scholarly journals Finite-distance gravitational deflection of massive particles by a Kerr-like black hole in the bumblebee gravity model

2020 ◽  
Vol 101 (2) ◽  
Author(s):  
Zonghai Li ◽  
Ali Övgün
Keyword(s):  
Black Hole ◽  
Gravity Model ◽  
Massive Particles ◽  
Finite Distance ◽  
Gravitational Deflection

scholarly journals Finite-Distance Gravitational Deflection of Massive Particles by the Kerr-like Black Hole in the Bumblebee Gravity Model

2019 ◽  
Author(s):  
Zonghai Li ◽  
Ali Övgün
Keyword(s):  
Black Hole ◽  
Gravity Model ◽  
Gravitational Lensing ◽  
Deflection Angle ◽  
Geodesic Curvature ◽  
Surface Integral ◽  
Massive Particles ◽  
Finite Distance ◽  
The Deflection Angle ◽  
Gravitational Deflection

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.

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

2020 ◽  
Vol 80 (2) ◽  
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.

scholarly journals Rainbow Gravity Corrections to the Entropic Force

2018 ◽  
Vol 2018 ◽  
pp. 1-8 ◽  
Author(s):  
Zhong-Wen Feng ◽  
Shu-Zheng Yang
Keyword(s):  
Black Hole ◽  
Field Equation ◽  
Quantum Gravity ◽  
Gravity Model ◽  
Einstein Field Equation ◽  
Friedmann Equation ◽  
Quantum Corrections ◽  
Entropic Force ◽  
Planck Length ◽  
Multifunctional Properties

The entropic force attracts a lot of interest for its multifunctional properties. For instance, Einstein’s field equation, Newton’s law of gravitation, and the Friedmann equation can be derived from the entropic force. In this paper, utilizing a new kind of rainbow gravity model that was proposed by Magueijo and Smolin, we explore the quantum gravity corrections to the entropic force. First, we derive the modified thermodynamics of a rainbow black hole via its surface gravity. Then, according to Verlinde’s theory, the quantum corrections to the entropic force are obtained. The result shows that the modified entropic force is related not only to the properties of the black hole but also to the Planck length lp and the rainbow parameter γ. Furthermore, based on the rainbow gravity corrected entropic force, the modified Einstein field equation and the modified Friedmann equation are also derived.

scholarly journals Global embeddings and hydrodynamic properties of Kerr black hole

2016 ◽  
Vol 31 (35) ◽  
pp. 1650204
Author(s):  
Soon-Tae Hong
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Equatorial Plane ◽  
Kerr Black Hole ◽  
Kerr Spacetime ◽  
Stable Circular Orbit ◽  
Massive Particles ◽  
Flat Embedding ◽  
Bound Orbits ◽  
The Impact

In the presence of a rotating Kerr black hole, we investigate hydrodynamics of the massive particles and massless photons to construct relations among number density, pressure and internal energy density of the massive particles and photons around the rotating Kerr black hole and to study an accretion onto the black hole. On equatorial plane of the Kerr black hole, we investigate the bound orbits of the massive particles and photons around the black hole to produce their radial, azimuthal and precession frequencies. With these frequencies, we study the black holes GRO J1655-40 and 4U 1543-47 to explicitly obtain the radial, azimuthal and precession frequencies of the massive particles in the flow of perfect fluid. We next consider the massive particles in the stable circular orbit of radius of 1.0 ly around the supernovas SN 1979C, SN 1987A and SN 2213-1745 in the Kerr curved spacetime, and around the potential supermassive Schwarzschild black holes M87, NGC 3115, NGC 4594, NGC 3377, NGC 4258, M31, M32 and Galatic center, to estimate their radial and azimuthal frequencies, which are shown to be the same results as those in no precession motion. The photon unstable orbit is also discussed in terms of the impact parameter of the photon trajectory. Finally, on the equatorial plane of the Kerr black hole, we construct the global flat embedding structures possessing (9 + 3) dimensionalities outside and inside the event horizon of the rotating Kerr black hole. Moreover, on the plane, we investigate the warp products of the Kerr spacetime.

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