Rotation of polarization in an external gravitational field is one of the effects of general relativity that can serve as a basis for its precision tests. A careful analysis of reference frames is crucial for a proper evaluation of this effect. We introduce an operationally-motivated local reference frame that allows for a particularly simple description. We present a solution of null geodesics in Kerr space-time that is organized around a new expansion parameter, allowing a better control of the series, and use it to calculate the resulting polarization rotation. While this rotation depends on the reference-frame convention, we demonstrate a gauge-independent geometric phase for closed paths in general space-times.
Quasi-normal modes (QNMs) uniquely characterize the final black-hole. Till now, only the QNM frequency and damping time are used to test General relativity. In this work, we show explicitly that another property of the QNMs --- their polarization --- can be a reliable tool for probing gravity. We provide a consistent test for General relativity by considering Chern-Simons gravity. Distinguishing Chern-Simons gravity from General relativity using only template matching is highly challenging. Thus a parameter that can differentiate between Chern-Simons gravity and GR will be a suitable candidate…
Two polarization modes of gravitational wave are derived from the general relativity which are plus and cross modes. However, the alternative theories of gravity can yield the gravitational wave with up to six polarizations. Searching for the polarizations beyond plus and cross is an important test of general relativity. In principle, one space-borne detector, like LISA, could measure the gravitational wave polarizations from a long time observation with its orbital motion. With the comparable sensitivities, the joint LISA and TAIJI missions will improve the observations on the polarization pr…
General Relativity is a hugely successful description of gravitation. However, both theory and observations suggest that General Relativity might have significant classical and quantum corrections in the Strong Gravity regime. Testing the strong field limit of gravity is one of the main objectives of the future gravitational wave detectors. One way to detect strong gravity is through the polarization of gravitational waves. For quasi-normal modes of black-holes in General Relativity, the two polarisation states of gravitational waves have the same amplitude and frequency spectrum. Using the pr…
We determine the possible gravitational wave polarizations in two general classes of teleparallel gravity theories, using the metric and symmetric teleparallel geometries. For this purpose we apply the Newman-Penrose formalism, and find that depending on the choice of parameters, the $\mathrm{E}(2)$ class of the theories is one of $\mathrm{N}_2, \mathrm{N}_3, \mathrm{III}_5, \mathrm{II}_6$, corresponding to two to six polarizations, where all of them include the two tensor polarizations known from general relativity. We also find classes of theories apart from general relativity which yield th…
Pulsar timing arrays (PTA) have the promise to detect gravitational waves (GWs) from sources which are in a unique frequency range of 10^-9 - 10^-6 Hz. This in turn also provides an opportunity to test the theory of general relativity in the low frequency regime. The central concept of the detection of GWs with PTA lies in measuring the time of arrival difference of the pulsar signal due to the passing of GWs i.e. the pulses get red-shifted. In this paper we provide a complete derivation of the redshift computation for all six possible polarizations of GW which arise due to the modifcations to…
The direct detection of gravitational waves by LIGO/Virgo opened the possibility to test General Relativity and its alternatives in the high speed, strong field regime. Alternative theories of gravity generally predict more polarizations than General Relativity, so it is important to study the polarization contents of theories of gravity to reveal the nature of gravity. In this talk, we analyzed the polarizations contents of Horndeski theory and $f(R)$ gravity. We found out that in addition to the familiar plus and cross polarizations, a \emph{massless} Horndeski theory predicts an extra trans…
The physical foundations for the geometric structure of relativistic theories of gravitation. From General Relativity to Extended Theories of Gravity through Ehlers-Pirani-Schild approach
Geometric description of lightlike foliations by an observer in general relativity
本文从纯几何的角度，在$n$维的时空流形中，引入了类光分布和叶理（维数和余维为1）的新概念和性质。给定一个观察者和一个维数或余维为1的类光分布$Ω$，其类光方向被分解为两个向量场：一个表示观察者的类时向量场$U$和一个表示$Ω$在这个观察者身上传播的相对方向的类空向量场$S$。定义了一个新的分布$Ω_U^-$，对于观察者$U$具有相反的相对传播方向。如果两个分布$Ω$和$Ω_U^-$都是可积的，则对Ω，Ω_U^- $ represents the wave fronts of a stationary wave for the observer $ U $. However, we show in an example that the integrability of $ Ω $ does not imply the integrability of $ Ω_U^-$。
We study disc galaxies in the framework of General Relativity to focus on the possibility that, even in the low energy limit, there are relevant corrections with respect to the purely Newtonian approach. Our analysis encompasses the model both considering a low energy expansion and exact solutions, making it clear the connection between these different approaches. In particular, we focus on two different limits: the well known gravitomagnetic analogy and a new limit, called strong gravitomagnetism, which has corrections in c of the same order as the Newtonian terms. We show that these two limi…
The geometric trinity of gravity offers a platform in which gravity can be formulated in three analogous approaches, namely curvature, torsion and nonmetricity. In this vein, general relativity can be expressed in three dynamically equivalent ways which may offer insights into the different properties of these decompositions such as their Hamiltonian structure, the efficiency of numerical analyses, as well as the classification of gravitational field degrees of freedom. In this work, we take a $3+1$ decomposition of the teleparallel equivalent of general relativity and the symmetric teleparall…
In the general theory of relativity, gravitational waves have two possible polarizations, which are transverse and traceless with helicity $\pm 2$. Some alternatives theories contain additional helicity $0$ and helicity $\pm 1$ polarization modes. Here, we consider a hypothetical "pure vector" theory in which gravitational waves have only two possible polarizations, with helicity $\pm 1$. We show that if these polarizations are allowed to rotate as the wave propagates, then for certain source locations on the sky, the strain outputs of three ideal interferometric gravitational wave detectors c…
