On the Energy-Momentum Density of Gravitational Plane Waves

By embedding Einstein's original formulation of GR into a broader context we show that a dynamic covariant description of gravitational stress-energy emerges naturally from a variational principle. A tensor $T^G$ is constructed from a contraction of the Bel tensor with a symmetric covariant second degree tensor field $\Phi$ and has a form analogous to the stress-energy tensor of the Maxwell field in an arbitrary space-time. For plane-fronted gravitational waves helicity-2 polarised (graviton) states can be identified carrying non-zero energy and momentum.Comment: 10 pages, no figure

Quantum phase shift and neutrino oscillations in a stationary, weak gravitational field

A new method based on Synge's world function is developed for determining within the WKB approximation the gravitationally induced quantum phase shift of a particle propagating in a stationary spacetime. This method avoids any calculation of geodesics. A detailed treatment is given for relativistic particles within the weak field, linear approximation of any metric theory. The method is applied to the calculation of the oscillation terms governing the interference of neutrinos considered as a superposition of two eigenstates having different masses. It is shown that the neutrino oscillations are not sensitive to the gravitomagnetic components of the metric as long as the spin contributions can be ignored. Explicit calculations are performed when the source of the field is a spherical, homogeneous body. A comparison is made with previous results obtained in Schwarzschild spacetime.Comment: 14 pages, no figure. Enlarged version; added references. In the Schwarzschild case, our results on the non-radial propagation are compared with the previous work

Direction of light propagation to order G^2 in static, spherically symmetric spacetimes: a new derivation

A procedure avoiding any integration of the null geodesic equations is used to derive the direction of light propagation in a three-parameter family of static, spherically symmetric spacetimes within the post-post-Minkowskian approximation. Quasi-Cartesian isotropic coordinates adapted to the symmetries of spacetime are systematically used. It is found that the expression of the angle formed by two light rays as measured by a static observer staying at a given point is remarkably simple in these coordinates. The attention is mainly focused on the null geodesic paths that we call the "quasi-Minkowskian light rays". The vector-like functions characterizing the direction of propagation of such light rays at their points of emission and reception are firstly obtained in the generic case where these points are both located at a finite distance from the centre of symmetry. The direction of propagation of the quasi-Minkowskian light rays emitted at infinity is then straightforwardly deduced. An intrinsic definition of the gravitational deflection angle relative to a static observer located at a finite distance is proposed for these rays. The expression inferred from this definition extends the formula currently used in VLBI astrometry up to the second order in the gravitational constant G.Comment: 19 pages; revised introduction; added references for introduction; corrected typos; published in Class. Quantum Gra

Non-metric chaotic inflation

We consider inflation within the context of what is arguably the simplest non-metric extension of Einstein gravity. There non-metricity is described by a single graviscalar field with a non-minimal kinetic coupling to the inflaton field $\Psi$, parameterized by a single parameter $\gamma$. We discuss the implications of non-metricity for chaotic inflation and find that it significantly alters the inflaton dynamics for field values $\Psi \gtrsim M_P/\gamma$, dramatically changing the qualitative behaviour in this regime. For potentials with a positive slope non-metricity imposes an upper bound on the possible number of e-folds. For chaotic inflation with a monomial potential, the spectral index and the tensor-to-scalar ratio receive small corrections dependent on the non-metricity parameter. We also argue that significant post-inflationary non-metricity may be generated.Comment: 7 pages, 1 figur

Secular evolution of eccentricity in protoplanetary discs with gap-opening planets

We explore the evolution of the eccentricity of an accretion disc perturbed by an embedded planet whose mass is sufficient to open a large gap in the disc. Various methods for representing the orbit-averaged motion of an eccentric disc are discussed. We characterize the linear instability that leads to the growth of eccentricity by means of hydrodynamical simulations. We numerically recover the known result that eccentricity growth in the disc is possible when the planet-to-star mass ratio exceeds 3 × 10$^{−3}$. For mass ratios larger than this threshold, the precession rates and growth rates derived from simulations, as well as the shape of the eccentric mode, compare well with the predictions of a linear theory of eccentric discs. We study mechanisms by which the eccentricity growth eventually saturates into a non-linear regime.We acknowledge support from STFC through grant ST/L000636/1

