Extremal Black Holes in Dynamical Chern-Simons Gravity

Rapidly rotating black hole solutions in theories beyond general relativity play a key role in experimental gravity, as they allow us to compute observables in extreme spacetimes that deviate from the predictions of general relativity. Such solutions are often difficult to find in beyond-general-relativity theories due to the inclusion of additional fields that couple to the metric non-linearly and non-minimally. In this paper, we consider rotating black hole solutions in one such theory, dynamical Chern-Simons gravity, where the Einstein-Hilbert action is modified by the introduction of a dynamical scalar field that couples to the metric through the Pontryagin density. We treat dynamical Chern-Simons gravity as an effective field theory and work in the decoupling limit, where corrections are treated as small perturbations from general relativity. We perturb about the maximally-rotating Kerr solution, the so-called extremal limit, and develop mathematical insight into the analysis techniques needed to construct solutions for generic spin. First we find closed-form, analytic expressions for the extremal scalar field, and then determine the trace of the metric perturbation, giving both in terms of Legendre decompositions. Retaining only the first three and four modes in the Legendre representation of the scalar field and the trace, respectively, suffices to ensure a fidelity of over 99% relative to full numerical solutions. The leading-order mode in the Legendre expansion of the trace of the metric perturbation contains a logarithmic divergence at the extremal Kerr horizon, which is likely to be unimportant as it occurs inside the perturbed dynamical Chern-Simons horizon. The techniques employed here should enable the construction of analytic, closed-form expressions for the scalar field and metric perturbations on a background with arbitrary rotation.Comment: 25+9 pages (single column), 10 figures, 1 table; matches published versio

The Barbero-Immirzi Parameter as a Scalar Field: K-Inflation from Loop Quantum Gravity?

We consider a loop-quantum gravity inspired modification of general relativity, where the Holst action is generalized by making the Barbero-Immirzi (BI) parameter a scalar field, whose value could be dynamically determined. The modified theory leads to a non-zero torsion tensor that corrects the field equations through quadratic first-derivatives of the BI field. Such a correction is equivalent to general relativity in the presence of a scalar field with non-trivial kinetic energy. This stress-energy of this field is automatically covariantly conserved by its own dynamical equations of motion, thus satisfying the strong equivalence principle. Every general relativistic solution remains a solution to the modified theory for any constant value of the BI field. For arbitrary time-varying BI fields, a study of cosmological solutions reduces the scalar field stress-energy to that of a pressureless perfect fluid in a comoving reference frame, forcing the scale factor dynamics to be equivalent to those of a stiff equation of state. Upon ultraviolet completion, this model could provide a natural mechanism for k-inflation, where the role of the inflaton is played by the BI field and inflation is driven by its non-trivial kinetic energy instead of a potential.Comment: Phys. Rev. D78, 064070 (2008

Computing Jacobi Forms

We describe an implementation for computing holomorphic and skew-holomorphic Jacobi forms of integral weight and scalar index on the full modular group. This implementation is based on formulas derived by one of the authors which express Jacobi forms in terms of modular symbols of elliptic modular forms. Since this method allows to generate a Jacobi eigenform directly from a given modular eigensymbol without reference to the whole ambient space of Jacobi forms it makes it possible to compute Jacobi Hecke eigenforms of large index. We illustrate our method with several examples.Comment: 14 pages, 5 tables, Cython implementation of algorithm included. Revised version. To appear in the LMS Journal of Computation and Mathematic

The role of intermediaries in the synchronization of pulse-coupled oscillators

The role of intermediaries in the synchronization of small groups of light controlled oscillators (LCO) is addressed. A single LCO is a two-time-scale phase oscillator. When pulse-coupling two LCOs, the synchronization time decreases monotonously as the coupling strength increases, independent of the initial conditions and frequency detuning. In this work we study numerically the effects that a third LCO induces to the collective behavior of the system. We analyze the new system by dealing with directed heterogeneous couplings among the units. We report a novel and robust phenomenon, absent when coupling two LCOs, which consists of a discontinuous relationship between the synchronization time and coupling strength or initial conditions. The mechanism responsible for the appearance of such discontinuities is discussed.Comment: 11 pages, 8 figure

