The Asymptotic Symmetries Of Black Hole Horizon

The microscopic origin of black hole entropy provides a concrete entry point for people to study quantum gravity theory.Based on the idea of gauge/gravity duality,Strominger et al.found that there exist asymptotic conformal symmetry on the near horizon of extremal Kerr black hole.Based on this feature,they suspected that the quantum gravity defined on extremal Kerr black hole was dual with conformal field theory,and thay also proved that the entropy of extremal black holes can be obtained by calculating the number of microstates in the conformal field theory.For the Kerr black hole with arbitrary spin,Strominger et al.found that the solution space of scalar field on the near horizon of black hole spacetime preserved SL(2,R)× SL(2,R)symmetry.They speculated that the emergence of this symmetry was a reflection of the conformal symmetry of spacetime,they believed that there exist hidden conformal symmetry in the spacetime of Kerr black hole with arbitrary spins.And the duality relation of the quantum gravity defined on Kerr black hole and conformal field theory was also speculated under such assumption.By calculating the number of microscopic states of the conformal field theory,they also found that such microscopic result was consistent with the macroscopic result.People had also been trying to find asymptotic symmetry in the horizon of arbitrary Kerr black hole.By prescribing a physically sensible set of boundary conditions at the horizon,Donnay et al.proved that non-extremal black holes in four-dimensional general relativity exhibit an BMS-like asmptotic symmetry in their near horizon region,and thay also showed that the zero-mode were related to the entropy and angular momenta of the black hole.This paper will mainly introduce two works we have finished,including the extended symmetries at black hole horizons in generic dimensions and the hidden conformal symmetry for vector field on various black hole backgrounds.By attaching appropriate boundary conditions to the metric which can be used to describe the near horizon geometry of any dimensional black holes,one can obtain a asymptotic symmetry group which can be understood as extension of BMS,whose algebra contains two pieces of supertranslations and n-2 pieces of generalized superrotations.Coincidentally,the algebra for the generalized superrotations is exactly the same with the algebra of the complete intrinsic symmetry for five-dimensional extremal black hole in a rather different construction.In the case of stationary and axisymmetric black holes,the surface charges are calculated,and one can find that the zero-mode of supertranslation charge is related to the entropy and the temperature of the black hole,while the zero-mode of generalized superrotations part is related to the angular momentum of the black hole.Meanwhile,by investigating the separated equation of massless vector field on Kerr background,one can find the solution space of radical part preserve SL(2,R)× SL(2,R)symmetry at near region under low frequency limit.Moreover,the corresponding left-moving and right-moving temperatures are consistent with the predictions of the scalar field,and the microscopic entropy which consistent with the Hawking-Berkenstein entropy can be also successfully repeated with the help of the central charge predicted by the near-extreme Kerr black hole.This conclusion provides new support for the duality relation of the quantum gravity defined on Kerr background and conformal field theory.This paper will also intriduce the capability of the future space-based gravitational wave observatory,taking TianQin as an example,to test the no-hair theorem of General Relativity by using the ringdown signal from the coalescence of massive black hole binaries.One can parameterize the ringdown signal by the four strongest quasinormal modes and estimate the signal to noise ratio for various source parameters.The constraints both from single detections and from all the events combined throughout the lifetime of the observatory,for different astrophysical models,are also considered.At the end of the mission,TianQin will have constrained deviations of the frequency and decay time of the dominant(2,2)mode from the general relativistic predictions to within 0.2% and 1.5% respectively,the frequencies of the subleading modes can be also constrained within 0.3%.The results show that TianQin and LISA are highly complementary,by virtue of their different frequency windows.