Rotation in relativity and the propagation of light
E. Kajari, M. Buser, C. Feiler, W. P. Schleich
备注：
102 pages, 35 figures, The original publication is available at http://www.sif.it/SIF/en/portal/journals.html, to appear in "Atom Optics and Space Physics", Proceedings of the International School of Physics "Enrico Fermi", Course CLXVIII, edited by E. Arimondo, W. Ertmer, E. M. Rasel and W. P. Schleich, (IOS Press, Amsterdam) 2009
发表信息：
Proceedings of the International School of Physics "Enrico Fermi", Course CLXVIII, pp. 45-148 (2009)
We compare and contrast the different points of view of rotation in general relativity, put forward by Mach, Thirring and Lense, and Goedel. Our analysis relies on two tools: (i) the Sagnac effect which allows us to measure rotations of a coordinate system or induced by the curvature of spacetime, and (ii) computer visualizations which bring out the alien features of the Goedel Universe. In order to keep the paper self-contained, we summarize in several appendices crucial ingredients of the mathematical tools used in general relativity. In this way, our lecture notes should be accessible to researchers familiar with the basic elements of tensor calculus and general relativity.
BiGONLight, Bi-local Geodesic Operators framework for Numerical Light propagation, is a new tool for light propagation in Numerical Relativity. The package implements the Bi-local Geodesic Operators formalism, a new framework for light propagation in General Relativity. With BiGONLight it is possible to extract observables such as angular diameter distance, luminosity distance, magnification as well as new real-time observables like parallax and redshift drift within the same computation. As test-bed for our code we consider two cosmological models, the $Λ$CDM and the inhomogeneous Szekeres mo…
Any modification on gravity would affect not only gravitational wave (GW) generation but also GW propagation. Therefore, tests of general relativity (GR) with only GW generation or GW propagation will lead to an overestimate for deviations. Here we try to use one set of parameters to parameterize the modifications on both GW generation and GW propagation and then test GR with GW150914. In our simplest case, we find that graviton mass $μ<6.3\times10^{-23}{\rm eV/c^2}$ at $90\%$ C.L. and there are no deviations from GR at $90\%$ C.L..
The goal of this work was to investigate the propagation of the constraints in the ghost-free bimetric theory where the evolution equations are in standard 3+1 form. It is established that the constraints evolve according to a first-order symmetric hyperbolic system whose characteristic cone consists of the null cones of the two metrics. Consequently, the constraint evolution equations are well-posed, and the constraints stably propagate.
Owing to the existence of an invariant length at the Planck scale, Einstein special relativity breaks down at that scale. A possible solution to this problem is arguably to replace the Poincaré invariant Einstein special relativity by a de Sitter invariant special relativity. In addition to reconciling Lorentz symmetry with the existence of an invariant length, such replacement produces concomitant changes in all relativistic theories, including general relativity, which becomes what we have called 'de Sitter modified general relativity'. In this paper, the Newtonian limit of this theory is us…
Dynamics of spining particles in a homogeneous space with rotation as possible mechanism of the inertial mass formation and interpretation of quantum uncertainty principle in general relativity
Differential Forms and Wave Equations for General Relativity
最近，Choquet-Bruhat and York and Abrahams，Anderson，Choquet-Bruhat，and York（AACY）将广义相对论的3+1演化方程转换为规范协变和因果的“一阶对称双曲形式”，从而在广义相对论的柯西问题中将物理自由度和规范自由度清晰地分离开来。在它们的构造中，一个关键的成分是一个特定的波动方程，它控制着非本征曲率张量的光速传播。沿着类似的思路，我们构造了一个相关的波动方程，作为系统中描述真空广义相对论的关键方程。而AACY的方法是基于张量指数的方法，目前的配方是写在唯一的语言的微分形式。我们的方法从Sparling的四元依赖微分形式开始，我们的波动方程控制着Sparling的2-形式的传播，在“时间规范”中，它是从“非本征曲率1-形式”线性建立的。我们的波动方程的张量指数版本描述了（本质上是）阿诺特-德瑟-米斯纳引力动量的传播。
