Weak deflection angle of a dirty black hole

Abstract

In this paper, we present the weak deflection angle in a Schwarzschild black hole of mass $m$ surrounded by the dark matter of mass $M$ and thickness $\Delta r_s$. The Gauss-Bonnet theorem, formulated for asymptotic spacetimes, is found to be ill-behaved in the third-order of $1/\Delta r_s$ for very large $\Delta r_s$. Using the finite-distance for the radial locations of the source and the receiver, we derived the expression for the weak deflection angle up to the third-order of $1/\Delta r_s$ using Ishihara (\textit{et al.}) method. The result showed that the required dark matter thickness is $\sim 2\sqrt{3mM}$ for the deviations in the weak deflection angle to occur. Such thickness requirement is better by a factor of 2 as compared to the deviations in the shadow radius ($\sim \sqrt{3mM}$). It implies that the use of the weak deflection angle in detecting dark matter effects in one's galaxy is better than using any deviations in the shadow radius.

arXiv comment6 pages, 1 figure; expressions in section 4 simplified thoroughly; accepted for publication in Chinese Journal of Physics

References in corpus (53)

• Observation of Gravitational Waves from a Binary Black Hole Merger
• First M87 Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole
• Seven-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Sky Maps, Systematic Errors, and Basic Results
• Schwarzschild black hole lensing
• Relativistic images of Schwarzschild black hole lensing
• First Dark Matter Results from the XENON100 Experiment
• Weak Gravitational Lensing and its Cosmological Applications
• Probing the Coevolution of Supermassive Black Holes and Galaxies Using Gravitationally Lensed Quasar Hosts
• The observational evidence for horizons: from echoes to precision gravitational-wave physics
• Generating rotating regular black hole solutions without complexification
• Compound gravitational lensing as a probe of dark matter substructure within galaxy halos
• Tests for the existence of horizons through gravitational wave echoes
• Applications of the Gauss-Bonnet theorem to gravitational lensing
• Shadow of a black hole surrounded by dark matter
• Search for Dark Matter WIMPs using Upward Through-going Muons in Super-Kamiokande
• Gravitational bending angle of light for finite distance and the Gauss-Bonnet theorem
• The radial velocity dispersion profile of the Galactic halo: Constraining the density profile of the dark halo of the Milky Way
• Gravitational lensing in the Kerr-Randers optical geometry
• Gravitational Lensing by Rotating Wormholes
• Dirty blackholes: Thermodynamics and horizon structure
• Shadow and Deflection Angle of Rotating Black Holes in Perfect Fluid Dark Matter with a Cosmological Constant
• Light deflection by Damour-Solodukhin wormholes and Gauss-Bonnet theorem
• Shadow cast and Deflection angle of Kerr-Newman-Kasuya spacetime
• Flux ratios as a probe of dark substructures in quadruple-image gravitational lenses
• Black Hole Surrounded by a Dark Matter Halo in the M87 Galactic Center and its Identification with Shadow Images
• Gravitomagnetic bending angle of light with finite-distance corrections in stationary axisymmetric spacetimes
• Finite-distance corrections to the gravitational bending angle of light in the strong deflection limit
• The effect of the Brane-Dicke coupling parameter on weak gravitational lensing by wormholes and naked singularities
• Gravitational Lensing Under the Effect of Weyl and Bumblebee Gravities: Applications of Gauss-Bonnet Theorem
• Black Hole Space-time In Dark Matter Halo
• Dirty black holes: Entropy as a surface term
• Weak gravitational lensing of regular black holes with cosmic strings using the Gauss-Bonnet theorem
• Black Hole Shadow of Sgr A${}^{\ast }$ in Dark Matter Halo
• Rotating Black Hole Shadow in Perfect Fluid Dark Matter
• Weak Gravitational lensing by phantom black holes and phantom wormholes using the Gauss-Bonnet theorem
• Finite-distance gravitational deflection of massive particles by the Kerr-like black hole in the bumblebee gravity model
• Deflection angle of photon through dark matter by black holes and wormholes using the Gauss-Bonnet theorem
• Echoes of compact objects: new physics near the surface and matter at a distance
• Quasinormal Modes of Dirty Black Holes
• Weak gravitational lensing by Kerr-MOG Black Hole and Gauss-Bonnet theorem
• Deflection angle of light for an observer and source at finite distance from a rotating global monopole
• Pseudo-complex General Relativity
• Gravitational lensing shear by an exotic lens object with negative convergence or negative mass
• Euclidean Black Hole Vortices
• Strong Gravitational Lensing by a Charged Kiselev Black Hole
• Weak gravitational lensing by two-power-law densities using the Gauss-Bonnet theorem
• Negative time delay of light by a gravitational concave lens
• Indirect search for dark matter: prospects for GLAST
• Absorption by dirty black holes: null geodesics and scalar waves
• Microlensed image centroid motions by an exotic lens object with negative convergence or negative mass
• An Alternative Scenario for Non-Abelian Quantum Hair
• Testing two alternatives theories to dark matter with the Milky Way dynamics
• Dirty Black Holes and Hairy Black Holes

