Deflection and Gravitational lensing of null and timelike signals in the Kiselev black hole spacetime in the weak field limit

Abstract

In this work we study the deflection and gravitational lensing of null and timelike signals in the Kiselev spacetime in the weak field limit, to investigate the effects of the equation of state parameter $\omega$ and the matter amount parameter $\alpha$. In doing this, we extend a perturbative method previously developed for asymptotically flat spacetimes whose metric functions have integer-power asymptotic expansions to the case that may or may not be asymptotically flat but with non-integer power expansions. It is found that in the asymptotically flat case ($-1/3<\omega <0$) the deflection angles are expressable as quasi-power series of the dimensionless quantities $M/b,b/r_{s,d}$ and $\alpha /M^{1+3\omega }$ where $M,b,r_{s,d}$ are respectively the lens mass, impact parameter and source/detector radius. A similar series exists for the non-asymptotically flat case of ($-1<\omega <-1/3$), but with the closest radius $r_0$ replacing $b$. In the asymptotically flat (or non-flat) case, the increase of $\alpha$ or decrease of $\omega$ will increase (or increase) the deflection angle. Since the obtained deflection angles naturally take into account the finite distance effect of the source and the detector, we can establish an exact gravitational lensing equation, from which the apparent angles of the images and their magnifications are solved. It is found that generally for the asymptotically flat case, increasing $\alpha$ or decreasing $\omega$ will increase the apparent angles of the images. While for the non-asymptotically flat case, increasing $\alpha$ or $\omega$ will both lead to smaller apparent angles.

arXiv comment19 pages, 7 figures; to match the version to appear in Classical and Quantum Gravity

References in corpus (45)

• Observation of Gravitational Waves from a Binary Black Hole Merger
• GW170817: Observation of Gravitational Waves from a Binary Neutron Star Inspiral
• First M87 Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole
• GW151226: Observation of Gravitational Waves from a 22-Solar-Mass Binary Black Hole Coalescence
• Weak Gravitational Lensing
• Dark Energy and the Accelerating Universe
• First Sagittarius A* Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole in the Center of the Milky Way
• First M87 Event Horizon Telescope Results. VI. The Shadow and Mass of the Central Black Hole
• Multi-messenger observations of a flaring blazar coincident with high-energy neutrino IceCube-170922A
• Neutrino emission from the direction of the blazar TXS 0506+056 prior to the IceCube-170922A alert
• Quintessence and black holes
• First Sagittarius A* Event Horizon Telescope Results. VI: Testing the Black Hole Metric
• Quintessence: A Review
• Dark Energy vs. Modified Gravity
• Weak Gravitational Lensing and its Cosmological Applications
• Applications of the Gauss-Bonnet theorem to gravitational lensing
• Multiple Images of a Highly Magnified Supernova Formed by an Early-Type Cluster Galaxy Lens
• A Robust Determination of the Time Delay in 0957+561A,B and a Measurement of the Global Value of Hubble's Constant
• The mass distribution in the Galactic Centre from interferometric astrometry of multiple stellar orbits
• iPTF16geu: A multiply imaged, gravitationally lensed type Ia supernova
• The Contribution of the Cosmological Constant to the Relativistic Bending of Light Revisited
• Weak lensing in a plasma medium and gravitational deflection of massive particles using the Gauss-Bonnet theorem. A unified treatment
• Ultrahigh Energy Cosmic Rays
• Schwarzschild black hole surrounded by quintessence: Null geodesics
• Deflection Angle and Shadow Behaviors of Quintessential Black Holes in arbitrary Dimensions
• The Kiselev black hole is neither perfect fluid, nor is it quintessence
• Probing the distribution of dark matter in the Abell 901/902 supercluster with weak lensing
• Classical tests for Weyl gravity: deflection of light and time delay
• Weak lensing study of low mass galaxy groups: implications for Omega_m
• Gravitational lensing of massive particles in Reissner-Nordström spacetime
• Strong Gravitational Lensing by Kiselev Black Hole
• Gravitational deflection angle of light: Definition by an observer and its application to an asymptotically nonflat spacetime
• Gravitational lensing of massive particles in Schwarzschild gravity
• The finite-distance gravitational deflection of massive particles in stationary spacetime: a Jacobi metric approach
• Strong Gravitational Lensing by a Charged Kiselev Black Hole
• Geometrization of light bending and its application to SdSw spacetime
• Direct Probe of Dark Energy through Gravitational Lensing Effect
• Study of circular geodesics and shadow of rotating charged black hole surrounded by perfect fluid dark matter immersed in plasma
• Analytical formulas for gravitational lensing: higher order calculation
• The perturbative approach for the weak deflection angle
• Possibility of Identifying Matter around Rotating Black Hole with Black Hole Shadow
• Perturbative deflection angle for signal with finite distance and general velocities
• Studying Gravitational Deflection of Light by Kiselev Black Hole via Homotopy Perturbation Method
• Constraining the spacetime spin using time delay in stationary axisymmetric spacetimes
• Deflection angle with electromagnetic interaction and gravitational-electromagnetic dual lensing

Cited by in corpus (5)

• On the analytic generalization of particle deflection in the weak field regime and shadow size in light of EHT constraints for Schwarzschild-like black hole solutions
• Traces of quantum fuzziness on the black hole shadow and particle deflection in the multi-fractional theory of gravity
• On the global Gaussian bending measure and its applications in stationary spacetimes
• Probing dark fluids and modified gravity with gravitational lensing
• Deflection in higher dimensional spacetime and asymptotically non-flat spacetimes