Testing gravity at the second post-Newtonian level through gravitational deflection of massive particles

In this paper, we study the weak gravitational deflection angle of relativistic massive particles by the Kerr-like black hole in the bumblebee gravity model. In particular, we focus on weak field limits and calculate the deflection angle for a receiver and source at a finite distance from the lens. To this end, we use the Gauss-Bonnet theorem of a two-dimensional surface defined by a generalized Jacobi metric. The spacetime is asymptotically non-flat due to the existence of a bumblebee vector field. Thus the deflection angle is modified and can be divided into three parts: the surface integral of the Gaussian curvature, the path integral of a geodesic curvature of the particle ray and the change in the coordinate angle. In addition, we also obtain the same results by defining the deflection angle. The effects of the Lorentz breaking constant on the gravitational lensing are analyzed. We then consider the finite-distance correction for the deflection angle of massive particles.

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Gravitational deflection of relativistic massive particles

American Journal of Physics ◽

10.1119/1.12268 ◽

1980 ◽

Vol 48 (1) ◽

pp. 72-78 ◽

Cited By ~ 3

Author(s):

Mark P. Silverman

Keyword(s):

Massive Particles ◽

Gravitational Deflection

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The finite-distance gravitational deflection of massive particles in stationary spacetime: a Jacobi metric approach

The European Physical Journal C ◽

10.1140/epjc/s10052-020-7665-8 ◽

2020 ◽

Vol 80 (2) ◽

Cited By ~ 8

Author(s):

Zonghai Li ◽

Junji Jia

Keyword(s):

Black Hole ◽

Deflection Angle ◽

Kerr Black Hole ◽

Relativistic Velocity ◽

Massive Particles ◽

Finite Distance ◽

The Deflection Angle ◽

Jacobi Metric ◽

Optical Metric ◽

Gravitational Deflection

Abstract In this paper, we study the weak gravitational deflection of relativistic massive particles for a receiver and source at finite distance from the lens in stationary, axisymmetric and asymptotically flat spacetimes. For this purpose, we extend the generalized optical metric method to the generalized Jacobi metric method by using the Jacobi–Maupertuis Randers–Finsler metric. More specifically, we apply the Gauss–Bonnet theorem to the generalized Jacobi metric space and then obtain an expression for calculating the deflection angle, which is related to Gaussian curvature of generalized optical metric and geodesic curvature of particles orbit. In particular, the finite-distance correction to the deflection angle of signal with general velocity in the the Kerr black hole and Teo wormhole spacetimes are considered. Our results cover the previous work of the deflection angle of light, as well as the deflection angle of massive particles in the limit for the receiver and source at infinite distance from the lens object. In Kerr black hole spacetime, we compared the effects due to the black hole spin, the finite-distance of source or receiver, and the relativistic velocity in microlensings and lensing by galaxies. It is found in these cases, the effect of black hole spin is usually a few orders larger than that of the finite-distance and relativistic velocity, while the relative size of the latter two could vary according to the particle velocity, source or observer distance and other lensing parameters.

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Gravitational deflection of massive particles in Schwarzschild-de Sitter spacetime

The European Physical Journal C ◽

10.1140/epjc/s10052-020-8382-z ◽

2020 ◽

Vol 80 (9) ◽

Author(s):

Guansheng He ◽

Xia Zhou ◽

Zhongwen Feng ◽

Xueling Mu ◽

Hui Wang ◽

...

Keyword(s):

Neutral Particle ◽

Deflection Angle ◽

Weak Field ◽

De Sitter Spacetime ◽

De Sitter ◽

Field Limit ◽

Weak Field Limit ◽

Sitter Spacetime ◽

Massive Particles ◽

Gravitational Deflection

AbstractIn this paper, the gravitational deflection of a relativistic massive neutral particle in the Schwarzschild-de Sitter spacetime is studied via the Rindler–Ishak method in the weak-field limit. When the initial velocity $$v_0$$ v 0 of the particle tends to the speed of light, the result is consistent with that obtained in the previous work for the light-bending case. Our result is reduced to the Schwarzschild deflection angle of massive particles up to the second order, if the contributions from the cosmological constant $$\varLambda $$ Λ are dropped. The observable correctional effects due to the deviation of $$v_0$$ v 0 from light speed on the $$\varLambda $$ Λ -induced contributions to the deflection angle of light are also analyzed.

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