Spontaneous Scalarization Of Black Holes In Quadratic Gravity Theory

As one of the two cornerstones of modern physics,General Relativity(GR)has been well proved in various high-precision experiments.But there are still some ques-tions in nature that GR cannot answer,Such as incompatibility with quantum gauge theory,the matter-antimatter asymmetry,the late-time acceleration of the universe,the galaxy rotation curves,and the existence of singularities.Thus,it is believed that at least at certain scales,GR needs to be modified.The quadratic gravity theories were originally proposed to solve practical physical problems,But then it is found that this kind of theories can also be used as an effective field theory description of a more fundamental theory.Therefore,the study of quadratic gravity theories may give a strong impetus to the development of the gravitational physics.In this paper7 we study the spontaneous scalarization regime of black holes in quadratic gravity theories via a combination of analytical analysis and numerical calculation,,through which black holes in GR can generate a new degree of freedom,i.e.,scalar charges.In chapter 2,we introduce two sorts of quadratic gravity theories,includ-ing the Einstein-scalar-Chern-Simons(EsCS)gravity theory,which introduces the parity-violating Chern-Simons curvature invariant to explain the matter-antimatter asymmetry in the universe,and the Einstein-scalar-Gauss-Bonnet gravity theory,which introduces the Gauss-Bonnet curvature invariant to interpret the late-time acceleration of the universe.In chapter 37 we discusses the existence of the sponta-neous scalarization regime of black holes in these two kinds of gravity theories and the scalarization phenomenon of Schwarzschild black holes.In chapter 4,Firstly,using numerical methods,we obtain scalarized black holes formed by spontaneous scalarization in static spacetime.Then,we construct analytical expressions for the metric functions and scalar field configurations for these scalarized black hole solu?tions approximately by employing the continued fraction parametrization method of which the error converges.It is found that the error between the analytic approxi-mation and the numerical solution is relatively small.Therefore,to deal with certain physical problems,the analytic approximate representations can be treated as exact solutions.As an example7 we verify that a Schwarzschild black hole has better ther-modynamic stability than a scaled-down black hole by using these representations.In chapter 5,we take EsCS gravity theory as an example,and study the perturbations on the background of a Kerr black hole numerically.We found that the Kerr black hole becomes unstable in a certain region of the parameter space,which indicates that some Kerr black holes in this theory will get spontaneously scalarized.These scalarized black holes may not only provide theoretical researchers with new research directions,but also provide some explanations for future experimental results with higher accuracy.