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Register a new userGravitational lensing of massive particles in Schwarzschild gravity
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Both massless light ray and objects with nonzero mass experience trajectory bending in a gravitational field. In this work the bending of trajectories of massive objects in a Schwarzschild spacetime and the corresponding gravitational lensing (GL) effects are studied. A particle sphere for Schwarzschild black hole (BH) is found with its radius a simple function of the particle velocity and proportional to the BH mass. A single master formula for both the massless and massive particle bending angle is found, in the form of an elliptic function depending only on the velocity and impact parameter. This bending angle is expanded in both large and small velocity limits and large and small impact parameter limits. The corresponding deflection angle for weak and strong GL of massive particles are analyzed, and their corrections to the light ray deflection angles are obtained. The dependence of the deflection angles on the source angle and the particle speed is investigated. Finally we discuss the potential applications of the results in hypervelocity star observations and in determining mass/mass hierarchy of slow particles/objects.
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We investigate the strong gravitational lensing for black hole with scalar charge in massive gravity. We find that the scalar charge and the type of the black hole significantly affect the radius of the photon sphere, deflection angle, angular image position, angular image separation, relative magnifications and time delay in strong gravitational lensing. Our results can be reduced to that of the Schwarzschild and Reissner-Nordstr$ddot{o}$m black holes in some special cases.
We study motion of test particles and photons in the vicinity of (2+1) dimensional Gauss-Bonnet (GB) BTZ black hole. We find that the presence of the coupling constant serves as an attractive gravitational charge, shifting the innermost stable circular orbits outward with respect to the one for this theory in 4 dimensions. Further we consider the gravitational lensing, to test the GB gravity in (2+1) dimensions and show that the presence of GB parameter causes the bending angle to grow up first with the increase of the inverse of closest approach distance, $u_0$, then have its maximum value for specific $u_0^*$, and then reduce until zero. We also show that increase in the value of the GB parameter makes the bending angle smaller and the increase in the absolute value of the negative cosmological constant produces opposite effect on this angle.
In this article, we develop a formalism which is different from the standard lensing scenario and is necessary for understanding lensing by gravitational fields which arise as solutions of the effective Einstein equations on the brane. We obtain general expressions for measurable quantities such as time delay, deflection angle, Einstein ring and magnification. Subsequently, we estimate the deviations (relative to the standard lensing scenario) in the abovementioned quantities by considering the line elements for clusters and spiral galaxies obtained by solving the effective Einstein equations on the brane. Our analysis reveals that gravitational lensing can be a useful tool for testing braneworld gravity as well as the existence of extra dimensions.
The direct detection of gravitational waves now provides a new channel of testing gravity theories. Despite that the parametrized post-Einsteinian framework is a powerful tool to quantitatively investigate effects of modification of gravity theory, the gravitational waveform in this framework is still extendable. One of such extensions is to take into account the gradual activation of dipole radiation due to massive fields, which are still only very weakly constrained if their mass $m$ is greater than $10^{-16}$ eV from pulsar observations. Ground-based gravitational-wave detectors, LIGO, Virgo, and KAGRA, are sensitive to this activation in the mass range, $10^{-14}$ eV $lesssim m lesssim 10^{-13}$ eV. Hence, we discuss a dedicated test for dipole radiation due to a massive field using the LIGO-Virgo collaborations open data. In addition, assuming Einstein-dilaton-Gauss-Bonnet (EdGB) type coupling, we combine the results of the analysis of the binary black hole events to obtain the 90% confidence level constraints on the coupling parameter $alpha_{rm EdGB}$ as $sqrt{alpha_{rm EdGB}} lesssim 2.47$ km for any mass less than $6 times 10^{-14}$ eV for the first time, including $sqrt{alpha_{rm EdGB}} lesssim 1.85$ km in the massless limit.
We study the polarizations of gravitational waves (GWs) in two classes of extended gravity theories. First, we formulate the polarizations in linear massive gravity (MG) with generic mass terms of non-Fierz-Pauli type by identifying all the independent variables that obey Klein-Gordon-type equations. The dynamical degrees of freedom (dofs) in the generic MG consist of spin-2 and spin-0 modes, the former breaking down into two tensor (helicity-2), two vector (helicity-1) and one scalar (helicity-0) components, while the latter just corresponding to a scalar. We find convenient ways of decomposing the two scalar modes of each spin into distinct linear combinations of the transverse and longitudinal polarizations with coefficients directly expressed by the mass parameters, thereby serving as a useful tool in measuring the masses of GWs. Then we analyze the linear perturbations of generic higher-curvature gravity (HCG) whose Lagrangian is an arbitrary polynomial of the Riemann tensor. On a flat background, the linear dynamical dofs in this theory are identified as massless spin-2, massive spin-2, and massive spin-0 modes. As its massive part encompasses the identical structure to the generic MG, GWs in the generic HCG provide six massive polarizations on top of the ordinary two massless modes. In parallel to MG, we find convenient representations for the scalar-polarization modes directly connected to the parameters of HCG. In this analysis, we employ two distinct methods; One takes full advantage of the partial equivalence between the generic HCG and MG at the linear level, whereas the other relies upon a gauge-invariant formalism. We confirm that the two results agree. We also discuss methods to determine the theory parameters by GW-polarization measurements. Our method does not require measuring the propagation speeds or the details of the waveforms of the GWs. [Abridged]
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