Gauge Invariant Effective Stress-Energy Tensors for Gravitational Waves

It is shown that if a generalized definition of gauge invariance is used, gauge invariant effective stress-energy tensors for gravitational waves and other gravitational perturbations can be defined in a much larger variety of circumstances than has previously been possible. In particular it is no longer necessary to average the stress-energy tensor over a region of spacetime which is larger in scale than the wavelengths of the waves and it is no longer necessary to restrict attention to high frequency gravitational waves.Comment: 11 pages, RevTe

RKR_K anomalies and simplified limits on Z′Z' models at the LHC

The LHCb collaboration has recently reported a 2.5 $\sigma$ discrepancy with respect to the predicted value in a test of lepton universality in the ratio $R_{K^*}= \hbox{BR}(B \to K^* \mu^+ \mu^-) / \hbox{BR}(B \to K^* e^+ e^-)$. Coupled with an earlier observation of a similar anomaly in $R_{K}$, this has generated significant excitement. A number of new physics scenarios have been proposed to explain the anomaly. In this work we consider simplified limits on $Z'$ models from ATLAS and CMS searches for new resonances in dilepton and dijet modes, and we use the simplified limits variable $\zeta$ to correlate the results of the resonance and B-decay experiments. By examining minimal $Z'$ models that can accomodate the observed LHCb results, we show that the high-mass resonance search results are begining to be sensitive to these models and that future results will be more informative.Comment: 24 pages, 5 figures. Typo corrected, resulting in strengthened limits. Additional references added; minor corrections found in referee process include

Energy density and pressure of long wavelength gravitational waves

Inflation leads us to expect a spectrum of gravitational waves (tensor perturbations) extending to wavelengths much bigger than the present observable horizon. Although these gravity waves are not directly observable, the energy density that they contribute grows in importance during the radiation- and dust-dominated ages of the universe. We show that the back reaction of tensor perturbations during matter domination is limited from above, since gravitational waves of wavelength $\lambda$ have a share of the total energy density $\Delta \rho(\lambda)/\rho$ during matter domination that is at most equal to the share of the total energy density that they had when the mode $\lambda$ exited the Hubble radius $H^{-1}$ during inflation. This work is to be contrasted to that of Sahni, who analyzed the energy density of gravity waves only insofar as their wavelengths are smaller than $H^{-1}$. Such a cut-off in the spectral energy of gravity waves leads to the breakdown of energy conservation, and we show that this anomaly is eliminated simply by taking into account the energy density and pressure of long wavelength gravitational waves as well as short wavelength ones.Comment: Updated one reference; 17 pages, no figure

Gravitational Geons Revisited

A careful analysis of the gravitational geon solution found by Brill and Hartle is made. The gravitational wave expansion they used is shown to be consistent and to result in a gauge invariant wave equation. It also results in a gauge invariant effective stress-energy tensor for the gravitational waves provided that a generalized definition of a gauge transformation is used. To leading order this gauge transformation is the same as the usual one for gravitational waves. It is shown that the geon solution is a self-consistent solution to Einstein's equations and that, to leading order, the equations describing the geometry of the gravitational geon are identical to those derived by Wheeler for the electromagnetic geon. An appendix provides an existence proof for geon solutions to these equations.Comment: 18 pages, ReVTeX. To appear in Physical Review D. Significant changes include more details in the derivations of certain key equations and the addition of an appendix containing a proof of the existence of a geon solution to the equations derived by Wheeler. Also a reference has been added and various minor changes have been mad

