25,922 research outputs found
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 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 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 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
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