We investigate propagation of gravitational waves in the most general teleparallel gravity model with second order field equations around the Minkowski background. We argue that in this case the most general Lagrangian at the first order of perturbations is given by the linear combination of quadratic invariants and hence coincides with the well-known new general relativity model. We derive the linearized field equations and analyze them using the principal polynomial and the Newman-Penrose formalism. We demonstrate that all gravitational wave modes propagate at the speed of light and there ar…
A very general class of axially-symmetric metrics in general relativity (GR) that includes rotations is used to discuss the dynamics of rotationally-supported galaxies. The exact vacuum solutions of the Einstein equations for this extended Weyl class of metrics allow us to deduce rigorously the following: (i) GR rotational velocity always exceeds the Newtonian velocity (thanks to Lenz's law in GR); (ii) A non-vanishing intrinsic angular momentum ($J$) for a galaxy demands the asymptotic constancy of the Weyl (vectorial) length parameter ($a$) -a behavior identical to that found for the Kerr me…
S-stars in the Galactic Center are excellent testbeds of various general relativistic effects. While previous works focus on modeling their orbital motion around Sgr A*--the supermassive black hole in the Galactic Center--here we explore the possibility of using the rotation of S-stars to test the de Sitter precession predicted by general relativity. We show that by reorienting the rotation axes of S-stars, de Sitter precession will change the apparent width of the absorption lines in the stellar spectra. Our numerical simulations suggest that the newly discovered S4714 and S62 are best suited…
We study the cosmological propagation of gravitational waves (GWs) beyond general relativity (GR) across homogeneous and isotropic backgrounds. We consider scenarios in which GWs interact with an additional tensor field and use a parametrized phenomenological approach that generically describes their coupled equations of motion. We analyze four distinct classes of derivative and non-derivative interactions: mass, friction, velocity, and chiral. We apply the WKB formalism to account for the cosmological evolution and obtain analytical solutions to these equations. We corroborate these results b…
Measuring in a single location on Earth its angular rotation rate with respect to the celestial frame, with a sensitivity enabling access to the tiny Lense-Thirring effect is an extremely challenging task. GINGERINO is a large frame ring laser gyroscope, operating free running and unattended inside the underground laboratory of the Gran Sasso, Italy. The main geodetic signals, i.e., Annual and Chandler wobbles, daily polar motion and Length of the Day, are recovered from GINGERINO data using standard linear regression methods, demonstrating a sensitivity better than 1 prad/s, therefore close t…
Recently, it has been suggested that the phenomenology of flat rotation curves observed at large radii in the equatorial plane of disk galaxies can be explained as a manifestation of General Relativity instead of the effect of Dark Matter halos. In this paper, by using the well known weak field, low velocity gravitomagnetic formulation of GR, the expected rotation curves in GR are rigorously obtained for purely baryonic disk models with realistic density profiles, and compared with the predictions of newtonian gravity for the same disks in absence of Dark Matter. As expected, the resulting rot…
Alternative theories of gravity predict modifications in the propagation of gravitational waves (GW) through space-time. One of the smoking-gun predictions of such theories is the change in the GW luminosity distance to GW sources as a function of redshift relative to the electromagnetic (EM) luminosity distance expected from EM probes. We propose a multi-messenger test of the theory of general relativity from the propagation of gravitational waves by combining EM and GW observations to resolve these issues from GW sources without EM counterparts (which are also referred to as dark standard si…
