Evolution Of Perturbations In The Black Hole Spacetime And Quantum Information In The Relativistic Framework

This thesis is devoted to the investigation of the quasinormal modes(QNMs),power-law tail,quantum entanglement and quantum teleportation in the black holephysics which is an intersectional field of general relativity,quantum mechanics,string theory,thermodynamics,statistics,and so on.The QNMs of the Schwarzschild black hole,Schwarzschild black hole with aglobal monopole(SBHGM)and stationary axisymmetric Einstein-Maxwell dilatonaxion(EMDA)black hole are investigated by using the continued fraction method proposed by Leaver.Our main conclusions are as follows:(1)The QNMs associatedwith the decay of massless arbitrary spin fields around a Schwarzschildblack hole become evenly spaced for large angular quantum number l(for the boson perturbations)and j(for the fermion perturbations),and the spacing isgiven by△_ω=2/3(?)-0.0000i which is independent of the spin number s andovertone number n.It is also shown that the spacing for imaginary part of theQNMs at high overtones is equidistant and equals -1/(4M),which is independentof l(or j)and s.(2)The real part of the QNMs for arbitrary spin fields in thebackground of a SBHGM decreases as the symmetry breaking scale parameter Hincreases but the imaginary part increases instead.For the large overtone numbern,these QNMs become evenly spaced and the spacing for the imaginary partequals -(1-H)^3/2/(4M)which is dependent on H but independent on the quantum number l and spin number s.(3)The massless scalar quasinormal frequenciesof a stationary axisymmetric EMDA black hole move counterclockwise and get a spiral-like shape in the complex plane as the angular momentum per unit massa increases to its extremal value or the dilaton D decreases to its extremal value for the rotating black hole.However,for the non-rotating Garfinkle-Horowitz-Strominger(GHS)dilaton black hole,the dilaton parameter D,which is related tothe electric charge of this EMDA black hole,cannot make the frequencies spire inthe complex plane,which is qualitatively different from the charge of the Reissner-Nordstrom(RN)black hole.The so-call "Spiral-like Criterion" is obtained and itpoints out that the frequencies won't spire in the complex plane if the heat capacity for the considered black hole is always negative and vice versa.It seems to implythat there is some relation between the dynamical evolution and thermodynamicinstabilities for the black hole.The late-time behavior of arbitrary spin fields in the background of a SB-HGM is studied by using the black-hole Green's function method.It is surprisingly found that this late-time behavior is dominated by an inverse power-law tail t^-2[1+(?)] which is dependent on the symmetry breaking scale parameter H and the spin number s for each quantum number l,and asH→0 it reduces to the Schwarzschild case t^-(2l+3) which is independent on s.The entanglement between two modes of free scalar and Dirac fields as seenby two relatively accelerated observers is investigated and the effect of the Hawking temperature on the entanglement and teleportation for the scalar field in amost general,static and asymptotically flat black hole with spherical symmetry isalso analyzed.Our main conclusions are as follows:(1)It is found that the sameinitial entanglement for an initial state parameterαand its "normalized partner"(?) will be degraded by the Unruh effect along two different trajectoriesexcept for the maximally entangled state,which just shows the inequivalence ofthe quantization for a free field in Minkowski and Rindler coordinates.In the infinite-acceleration limit,the state does not have distillable entanglement for anyαfor the scalar field,but always remains entangled to a degree that is dependentonαfor the Dirac field.It is also interesting to note that in this limit the mutualinformation equals just half of the initial mutual information; this result isindependent ofαand the type of field.(2)It is shown that the same initial entanglement for the state parameterαand its "normalized partners"(?) willbe degraded by the Hawking effect with increasing Hawking temperature alongtwo different trajectories except for the maximally entangled state.In the infiniteHawking temperature limit,corresponding to the case of the black hole evaporating completely,the state has no longer distillable entanglement for anyα.It isinteresting to note that the mutual information in this limit equals just half ofthe initial mutual information.It has also been demonstrated that the fidelity ofteleportation decreases as the Hawking temperature increases,which just indicatesthe degradation of entanglement.