An attempt to empirically evaluate the gravitational deflection of light in the modified Newtonian dynamics.

Details An attempt to empirically evaluate the gravitational deflection of light in the modified Newtonian dynamics. An attempt to empirically evaluate the gravitational deflection of light in the modified Newtonian dynamics.

Apr 1995

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1995a%26a...296..264q&link_type=abstract

Astronomy and Astrophysics, v.296, p.264

Astronomy and Astrophysics

Astrophysics

20

Gravitation, Gravitational Lensing, Dark Matter

Scientific paper

The deflection angle {DELTA}φ of light rays by the gravitational field of a spherical system M(r) is empirically evaluated using the MOdified Newtonian Dynamics (MOND). It is shown that {DELTA}φ with an impact parameter r0 can be expressed by the measured rotation velocity v(r) as {DELTA}φ(r0) = 2{Integral}_r0_infinity^[(v^2^(r)) / (c^2^)x(r0dr) / (rsqrt(r ^2^-r0^2^))], where v(r) = (Ga0M(r))^1 / 4^ for r0>r_c_ and v(r) = srq(GM(r)) / (r)) for r0 <= r_c_} and r_c_ is the critical radius that is determined by the critical acceleration a0. In the Newtonian limit of the gravitational acceleration a >> a0, {DELTA}φ approaches {DELTA}φ = 2Gm(r0) / c^2^r0 with the projected surface mass m(r0). Whilst the asymptotic value of {DELTA}φ reaches a constant π(vinfinity_ / c)^2^ in the low-acceleration limit of a << a0. Taking the conventional correction of a factor of 2 from the theory of general relativity into account and utilizing the relation between rotation velocity v and velocity dispersion σ, MOND results naturally in a constant deflection, 4π(σ / c)^2^, which has been widely used in the present-day study of gravitational lensing by galaxies and clusters of galaxies, implying that without introducing the massive halos acting as r^-2^ for dark matter MOND has no difficulty in reproducing the known cases of gravitational lensing associated with galaxies and clusters of galaxies.

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