We analyse the influence of Earth's rotation (both around its own axis and around the Sun) on the propagation of light in optical media. This is done using both geometrical optics and a perturbative calculation based on Maxwell's equations in rotating coordinates in flat spacetime. Considering light propagation in cylindrical step-index waveguides in particular, the first order correction to electromagnetic modes is computed. The calculation shows that Earth's rotation causes a weak mode coupling, giving rise to sidebands, whose amplitudes are computed as well. The correction to the dispersion…
Explicit form of the Scalar-Tensor metric to be used for propagation of light in the Solar system in continuity of the GR IAU2000 metric
IAU 2000决议推荐的度规允许在广义相对论框架中的c-3水平上计算光的传播。在最近的一篇论文[1]中，受到即将进行的涉及太阳系中光传播的空间实验（ASTROD，GAIA，LATOR，ODYSSEY，SAGAS，SIM，TIPO，...）的启发，我们提出了在c-4水平上对IAU度规方程的一种扩展。这是在广义相对论的框架下进行的。然而，标量-张量理论可能会引起数值上与c-4广义相对论项相当的修正。因此，本文提出了将[1]推广到标量张量情形。一个强层次系统（如太阳系）的情况下强调。在这种情况下，提出了一个明确的度量解决方案。
In the paraxial regime of Newtonian optics, propagation of an ensemble of rays is represented by a symplectic ABCD transfer matrix defined on a reduced phase space. Here, we present its analogue for general relativity. Starting from simultaneously applied null geodesic actions for two curves, we obtain a geodesic deviation action up to quadratic order. We achieve this by following a preexisting method constructed via Synge's world function. We find the corresponding Hamiltonian function and the reduced phase space coordinates that are composed of the components of the Jacobi fields projected o…
In the canonical model of a pulsar, rotational energy is transmitted through the surrounding plasma via two electrical circuits, each connecting to the star over a small region known as a "polar cap." For a dipole-magnetized star, the polar caps coincide with the magnetic poles (hence the name), but in general, they can occur at any place and take any shape. In light of their crucial importance to most models of pulsar emission (from radio to X-ray to wind), we develop a general technique for determining polar cap properties. We consider a perfectly conducting star surrounded by a force-free m…
In this work we study the properties of rigidly rotating neutral dust solutions in general relativity. This class of solutions gained relevance recently due to applications to the dynamics of spiral galaxies. We show that this class could be interpreted as a rigid body in general relativity and we analyze the different properties respect to the rigidly rotating disk in special relativity: for example, the general relativistic counterpart shows no Doppler effect for a light signal emitted and received from any two points at rest respect to the rigid body. This effect can be important to test th…
Rapidly and differentially rotating compact stars are believed to be formed in binary neutron star merger events, according to both numerical simulations and the multi-messenger observation of GW170817. The lifetime and evolution of such a differentially rotating star, is tightly related to the observations in the post-merger phase. Various studies on the maximum mass of differentially rotating neutron stars have been done in the past, most of which assume the so-called $j$-const law as the rotation profile inside the star and consider only neutron star equations of state. In this paper, we ex…
Stellar rotation of S301 as a macroscopic gyroscope to test general relativity
Universitat Politècnica de València（瓦伦西亚理工大学）；Max Planck Institute for Extraterrestrial Physics（马克斯·普朗克地外物理研究所）；Kavli Institute for Astronomy and Astrophysics at Peking University（北京大学 Kavli 天体物理学与天文研究所）；Astronomy Department, School of Physics, Peking University（北京大学物理学院天文学系）；Beijing Institute of Mathematical Sciences and Applications（北京应用数学与物理研究所）；University of California, Berkeley（加州大学伯克利分校）；Technical University of Munich（慕尼黑工业大学）
The investigation of relativistic effects in the most general way requires a unified treatment of light propagation in cosmology. This goal can be achieved with the new interpretation of the geodesic deviation equation in terms of the bilocal geodesic operators (BGO). The BGO formalism extends the standard formulation, providing a unified framework to describe all possible optical phenomena due to the interaction between light and spacetime curvature. In my dissertation, I present {\tt BiGONLight}, a {\tt Mathematica} package that applies the BGO formalism to study light propagation in numeric…