Gravitational waves in general relativity contain two polarization degrees of freedom, commonly labeled plus and cross. Besides those two tensor modes, generic theories of gravity predict up to four additional polarization modes: two scalar and two vector. Detection of nontensorial modes in gravitational wave data would constitute a clean signature of physics beyond general relativity. Previous measurements have pointed to the unambiguous presence of tensor modes in gravitational waves, but the presence of additional generic nontensorial modes has not been directly tested. We propose a model-i…
This document contains a description of physics entirely based on a geometric presentation: all of the theory is described giving only a pseudo-riemannian manifold (M, g) of dimension n > 5 for which the g tensor is, in studied domains, almost everywhere of signature (-, -, +, ..., +). No object is added to this space-time, no general principle is supposed. The properties we impose to some domains of (M, g) are only simple geometric constraints, essentially based on the concept of "curvature". These geometric properties allow to define, depending on considered cases, some objects (frequently d…
Gravity theories beyond general relativity (GR) can change the properties of gravitational waves: their polarizations, dispersion, speed, and, importantly, energy content are all heavily theory- dependent. All these corrections can potentially be probed by measuring the stochastic gravitational- wave background. However, most existing treatments of this background beyond GR overlook modifications to the energy carried by gravitational waves, or rely on GR assumptions that are invalid in other theories. This may lead to mistranslation between the observable cross-correlation of detector outputs…
The classifying space of inertial reference frames in special relativity is naturally hyperbolic. There is a remarkable interplay between central elements of hyperbolic geometry and those of special relativity -- which, to a certain extent, have already been observed in the past -- that we present and further discuss in the paper. We aim at a geometrization of special relativity at the level of kinematic space by giving to physical concepts/phenomena purely geometric definitions/descriptions. In this way, the differences between special relativity and classical mechanics can be seen as a manif…
Projective invariance is a symmetry of the Palatini version of General Relativity which is not present in the metric formulation. The fact that the Riemann tensor changes nontrivially under projective transformations implies that, unlike in the usual metric approach, in the Palatini formulation this tensor is subject to a gauge freedom, which allows some ambiguities even in its scalar contractions. In this sense, we show that for the Schwarzschild solution there exists a projective gauge in which the (affine) Kretschmann scalar, $K\equiv {R^α}_{βμν}{R_α}^{βμν}$, can be set to vanish everywhere…
In the present work, a theoretical framework focussing on local geometric deformations is introduced in order to cope with the problem of how to join spacetimes with different geometries and physical properties. Using this framework, it is shown that two Lorentzian manifolds can be matched in agreement with the well-known Darmois-Israel junction conditions by locally deforming the associated spacetime metrics in relation to each other. Based on the insight that metrics can be suitably matched in this way, it is shown that the underlying geometric approach allows the characterization of local s…
Well-posed geometric boundary data in General Relativity, II: twisted Dirichlet boundary data
Institute of Geometry and Physics, University of Science and Technology of China（中国科学技术大学几何与物理研究所）；Department of Mathematics, Stony Brook University（石溪大学数学系）
By using the gravitational decoupling through the minimal geometric deformation approach (MGD-decoupling), we show a simple and powerful method to generate physically acceptable exact analytical solutions for anisotropic stellar distributions in general relativity. We find that some perfect fluid configurations could be incompatible with anisotropic effects produced by scalar fields.
The choice of gauge in numerical relativity is crucial in avoiding coordinate and curvature singularities. In addition, the gauge can affect the well-posedness of the system. In this work, we consider the mean gauges, established with respect to the geometric mean metric $h = g \, (g^{-1}f)^{1/2}$ in bimetric relativity. We consider three gauge conditions widely used in numerical relativity and compute them with respect to the geometric mean: The 1+log gauge condition and the maximal slicing for the lapse function of $h$, and the $Γ$-driver gauge condition for the shift vector of $h$. In addit…
In this paper I give overviews of the polysymplectic approach to covariant Hamiltonian field theory and the simplest geometric quantization of classical particle theories. I then give a synopsis of a recently proposed toy model for applying this geometric quantization map to polysymplectic field theory. I show that no special difficulties arise when this toy model is applied to general relativity. I then sketch the reasons why the standard tools of covariant Hamiltonian field theory are not up to the challenge of GR, so that the resulting quantum theory cannot be taken seriously. A few remarks…
In the present work, the spin-coefficient formalism of Newman and Penrose is used to formulate geometric constraints for the existence of Kerr-Schild groups, i.e. continuous groups of generalized Kerr-Schild transformations. In addition, by characterizing the geometric structure of the deformed Einstein tensor of the generalized Kerr-Schild class, restrictions are imposed on the existence of apparent conservation laws in generic spacetimes, which are defined via considering special Kerr-Schild currents whose associated Kerr-Schild vector fields coincide with timelike Killing vector fields of p…
We investigate the production of gravitational waves during the inspiral of compact binaries close to their merger in the context of a conformal gravity model. The model incorporates five massive polarization degrees of freedom, besides the two massless gravitational wave polarizations of general relativity. For small graviton mass, we find that the amplitude of the gravitational waves is strongly suppressed as compared to general relativity and decreases as coalescence is approached, which contradicts the observational fact. We conclude that this model with small graviton mass, including a re…
Durgapal's fifth isotropic solution describing spherically symmetric and static matter distribution is extended to an anisotropic scenario. To do so we employ the gravitational decoupling through the minimal geometric deformation scheme. This approach allows to split Einstein's field equations in two simply set of equations, one corresponding to the isotropic sector and other to the anisotropic sector described by an extra gravitational source. The isotropic sector is solved by the Dugarpal's model and the anisotropic sector is solved once a suitable election on the minimal geometric deformati…
