Gravitational Lensing And Time Delay In Curved Spacetime

From general relativity,we know that photons are deviated from their straight path when they pass close to a compact and massive body.The effect resulting from the deflection of light rays in a gravitational field is known as gravitational lensing,and the object causing a detectable deflection is usually named a gravi-tational lens.Similar to a natural and large telescope,gravitational lensing is an important astrophysical tool to extract information about distant stars which are too dim to be observed and detect the distribution of dark matter in the universe.Moreover,gravitational lensing can also be used to constrain the cosmological con-stants and examine a variety of different gravitational theories.Besides being bent by the gravitational field of the lens,the light rays are also delayed.And the time delay of light traveling from the source to the observer with the closest distance of approach is defined as the difference between the light travel time for the actual ray in the gravitational field of the lens(deflector)and the travel time for the straight path between the source and the observer in the absence of the lens(i.e.,if there were no gravitational fields).Time delay can be used to estimate the mass of the gravitational,lens,and can also be used to determine the Hubble constant when combining the measurement of angular image position of the gravitational lensing.In this paper,the gravitational lensing and time delay are studied as follows:First of all,we introduce the definition,classification and calculation methods of the strong gravitational lensing and time delay.And the deflection angle,ob-servables and time delay of Schwarzschild black hole are calculated by using these methods.Then,we investigate the strong gravitational lensing and time delay for black holes with scalar hair in massive gravity.We can see,with the increase of scalar hair,that the minimum impact parameter,angular image position and relative magnitude increase,while the deflection angle and the angle image separation decrease.At,the same time,we find the time delay decreases remarkably with the increase of angular source position,and the influence of scalar hair on time delay is very small but regular compared with the angular source position.Furthermore,the strong gravitational lensing and time delay for charged black holes with scalar hair in Einstein-Maxwell-Dilaton theory are studied.We find,with the increase of scalar hair,that the radius of the photon sphere,minimum impact parameter,angular image position and relative magnitude increase,while the deflection angle and angular image separation decrease.We also show,for the primary relativistic image which is formed by the light does not loop around the lens and situated on the same side of the source,that the scalar hair increases the time delay.Additionally,we study strong gravitational lensing for photons coupled to Weyl tensor in a regular phantom black hole by discussing the difference between the relativistic images on the same side of the source.We find that the deflection angle will be larger when the light gets to the black hole closer by investigating how the coupling constant and phantom hair affect the difference of photon sphere radius,minimum impact parameter and deflection angle.Then,we study the difference of angular image position and the relative magnitudes of the first rela-tivistic image between the two types of different polarized photons,and find that the two images for different polarizations separate further and easier to distinguish when the phantom hair decreases or the absolute value of the coupling constant increases,and the image is brighter when it seats closer to the optical axis.