Speaker: Prof. Hideki Asada (Hirosaki University)

Title : Gravitomagnetic bending angle of light by rotating objects

Abstract:

One of the outstanding effects of the theory of general rela

tivity is the gravitational deflection of light by mass. The

angular momentum also contributes to the light deflection.

This deflection, which can be related with a vector part of

the gravitational field, may be called the gravitomagnetic d

eflection of light (because of its electromagnetic analogy),

though the gravitomagnetic deflection has not been observed

.

We discuss a possible method of more precisely calculating t

he bending angle of light in stationary, axisymmetric and as

ymptotically flat spacetimes. For this purpose, we consider

the light rays on the equatorial plane in the axisymmetric s

pacetime. We introduce a spatial metric to define the bendin

g angle of light in a finite-distance situation. We show tha

t the proposed bending angle of light is coordinate-invarian

t by using the Gauss-Bonnet theorem in differential geometry

. The non-vanishing geodesic curvature of the photon orbit w

ith the spatial metric is caused in gravitomagnetism, even t

hough the light ray in the four-dimensional spacetime follow

s the null geodesic. Finally, we consider Kerr spacetime as

an example in order to examine how the bending angle of lig

ht is computed by the present method. We discuss the finite-

distance corrections to the gravitomagnetic deflection angle

for two cases (1) the Sun and (2) Sgr A∗. The effects are

unlikely to be observed with present technology.

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