Entropy Of Sonic Black Hole Via The Brick Wall Model And Quantum Entanglement Under Lorentz Transformation

In this dissertation, two problems are inverstigated:we calculate the en-tropy of a four dimension sonic black by using the statistical mechanics, and we calculate the concurrence of two-body quantum state under Lorentz trans-formation.firstly, by using the brick wall method we calculate the free energy and the entropy of the massless and massive scalar field in a sonic black hole. By introducing a cutoff parameter the leading order divergences of the quantum fields can be regulated. Then we can calculate the free energy of the quan-tum fields, and entropy can be derived from the free energy using statistic for-mula. The leading order entropy turns out to be precisely in agreement with the Bekenstein-Hawking entropy(SBH) and the logarithmic correction are derived in the polynomial function of the entropy is the quantum effect.Secondly, We study the properties of quantum entanglement under lorentz transformation. Different from further studies, we find that if the momenta part of the spin-1/2 pair is appropriately correlated, the concurrence is invariant un-der lorentz transformation despite the entanglement of this state is not maximal, there is no transfer of entanglement between spin and momentum.