Kepler-1656b: a Dense Sub-Saturn With an Extreme Eccentricity

Kepler-1656b is a 5 $R_E$ planet with an orbital period of 32 days initially detected by the prime Kepler mission. We obtained precision radial velocities of Kepler-1656 with Keck/HIRES in order to confirm the planet and to characterize its mass and orbital eccentricity. With a mass of $48 \pm 4 M_E$, Kepler-1656b is more massive than most planets of comparable size. Its high mass implies that a significant fraction, roughly 80%, of the planet's total mass is in high density material such as rock/iron, with the remaining mass in a low density H/He envelope. The planet also has a high eccentricity of $0.84 \pm 0.01$, the largest measured eccentricity for any planet less than 100 $M_E$. The planet's high density and high eccentricity may be the result of one or more scattering and merger events during or after the dispersal of the protoplanetary disk.Comment: 10 pages, 6 figures, published in The Astronomical Journa

Optimal Routing and Control of Multiple Agents Moving in a Transportation Network and Subject to an Arrival Schedule and Separation Constraints

We address the problem of navigating a set of moving agents, e.g. automated guided vehicles, through a transportation network so as to bring each agent to its destination at a specified time. Each pair of agents is required to be separated by a minimal distance, generally agent-dependent, at all times. The speed range, initial position, required destination, and required time of arrival at destination for each agent are assumed provided. The movement of each agent is governed by a controlled differential equation (state equation). The problem consists in choosing for each agent a path and a control strategy so as to meet the constraints and reach the destination at the required time. This problem arises in various fields of transportation, including Air Traffic Management and train coordination, and in robotics. The main contribution of the paper is a model that allows to recast this problem as a decoupled collection of problems in classical optimal control and is easily generalized to the case when inertia cannot be neglected. Some qualitative insight into solution behavior is obtained using the Pontryagin Maximum Principle. Sample numerical solutions are computed using a numerical optimal control solver

The Isaacson expansion in quantum cosmology

This paper is an application of the ideas of the Born-Oppenheimer (or slow/fast) approximation in molecular physics and of the Isaacson (or short-wave) approximation in classical gravity to the canonical quantization of a perturbed minisuperspace model of the kind examined by Halliwell and Hawking. Its aim is the clarification of the role of the semiclassical approximation and the backreaction in such a model. Approximate solutions of the quantum model are constructed which are not semiclassical, and semiclassical solutions in which the quantum perturbations are highly excited.Comment: Revtex, 11 journal or 24 preprint pages. REPLACEMENT: A comment on previous work by Dowker and Laflamme is corrected. Utah preprint UU-REL-93/3/1

Chromospheric Activity of HAT-P-11: an Unusually Active Planet-Hosting K Star

Kepler photometry of the hot Neptune host star HAT-P-11 suggests that its spot latitude distribution is comparable to the Sun's near solar maximum. We search for evidence of an activity cycle in the CaII H & K chromospheric emission $S$-index with archival Keck/HIRES spectra and observations from the echelle spectrograph on the ARC 3.5 m Telescope at APO. The chromospheric emission of HAT-P-11 is consistent with a $\gtrsim 10$ year activity cycle, which plateaued near maximum during the Kepler mission. In the cycle that we observed, the star seemed to spend more time near active maximum than minimum. We compare the $\log R^\prime_{HK}$ normalized chromospheric emission index of HAT-P-11 with other stars. HAT-P-11 has unusually strong chromospheric emission compared to planet-hosting stars of similar effective temperature and rotation period, perhaps due to tides raised by its planet.Comment: 16 pages, 8 figures; accepted to the Astrophysical Journa

Long-Period Giant Companions to Three Compact, Multiplanet Systems

Understanding the relationship between long-period giant planets and multiple smaller short-period planets is critical for formulating a complete picture of planet formation. This work characterizes three such systems. We present Kepler-65, a system with an eccentric (e = 0.28 ± 0.07) giant planet companion discovered via radial velocities (RVs) exterior to a compact, multiply transiting system of sub-Neptune planets. We also use precision RVs to improve mass and radius constraints on two other systems with similar architectures, Kepler-25 and Kepler-68. In Kepler-68 we propose a second exterior giant planet candidate. Finally, we consider the implications of these systems for planet formation models, particularly that the moderate eccentricity in Kepler-65\u27s exterior giant planet did not disrupt its inner system