Many-body effects in magnetic inelastic electron tunneling spectroscopy

Magnetic inelastic electron tunneling spectroscopy (IETS) shows sharp increases in conductance when a new conductance channel associated to a change in magnetic structure is open. Typically, the magnetic moment carried by an adsorbate can be changed by collision with a tunneling electron; in this process the spin of the electron can flip or not. A previous one-electron theory [Phys. Rev. Lett. {\bf 103}, 176601 (2009)] successfully explained both the conductance thresholds and the magnitude of the conductance variation. The elastic spin flip of conduction electrons by a magnetic impurity leads to the well known Kondo effect. In the present work, we compare the theoretical predictions for inelastic magnetic tunneling obtained with a one-electron approach and with a many-body theory including Kondo-like phenomena. We apply our theories to a singlet-triplet transition model system that contains most of the characteristics revealed in magnetic IETS. We use two self-consistent treatments (non-crossing approximation and self-consistent ladder approximation). We show that, although the one-electron limit is properly recovered, new intrinsic many-body features appear. In particular, sharp peaks appear close to the inelastic thresholds; these are not localized exactly at thresholds and could influence the determination of magnetic structures from IETS experiments.Analysis of the evolution with temperature reveals that these many-body features involve an energy scale different from that of the usual Kondo peaks. Indeed, the many-body features perdure at temperatures much larger than the one given by the Kondo energy scale of the system.Comment: 10 pages and 6 figure

Non-perturbative renormalization group for the Kardar-Parisi-Zhang equation

We present a simple approximation of the non-perturbative renormalization group designed for the Kardar-Parisi-Zhang equation and show that it yields the correct phase diagram, including the strong-coupling phase with reasonable scaling exponent values in physical dimensions. We find indications of a possible qualitative change of behavior around $d=4$. We discuss how our approach can be systematically improved.Comment: 4 pages, 1 figure, references added, minor change

Approximate black hole binary spacetime via asymptotic matching

We construct a fully analytic, general relativistic, nonspinning black hole binary spacetime that approximately solves the vacuum Einstein equations everywhere in space and time for black holes sufficiently well separated. The metric is constructed by asymptotically matching perturbed Schwarzschild metrics near each black hole to a two-body post-Newtonian metric far from them, and a two-body post-Minkowskian metric farther still. Asymptotic matching is done without linearizing about a particular time slice, and thus it is valid dynamically and for all times, provided the binary is sufficiently well separated. This approximate global metric can be used for long dynamical evolutions of relativistic magnetohydrodynamical, circumbinary disks around inspiraling supermassive black holes to study a variety of phenomena.Comment: 17 pages, 8 figures, 1 table. Appendix added to match published versio

Constraining Lorentz-violating, Modified Dispersion Relations with Gravitational Waves

Modified gravity theories generically predict a violation of Lorentz invariance, which may lead to a modified dispersion relation for propagating modes of gravitational waves. We construct a parametrized dispersion relation that can reproduce a range of known Lorentz-violating predictions and investigate their impact on the propagation of gravitational waves. A modified dispersion relation forces different wavelengths of the gravitational wave train to travel at slightly different velocities, leading to a modified phase evolution observed at a gravitational-wave detector. We show how such corrections map to the waveform observable and to the parametrized post-Einsteinian framework, proposed to model a range of deviations from General Relativity. Given a gravitational-wave detection, the lack of evidence for such corrections could then be used to place a constraint on Lorentz violation. The constraints we obtain are tightest for dispersion relations that scale with small power of the graviton's momentum and deteriorate for a steeper scaling.Comment: 11 pages, 3 figures, 2 tables: title changed slightly, published versio

Constraining the evolutionary history of Newton's constant with gravitational wave observations

Space-borne gravitational wave detectors, such as the proposed Laser Interferometer Space Antenna, are expected to observe black hole coalescences to high redshift and with large signal-to-noise ratios, rendering their gravitational waves ideal probes of fundamental physics. The promotion of Newton's constant to a time-function introduces modifications to the binary's binding energy and the gravitational wave luminosity, leading to corrections in the chirping frequency. Such corrections propagate into the response function and, given a gravitational wave observation, they allow for constraints on the first time-derivative of Newton's constant at the time of merger. We find that space-borne detectors could indeed place interesting constraints on this quantity as a function of sky position and redshift, providing a {\emph{constraint map}} over the entire range of redshifts where binary black hole mergers are expected to occur. A LISA observation of an equal-mass inspiral event with total redshifted mass of 10^5 solar masses for three years should be able to measure $\dot{G}/G$ at the time of merger to better than 10^(-11)/yr.Comment: 11 pages, 2 figures, replaced with version accepted for publication in Phys. Rev. D