Surface singularities in Eddington-inspired Born-Infeld gravity

Eddington-inspired Born-Infeld gravity was recently proposed as an alternative to general relativity that offers a resolution of spacetime singularities. The theory differs from Einstein's gravity only inside matter due to nondynamical degrees of freedom, and it is compatible with all current observations. We show that the theory is reminiscent of Palatini f(R) gravity and that it shares the same pathologies, such as curvature singularities at the surface of polytropic stars and unacceptable Newtonian limit. This casts serious doubts on its viability.Comment: 5 pages. v2: minor corrections to match published versio

Plane curves with small linear orbits I

The `linear orbit' of a plane curve of degree d is its orbit in the projective space of dimension d(d+3)/2 parametrizing such curves under the natural action of PGL(3). In this paper we compute the degree of the closure of the linear orbits of most curves with positive dimensional stabilizers. Our tool is a nonsingular variety dominating the orbit closure, which we construct by a blow-up sequence mirroring the sequence yielding an embedded resolution of the curve. The results given here will serve as an ingredient in the computation of the analogous information for arbitrary plane curves. Linear orbits of smooth plane curves are studied in [A-F1].Comment: 34 pages, 4 figures, AmS-TeX 2.1, requires xy-pic and eps

Unstable Modes and Confinement in the Lattice Schr\"odinger Functional Approach

We analyze the problem of the Nielsen-Olesen unstable modes in the SU(2) lattice gauge theory by means of a recently introduced gauge-invariant effective action. We perform numerical simulations in the case of a constant Abelian chromomagnetic field. We find that for lattice sizes above a certain critical length the density of effective action shows a behaviour compatible with the presence of the unstable modes. We put out a possible relation between the dynamics of the unstable modes and the confinement.Comment: 15 pages, LaTeX2e file, 5 figure

Bures metric over thermal state manifolds and quantum criticality

We analyze the Bures metric over the manifold of thermal density matrices for systems featuring a zero temperature quantum phase transition. We show that the quantum critical region can be characterized in terms of the temperature scaling behavior of the metric tensor itself. Furthermore, the analysis of the metric tensor when both temperature and an external field are varied, allows to complement the understanding of the phase diagram including cross-over regions which are not characterized by any singular behavior. These results provide a further extension of the scope of the metric approach to quantum criticality.Comment: 9 pages, 4 figures, LaTeX problems fixed, references adde

Gravity with Auxiliary Fields

Modifications of General Relativity usually include extra dynamical degrees of freedom, which to date remain undetected. Here we explore the possibility of modifying Einstein's theory by adding solely nondynamical fields. With the minimal requirement that the theory satisfies the weak equivalence principle and admits a covariant Lagrangian formulation, we show that the field equations generically have to include higher-order derivatives of the matter fields. This has profound consequences for the viability of these theories. We develop a parametrization based on a derivative expansion and show that - to next to leading order - all theories are described by just two parameters. Our approach can be used to put stringent, theory-independent constraints on such theories, as we demonstrates using the Newtonian limit as an example.Comment: 5 pages, no figures; v2: clarifications and minor improvements, matches published versio

Sub-ohmic two-level system representation of the Kondo effect

It has been recently shown that the particle-hole symmetric Anderson impurity model can be mapped onto a $Z_2$ slave-spin theory without any need of additional constraints. Here we prove by means of Numerical Renormalization Group that the slave-spin behaves in this model like a two-level system coupled to a sub-ohmic dissipative environment. It follows that the $Z_2$ symmetry gets spontaneously broken at zero temperature, which we find can be identified with the on-set of Kondo coherence, being the Kondo temperature proportional to the square of the order parameter. Since the model is numerically solvable, the results are very enlightening on the role of quantum fluctuations beyond mean field in the context of slave-boson approaches to correlated electron models, an issue that has been attracting interest since the 80's. Finally, our results suggest as a by-product that the paramagnetic metal phase of the Hubbard model at half-filling, in infinite coordination lattices and at zero temperature, as described for instance by Dynamical Mean Field Theory, corresponds to a slave-spin theory with a spontaneous breakdown of a local $Z_2$ gauge symmetry.Comment: 4 pages, 5 figure

Matter around Kerr black holes in scalar-tensor theories: scalarization and superradiant instability

In electrovacuum stationary, asymptotically flat black holes in scalar-tensor theories of gravity are described by the Kerr-Newman family of solutions, just as in general relativity. We show that there exist two mechanisms which can render Kerr black holes unstable when matter is present in the vicinity of the black hole, as this induces an effective mass for the scalar. The first mechanism is a tachyonic instability that appears when the effective mass squared is negative, triggering the development of scalar hair --- a black hole version of "spontaneous scalarization". The second instability is associated with superradiance and is present when the effective mass squared is positive and when the black hole spin exceeds a certain threshold. The second mechanism is also responsible for a resonant effect in the superradiant scattering of scalar waves, with amplification factors as large as 10^5 or more.Comment: 11 pages, 3 figures. v2: published versio