Gravitational microlensing: results and perspectives in brief

Basics of standard theory of microlensing are introduced. Results of mi-crolensing observations toward Magellanic Clouds and relations with dark matter (DM) problem in our Galaxy are described. Pixel microlensing observations and recent discoveries of planets with microlensing observations are listed. Gravitational lensing is based on a simple physical phenomenon that in a gravitational field a light trajectories are bent (in some sense a gravitating body attracts photons). In the first time this fact was discussed by I. Newton [1], but the first derivation of the light bending angle was published by J. Soldner in the framework of Newtonian gravity [2]. In general relativity (GR) using a weak gravitational field approximation the correct bending angle is described by the following expression obtained by Einstein [3] just after his formulation of GR δϕ = 4GM c 2 p , (1) where M is a gravitating body mass, p is an impact parameter, c is a speed of light, G is the Newton constant. If M = M ⊙ and p = R ⊙ are Solar mass and radius respectively, the angle is equal to 1.75 ′′. In 1919 the law was firstly confirmed by A. Eddington for observations of light ray bending by the Solar gravitational field near its surface. Therefore, the Einstein prediction about light bending was confirmed by observations very soon after its discovery. Using Eq. (1) one can introduce the gravitational lens equation η = D s ξ/D d − D ds Θ(ξ), (2) where D s is a distance between a source and observer, D d is a distance between a gravitational lens and observer, D ds is a distance between a source and a lens, η, ξ define coordinates in source and lens planes, respectively, and Θ(ξ) = 4GM ξ/c 2 ξ 2 .