Gravitational Lenses

A stellar gravitational lens has the capacity to intensify by a factor in excess of 1000 the image of another star suitably aligned behind it. This capability, reported in 1936 by A. Einstein in response to a suggestion by R. W. Mandl, appears today not to be generally well known. In the present paper, the imaging properties of the gravitational lens are discussed, and mechanisms whereby lens effects might manifest themselves are evaluated. The relative proper motions of the stars in our galaxy will occasionally give rise to transitory alignments producing time symmetric pulses of light intensity. Typically, for two stars aligned to better than ∼ ${10}^{-8\mathrm{}}$ rad, the image configuration of the more distant, object star will be characterized by an intensification varying inversely with the angular separation of the stars. This inverse angular dependence persists until the disk of the object star, subtending perhaps ∼ ${10}^{-11\mathrm{}}$ rad, passes behind the center of the deflector star. It is estimated, for events involving the ∼ ${10}^9$ observable stars of the Milky Way, that $\frac{{\tau }_I}{A_M}\approx 3\times {10}^6$ sec, and ${\tau }_W{A}_M\approx 5\times {10}^7$ sec, where ${\tau }_I$ represents the mean interval between all events which will exhibit at closest alignment an intensity gain for the object star in excess of $A_M$, and ${\tau }_W$ denotes the temporal width of that pulse characterized by $A_M$. For the case of a globular cluster of ∼3×${10}^5$ deflector stars moving between the earth and the relatively dense object stellar population in the direction of the galactic center, we find $\frac{{\tau }_I}{A_M}\approx 3\times {10}^8$ sec, and ${\tau }_W{A}_M\approx 7\times {10}^6$ sec. For events involving stars entirely within a single globular cluster of ∼${10}^6$ stars, we find $\frac{{\tau }_I}{A_M}\approx 8\times {10}^7$ sec, and ${\tau }_W{A}_M\approx 3\times {10}^6$ sec, with $A_M$ restricted, in this case, to be less than ∼60. Unaccounted for white dwarf and neutron deflector stars are not likely to contribute more than a factor of ∼2 increase in the frequency of events. No planets of the sun are useful for producing image intensifications. As a result of their gravitational lens action upon the light from other stars, all stars are surrounded by radial spikes of concentrated light intensity. Such spikes might occasionally manifest themselves as luminous beams in cosmic dust or gas clouds. A statistical analysis of the images of distant galaxies might reveal spectral anomalies explicable in terms of red shifted object galaxies intensified by the lens action of nearer deflector galaxies.