Theoretical Study Of Testing Equivalence Principle On Black Hole Horizon Scale And Cosmological Scale

The equivalence principle is an important part of Einstein's general theory of rel-ativity.The violation of equivalence principle and the strength of its establishment condition are important marks to distinguish different gravitational theories and related new physics.Therefore,it is of great significance to test it in a variety of gravitational scales and physical environments.Based on this,this paper studies three aspects:1.The contemporary significance of the equivalence principle.2.Using the black hole photon ring to test the equivalence principle in the gravitational field of black hole event horizon scale.3.Using the effective field theory to analyze the phenomenological man-ifestations of the destruction of strong equivalence principle at the cosmological scale.1.According to the strength of the holding conditions,we divide the equivalence principle into weak equivalence principle,Einstein's equivalence principle and strong equivalence principle and explain them successively.For each equivalence principle,we classify and distinguish its physical meaning according to four basic properties:lo-calized,mechanical,non-gravitational and vacuumed.Then,we discuss the importance of the equivalence principle in classifying gravity theories and new physics,and intro-duce an example to illustrate the violation of equivalence principle and the strength of holding conditions are important guides to reflect how the new physical degrees of free-dom couple with the gravitational interaction,non-gravitational interaction and matter.2.We introduce the formation mechanism and physical properties of the black hole photon ring.Based on this,we characterize the observational properties of the black hole photon ring on the very long baseline interferometry,and introduce the rela-tionship between the black hole photon ring and the current event horizon telescope and the future very long baseline experiments in space.We then,for the first time,combine the equivalence principle with observations of black hole photon rings to investigate the possibility of testing the weak equivalence principle and Einstein equivalence principle at the event horizon scale.For both studies,we start from a general model to violate the weak and Einstein equivalence principle respectively and analyze the induced phe-nomenological behaviors.The results show that the violation of the weak equivalence principle makes the appearance of the black hole photon ring depend on the intrinsic frequency of photons,while the violation of Einstein equivalence principle makes it depend on the polarizations of photons.Finally,for the violation of these two equiva-lence principles,we select some specific examples to show the appearance of the black hole photon ring in detail by the methods of analytical approximation and numerical calculations.3.Violation of the strong equivalence principle is the characteristic of the modi-fied gravity theories.f(T)gravity is a new type of modified gravity theories emerging this year.We use the effective field theory of modified gravity to investigate the phe-nomenological behaviors of the violation of the strong equivalence principle for this type of gravity theories on the cosmological scale.For scalar perturbations,we de-rive the modified Newtonian gravitational constant and the post-Newtonian parameter y under the approximation of quasi-static and the fluctuation wavelength less than the Hubble horizon.For tensor perturbations,we derive that the gravitational waves travel at the speed of light.