Session X15: Relativistic Gravitation Theory

Orbital-plane precessional resonances for binary black-hole systems

We derive a new class of post-Newtonian precessional resonances for binary black holes (BBHs) with misaligned spins. According to the orbit-averaged spin-precession equations, the angle between the orbital angular momentum $\mathbf{L}$ and the total angular momentum $\mathbf{J}$ oscillates with a period $\tau$ during which time $\mathbf{L}$ precesses about $\mathbf{J}$ by an angle $\alpha$. If $\alpha$ is a rational multiple of 2$\pi$, the precession of $\mathbf{L}$ will be closed indicating a resonance between the polar and azimuthal evolution of $\mathbf{L}$. If $\alpha$ is an integer multiple of 2$\pi$, the misalignment between the angular momentum $\Delta\mathbf{L}$ radiated over the period $\tau$ and $\mathbf{J}$ will be minimized, as will the opening angle of the cone about which $\mathbf{J}$ precesses in an inertial frame. However, the direction of $\Delta\mathbf{L}$ will remain nearly fixed in an inertial frame over many precessional periods, causing the direction of $\mathbf{J}$ to tilt as inspiraling BBHs pass through such a resonance. Generic BBHs encounter many such resonances during an inspiral from large separations. We derive the evolution of $\mathbf{J}$ near a resonance and assess their detectability by gravitational-wave detectors and astrophysical implications.   

Four-hair relations for differentially rotating neutron stars in the weak-field limit

The opportunity to study physics at supra-nuclear densities through x-ray observations of neutron stars has led to in-depth investigations of certain approximately universal relations that can remove degeneracies in pulse profile models. One such set of relations, the three-hair relations, were found to hold in neutron stars that rotate rigidly, but neutron stars can also rotate differentially, as is the case for proto-neutron stars and hypermassive transient remnants of binary mergers. We extend the three-hair relations to differentially rotating stars for the first time with a generic rotation law using two approximations: a weak-field scheme (an expansion in powers of the neutron star compactness) and a perturbative differential rotation scheme (an expansion about rigid rotation). The resulting relations include the fourth moment, hence deemed the four-hair relations for differentially rotating neutron stars, and are found to be approximately independent of the equation of state to a higher degree than the three-hair relations for uniformly rotating stars. Our results can be instrumental in the development of four-hair relations for rapidly differentially rotating stars in full general relativity using numerical simulations.   

Testing Gravity Using Pulsar Scintillation Measurements

We propose to use pulsar scintillation measurements to test predictions of alternative theories of gravity. Comparing to single-path pulsar timing measurements, the scintillation measurements can achieve a factor of $10^4 \sim 10^5 $ improvement in timing accuracy, due to the effect of multi-path interference. The self-noise from pulsar also does not affect the interference pattern, where the data acquisition timescale is $10^3$ seconds instead of years. Therefore it has unique advantages in measuring gravitational effect or other mechanisms (at mHz and above frequencies) on light propagation. We illustrate its application in constraining scalar gravitational-wave background and measuring gravitational-wave speed, in which cases the sensitivities are greatly improved with respect to previous limits. We expect much broader applications in testing gravity with existing and future pulsar scintillation observations.   

Self-forces on static bodies in arbitrary dimensions

I will present exact expressions for the scalar and electromagnetic self-forces and self-torques acting on arbitrary static extended bodies in arbitrary static spacetimes with any number of dimensions. Non-perturbatively, these results are identical in all dimensions. Meaningful point particle limits are quite different, however. I will discuss how such limits are defined and evaluated, resulting in simple ``regularization algorithms'' which can be used in concrete calculations. In them, self-interaction is shown to be progressively less important in higher numbers of dimensions, generically competing in magnitude with increasingly high-order extended-body effects. Conversely, self-interaction effects can be relatively large in $1+1$ and $2+1$ dimensions. It will further be shown that there is considerable freedom to use different ``effective fields'' in the laws of motion. Different choices give rise to different inertias, gravitational forces, and electromagnetic or scalar self-forces. However, the particular combinations of these quantities which are observable remain invariant under all possible field redefinitions.   