Note on Varying Speed of Light Cosmologies

The various requirements on a consistent varying speed of light (`VSL') theory are surveyed, giving a short check-list of issues that should be satisfactorily handled by such theories.Comment: 6 pages; to appear in the GRG Journa

Eccentricity evolution during planet-disc interaction

During the process of planet formation, the planet-disc interactions might excite (or damp) the orbital eccentricity of the planet. In this paper, we present two long (t ~ 3 × 10 5 orbits) numerical simulations: (a) one (with a relatively light disc, M d /M p = 0.2), where the eccentricity initially stalls before growing at later times and (b) one (with a more massive disc, M d /M p = 0.65) with fast growth and a late decrease of the eccentricity. We recover the well-known result that a more massive disc promotes a faster initial growth of the planet eccentricity. However, at late times the planet eccentricity decreases in the massive disc case, but increases in the light disc case. Both simulations show periodic eccentricity oscillations superimposed on a growing/decreasing trend and a rapid transition between fast and slow pericentre precession. The peculiar and contrasting evolution of the eccentricity of both planet and disc in the two simulations can be understood by invoking a simple toy model where the disc is treated as a second point-like gravitating body, subject to secular planet-planet interaction and eccentricity pumping/damping provided by the disc. We show how the counterintuitive result that the more massive simulation produces a lower planet eccentricity at late times can be understood in terms of the different ratios of the disc-to-planet angular momentum in the two simulations. In our interpretation, at late times the planet eccentricity can increase more in low-mass discs rather than in high-mass discs, contrary to previous claims in the literature.This work has been supported by the DISCSIM project, grant agreement 341137 funded by the European Research Council under ERC-2013-ADG. JT acknowledges support from STFC through grant ST/L000636/1. This work used the Wilkes GPU cluster at the University of Cambridge High Performance Computing Service (http://www.hpc.cam.ac.uk/), provided by Dell Inc., NVIDIA and Mellanox, and part funded by STFC with industrial sponsorship from Rolls Royce and Mitsubishi Heavy Industries. We also thank the MIAPP for hosting us for the ‘Protoplanetary Disks and Planet Formation and Evolution’ topical workshop held in Munich during June 2017. All the figures were generated with the python-based package matplotlib (Hunter 2007)

The origin of the eccentricity of the hot Jupiter in CI Tau

Following the recent discovery of the first radial velocity planet in a star still possessing a protoplanetary disc (CI Tau), we examine the origin of the planet's eccentricity (e $\sim 0.3$). We show through long timescale ($10^5$ orbits) simulations that the planetary eccentricity can be pumped by the disc, even when its local surface density is well below the threshold previously derived from short timescale integrations. We show that the disc may be able to excite the planet's orbital eccentricity in $<$ a Myr for the system parameters of CI Tau. We also perform two planet scattering experiments and show that alternatively the observed planet may plausibly have acquired its eccentricity through dynamical scattering of a migrating lower mass planet, which has either been ejected from the system or swallowed by the central star. In the latter case the present location and eccentricity of the observed planet can be recovered if it was previously stalled within the disc's magnetospheric cavity.This work has been supported by the DISCSIM project, grant agreement 341137 funded by the European Research Council under ERC-2013-ADG, and from STFC through grant ST/L000636/1. This work used the DIRAC Shared Memory Processing and Data Analytic systems, both at the University of Cambridge and operated, respectively, by the COSMOS Project at the Department of Applied Mathematics and Theoretical Physics and the Cambridge High Performance Computing Service, on behalf of the STFC DiRAC HPC Facility (www.dirac.ac.uk). This equipment was funded by BIS National E-infrastructure capital grants ST/J005673/1 and ST/K001590/1, STFC capital grants ST/H008586/1, ST/H008861/1 and ST/H00887X/1, STFC DiRAC Operations grant ST/K00333X/1, and STFC DiRAC Operations grant ST/K00333X/1. DiRAC is part of the National E-Infrastructure.This is the final version of the article. It first appeared from Oxford University Press via https://doi.org/10.1093/mnrasl/slw18

Time-Varying Gravitomagnetism

Time-varying gravitomagnetic fields are considered within the linear post-Newtonian approach to general relativity. A simple model is developed in which the gravitomagnetic field of a localized mass-energy current varies linearly with time. The implications of this temporal variation of the source for the precession of test gyroscopes and the motion of null rays are briefly discussed.Comment: 10 pages; v2: slightly expanded version accepted for publication in Class. Quantum Gra