The Shadow Cast By Hayward Black Hole Surrounded By Quintessence

With the progress of the Event Horizon Telescope,the observation of black holes is becoming more and more important.Therefore,it is very necessary to study the observed effect of black hole theoretically.Cosmological constants and the existence of dark energy around black holes have considerable consequences on the black hole's spacetime geometry.When cosmological constants and dark energy are taken into account,space-time becomes non-asymptotically flat.At this point,the black hole will have a cosmological event horizon.Outside the cosmological event horizon,the observers can not observe the black hole information.So the general method which places the observer at an infinite distance no longer works.We took a new approach to studying the shadow of a black hole by setting the observers to a fixed position within the cosmological event horizon,and then firing photons from the observers' position into the past.So we take a new approach to the study of black hole shadows.First,the observer should be fixed at a position within the cosmological event horizon.And from that position,photons are emitted toward the past.These photons can be roughly divided into two categories: those that are absorbed because of the black hole's gravity,and those that are not absorbed and reach the background source.The dividing line between the two kinds of photons is the spherical optical geodesic,and the distribution area of the spherical optical geodesic is called the photon region.The boundary curve of the black hole shadow can be obtained from the spherical optical geodesic.In this paper,we discuss the optical properties of a black hole with a non-zero cosmological constant ? and a nonlinear magnetic charge Q under quintessence dark energy.The dark energy model we used is quintessence dark energy model,which is widely used and can be described by two parameters wq and ?.Setting the state parameter wq =-3/2,we studied the horizons,the photon region and the shadow of this black hole.It turned out that for a fixed quintessential parameter?,in a certain range,with the increase of the rotation parameter a and magnetic charge Q,the inner horizon radius increases while the outer horizon radius decreases.And the cosmological horizon r? decreases when ? or ? increases.The shapes of photon region were then studied and depicted through graphical illustrations.From the results of the calculations,the rotation will deform the photon region.For the cosmological constant,it makes the photon region smaller.The influence of quintessence dark energy should be discussed in two cases.Finally,we get the analytical form of the boundary of the black hole's shadow from the expression of the photon region,and discuss the influence of quintessence parameter ? and cosmological constant ? on the black hole's shadow with fixed observer position in the external communication domain.The obtained result demonstrates that,due to the dragging effect,the black hole spin elongates its shadow in the direction of the rotational axis? and the presence of the nonlinear magnetic charge Q aggravates the deformation.The quintessence parameter ? and the cosmological constant ? both significantly reduce the area of the black hole shadow.