Cited by in corpus (31)

• Nonlinear electrodynamics effects on the black hole shadow, deflection angle, quasinormal modes and greybody factors
• Probing a nonlinear electrodynamics black hole with thin accretion disk, shadow and deflection angle with M87* and Sgr A* from EHT
• Shadows and gravitational weak lensing by the Schwarzschild black hole in the string cloud background with quintessential field
• Imprints of Dark Matter on Black Hole Shadows using Spherical Accretions
• Testing dynamical torsion effects on the charged black hole's shadow, deflection angle and greybody with M87* and Sgr. A* from EHT
• Schwarzschild-like black hole with a topological defect in bumblebee gravity
• Dehnen halo effect on a black hole in an ultra-faint dwarf galaxy
• Dark matter effect on the weak deflection angle by black holes at the center of Milky Way and M87 galaxies
• Shadow and weak deflection angle of extended uncertainty principle black hole surrounded with dark matter
• Testing Generalized Einstein-Cartan-Kibble-Sciama Gravity using Weak Deflection Angle and Shadow Cast
• Weak deflection angle of Kazakov-Solodukhin black hole in plasma medium using Gauss-Bonnet theorem and its greybody bonding
• Quasiperiodic oscillations, weak field lensing and shadow cast around black holes in Symmergent gravity
• Black hole in quantum wave dark matter
• Weak Gravitational Lensing in Dark Matter and Plasma Mediums for Wormhole-like Static Aether Solution
• Deflection angle and shadow of the Reissner-Nordström black hole with higher-order magnetic correction in Einstein-nonlinear-Maxwell fields
• Rotating dirty black hole and its shadow
• Weak deflection angle by Kalb-Ramond Traversable Wormhole in Plasma and Dark Matter Mediums
• Gravitational Lensing of Schwarzschild and Charged Black Holes Immersed in Perfect Fluid Dark Matter Halo
• Weak Deflection Angle, Hawking Radiation and Greybody Bound of Reissner-Nordström Black Hole Corrected by Bounce Parameter
• The Gravitational Bending of Acoustic Schwarzschild Black Hole
• Weak Deflection angle and Shadow by Tidal Charged Black Hole
• Probing Effective Loop Quantum Gravity on Weak Gravitational Lensing, Hawking Radiation and Bounding Greybody Factor by Black Holes
• Light Deflection Angle by Superentropic Black Holes
• Schwarzschild black hole surrounded by a cloud of strings in the background of perfect fluid dark matter
• Thermodynamics, Weak Gravitational Lensing, and Parameter Estimation of a Schwarzschild Black Hole Immersed in Hernquist Dark Matter Halo
• Weak Deflection angle of some classes of non-linear electrodynamics black holes via Gauss-Bonnet Theorem
• Time Delay of Light in the Gravitational lensing of Supermassive Black Holes in Dark Matter Halos
• Gravitational Lensing of Spherically Symmetric Black Holes in Dark Matter Halos
• Gravitational Lensing by a Dark Compact Object in Modified Gravity and Observational Constraints from Einstein Rings
• Probing Einstein-Maxwell-Scalar Black hole via Thin Accretion Disks and Shadows with EHT Observations of M87* and Sgr A*
• Investigating Graviton Mass Effects on Black Hole Lensing in dRGT Massive Gravity