The Research On Holographic Principle And Spontaneously Induced General Relativity

Under the framework of general relativity (GR), the information contained in ablack hole could be described by the horizon entropy. The degrees of freedom evenlyspread on the event horizon or the stretched horizon and there are no physicaldegrees of freedom that reside within the interior of a black hole. These insightpartially led to the proposition of the holographic principle. Although the horizonplays the role of vehicle of degrees of freedom, it seems innocent to in-falling matter.The apparent inconsistency suggests that the event horizon and the degrees offreedom of black holes are not well understood. However, if GR is a spontaneouslyinduced theory of gravity instead of a fundamental theory, the situation may bechanged.In some modified theories of gravity, there may exist one kind of solutions withvery specific features when some parameters have been selected properly. Thenovelty lies in that the spacetime outside the event horizon is described by GR whichis highly consistent with experimental observations, but a phase transition will occurprecisely at the would-have-been event horizon which makes the internal structure ofspacetime differing conceptually from the interior of usual black holes. In otherwords, the inner core is connected with a spontaneously induced GR exteriorthrough the horizon phase transition. It is interesting that the inner core ischaracterized by some nontrivial features, which could in a certain extent shed lighton some longstanding problems in GR, such as the black hole information puzzle.This thesis is just stretched out based on the research of this kind of theory.The questions studied in this thesis are closely related to the holographicprinciple. So we firstly introduce the holographic principle. Then we review theresearch of spontaneously induced GR. Our work focuses on the spontaneouslyinduced GR from the scalar-tensor gravity. We show by numerical methods that there are both novel inner cores either of which connects thetopological-Schwarzschild-AdS or Schwarzschild-dS exterior. Based on this, we alsofind an analytic expression of the core connecting a general GR exterior. We havechecked that the static analytic core has the nontrivial features, including thevanishing spatial volume, constant temperature, positive-definitive Komar mass, thefreezing light ray, and the locally holographic entropy packing. We also investigatewhether the f (R)gravity and Gauss-Bonnet gravity can accommodate thenontrivial core.