Hawking Radiation And Black Hole Entropy

The black hole theory have achieved remarkable success since Hawking radiation was discovered in 1970s. Although the existence of black hole is not confirmed now, the property of black hole fling down a challenge to the basic concept of physics and philosophy, which will surely become a landmark in the history of science。The thesis introduced the background of Hawking radiation and its twin brothers-information puzzle, namely, the pure quantum state is translated into mixed thermal state, which violates the underlying unitary theory. The method of Per Kraus, which is regarded as an candidate to resolve information puzzle, shows that Hawking radiation can be consid-ered as a tunneling process and the barrier is defined by the tunneling particle itself. Per Kraus investigated Hawking radiation as massless particles tunneling in Schwarzschild and Reissner-Nordstrom black holes. The result shows that the tunneling rate is related to the change of Bekenstein-Hawking entropy and the derived emission spectrum deviates from the pure thermal spectrum, but is consistent with an underlying unitary theory. The thesis will introduce many excellent work to extend the method of Per Kraus to the other black hole spacetime. The Hamilton Jacobi approach shows that the value of black hole temperature is twice as before with the method of Per Kraus. In order to deal with this problem, the thesis introduce the Isotropic coordinates and take into account the contribution of ingoing solution to the action, then the standard Hawking temperature is achieved. At the same time, the thesis point out that the imaginary part of action for ingoing particles is zero in the Painleve-Gullstrand coordinates.The property of black hole entropy is introduced in chapter two. Based on the second law of thermodynamics, black hole entropy, which will never decrease with time, equal to a quarter of black hole area. There are disturbing field around black hole, so it is hard for black hole to achieve equilibrium with itself. Generally speaking, a logarithmic correction term will be exist in the black hole entropy formula based on the effect of disturbing field. The coefficient of correction term can be regarded as model-dependent parameters. the thesis use the Laplace method to calculate black hole entropy corrections with thermal fluctuations in canonical ensemble, which allows black hole to exchange energy with surrounds. Another method shows that if we put black hole in a cavity of finite radius by immersing it in an isothermal bath, then the thermal equilibrium will be achieved between the black hole and surroundings. We extend this method to various black hole spacetime, then some interesting result is obtained. Finally, the thesis show that the observer in servo-coordinates will find that the value of black hole entropy is related to the position himself under the thermal fluctuations in Schwarzschild black holes.In the end of thesis, the thesis introduced the generalized uncertainty principle(GUP). It is shown that the GUP reduces to the conventional Heisenberg relation in situations of weak gravity but transcends it when gravitational effects can no longer be ignored. The GUP implies that there are a lower bound limit on the uncertainty in position. Based on GUP, the thesis investigate the quantum fluctuations on black hole entropy and tempera-ture in Schwarzschild black holes. Next, the thesis will introduce the extended uncertainty principle(EUP), the generalized extended uncertainty principle(GEUP) and the modified dis-persion relations(MDR), then the thesis extend these theory to investigate the property of black holes. Many excellent results are obtained.