The Cauchy horizon singularity inside Kerr black holes

The numerical technology that allows for the careful evolution of linearized fields inside Kerr black holes and the study of their behavior approaching the Cauchy horizon singularity includes a number of interesting aspects. The latter include compactified hyperboloidal coordinates and foliation, mixed type hyperbolic-elliptic PDE, and initial data evolution where all equal-coordinate hypersurfaces are spacelike. We review the need for the numerical technology that allows for the solution of the spin-2 Teukolsky equation inside Kerr black holes, and discuss the main features thereof. We present new results about the numerical properties of the Cauchy horizon singularity and their correspondence with the predictions of perturbative analysis. We then discuss present directions of study, which include the sub-dominant azimuthal modes, approaching the Cauchy horizon singularity along timelike directions, approaching the Marolf-Ori (``outflying'') singularity and the studying the fields along the Cauchy horizon.   

Gravitomagnetic acceleration of accretion disk matter to polar jets

The motion of the masses of an accretion disk around a black hole creates a general relativistic, gravitomagnetic field (GEM) from the moving matter (be it charged or uncharged) of the accretion disk. This GEM field accelerates moving masses (neutral or charged) near the accretion disk vertically upward and away from the disk, and then inward toward the axis of the disk. As the accelerated material nears the axis with approximately vertical angles, a frame dragging effect contributes to the formation of narrow jets emanating from the poles. This GEM effect is numerically evaluated in the first post Newtonian (1PN) approximation from observable quantities like the mass and velocity of the disk. This GEM force is linear in the total mass of the accretion disk matter and quadratic in the velocity of matter near to the disk with approximately the same velocity. Since these masses and velocities can be quite high in astrophysical contexts, the GEM force, which in other contexts is weak, is quite significant. This GEM effect is compared to the ordinary electromagnetic effects applied to this problem in the past..   

Dynamics In A Maximally Symmetric Universe

Our present understanding of the evolution of the universe relies upon the Friedmann- Robertson- Walker cosmological models. This model is so successful that it is now being considered as the Standard Model of Cosmology. So in this work we derive the Fried- mann equations using the Friedmann-Robertson-Walker metric together with Einstein field equation and then we give a simple method to reduce Friedmann equations to a second order linear differential equation when it is supplemented with a time dependent equation of state. Furthermore, as illustrative examples, we solve this equation for some specific time dependent equation of states. And also by using the Friedmann equations with some time dependent equation of state we try to determine the cosmic scale factor(the rate at which the universe expands) and age of the Friedmann universe, for the matter dominated era, radiation dominated era and for both matter and radiation dominated era by considering different cases. We have finally discussed the observable quantities that can be evidences for the accelerated expansion of the Friedmann universe.   

An Introduction to Gravitational Frenetics I: The Nature and Physical Significance of the Frenetic Field

After providing a very short review of Classical gravito-magnetism I will present a novel framework for the development and extension of the Classical theory of gravity. Specifically, I will first discuss the proposed, Lorentz-like force experienced by a moving mass in the presence of a rotating gravitational source, and then I will provide a first principles definition of the proposed \emph{Frenetic Field}. Of note this field has units of frequency and so provides for straight-forward comparison with previous Classical results. i.e., The Lens-Thirring Effect. I then continue with a discussion of a general gauge constraint of the Frenetic field in terms of a velocity field which depends upon both the mass and rotational velocity \emph{of} and the distance \emph{to} the source. This framework allows for direct comparison with Relativistic predictions where I find (minimally) first-order agreement for the refraction of light by a rotating gravitational source, and provide for a robust description of the temporal character of these "lenses" in terms of an absolute time parameter. I will conclude by extending the theoretical framework to the case of many sources and discuss implications for the evolution of accretion disks due to possible gravito-frenetic wave phenomena.   

Kinematically Accelerated Repulsions Due to Relative Motion between Mass Particles in an Accelerating Universe

An accelerated expansion of the universe, due only to relative particle motion, is described here in the form of a particular model that illustrates its physical cause. A simplified three particle universe is considered here by defining coordinate positions for effective mass-points because their size is extremely small compared to the distances between them. The three particles initially form a static isosceles triangular configuration. The third particle at the triangle's apex could only then determine its position relative to the triangle by measuring the apex angle subtended by the base particles. If the two base particles then exert for an instant a force between only themselves, they will move away from each other while the third particle could physically maintain its position relative to the universe only by referring to these other two existing particles. It would then be required that the apex particle would accelerate outwards and away from the base particles in order to regain the smaller size of the original apex angle and subsequently generate a Hubble expansion for the particles.