough accretion rates the planet should be detectable at infrared wavelengths. We aim to find whether detectable planet luminosities, $\gtrsim 10^{-3} \, \textrm{L}_\odot$, can occur when considering that the planet luminosity is coupled to the accretion, and also to study which other effects has the feedback on the dynamics of the circumplanetary and the gap regions. We model a planet with mass ratio $q=10^{-3}$, orbiting at 10 AU from a solar mass star, using a modified version of the 2D code FARGO-AD, which includes a prescription for the accretion and feedback luminosity of the planet. We find that the planetary feedback is able to partially deplete the circumplanetary disc, and to reduce the accretion rate onto the planet. However, detectable luminosities of $L_\textrm{p}\gtrsim 10^{-3}\, \textrm{L}_\odot$ are still produced. The feedback also contributes to partially refilling the gap, to heat up the coorbital region, and to perturb the orbital velocity of the gas.Comment: Submitted to MNRA

Lorentzian homogeneous spaces admitting a homogeneous structure of type T1+T3

We show that a Lorentzian homogeneous space admitting a homogeneous structure of type T1 + T3 is either a (locally) symmetric space or a singular homogeneous plane wave.Comment: 7 pages, Latex2e, a small note and a reference adde

A topological limit of gravity admitting an SU(2) connection formulation

We study the Hamiltonian formulation of the generally covariant theory defined by the Lagrangian 4-form L=e_I e_J F^{IJ}(\omega) where e^I is a tetrad field and F^{IJ} is the curvature of a Lorentz connection \omega^{IJ}. This theory can be thought of as the limit of the Holst action for gravity for the Newton constant G goes to infinity and Immirzi parameter goes to zero, while keeping their product fixed. This theory has for a long time been conjectured to be topological. We prove this statement both in the covariant phase space formulation as well as in the standard Dirac formulation. In the time gauge, the unconstrained phase space of theory admits an SU(2) connection formulation which makes it isomorphic to the unconstrained phase space of gravity in terms of Ashtekar-Barbero variables. Among possible physical applications, we argue that the quantization of this topological theory might shed new light on the nature of the degrees of freedom that are responsible for black entropy in loop quantum gravity.Comment: Appendix added where moldels leading to boundary degrees of freedom are constructed. This version will appear in PRD

Lorentz-covariant Hamiltonian analysis of BF gravity with the Immirzi parameter

We perform the Lorentz-covariant Hamiltonian analysis of two Lagrangian action principles that describe general relativity as a constrained BF theory and that include the Immirzi parameter. The relation between these two Lagrangian actions has been already studied through a map among the fields involved. The main difference between these is the way the Immirzi parameter is included, since in one of them the Immirzi parameter is included explicitly in the BF terms, whereas in the other (the CMPR action) it is in the constraint on the B fields. In this work we continue the analysis of their relationship but at the Hamiltonian level. Particularly, we are interested in seeing how the above difference appears in the constraint structure of both action principles. We find that they both possess the same number of first-class and second-class constraints and satisfy a very similar (off-shell) Poisson-bracket algebra on account of the type of canonical variables employed. The two algebras can be transformed into each other by making a suitable change of variablesComment: LaTeX file, no figure

Quantum mechanics without spacetime II : noncommutative geometry and the free point particle

In a recent paper we have suggested that a formulation of quantum mechanics should exist, which does not require the concept of time, and that the appropriate mathematical language for such a formulation is noncommutative differential geometry. In the present paper we discuss this formulation for the free point particle, by introducing a commutation relation for a set of noncommuting coordinates. The sought for background independent quantum mechanics is derived from this commutation relation for the coordinates. We propose that the basic equations are invariant under automorphisms which map one set of coordinates to another- this is a natural generalization of diffeomorphism invariance when one makes a transition to noncommutative geometry. The background independent description becomes equivalent to standard quantum mechanics if a spacetime manifold exists, because of the proposed automorphism invariance. The suggested basic equations also give a quantum gravitational description of the free particle.Comment: 8 page