Weak deflection angle of a dirty black hole

Pantig, Reggie C.; Rodulfo, Emmanuel T.

doi:10.1016/j.cjph.2020.06.015

Weak deflection angle of a dirty black hole

Mar 2, 2020

12 pages

Published in:

Chin.J.Phys. 66 (2020) 691-702

Published: Aug, 2020

e-Print:

2003.00764 [gr-qc]

DOI:

10.1016/j.cjph.2020.06.015

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Abstract: (arXiv)

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

\sim2\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.

Note:

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

Dirty black hole
Dark matter
Gauss-Bonnet theorem
Weak deflection angle
Finite-distance
black hole: Schwarzschild
dark matter
deflection
angular dependence
gravitation

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