Thermodynamics Aspects Of Gravity And Relevant Issues

The thermodynamics aspects of gravity theory are always interesting to theoretical physicists. It looks like that the thermodynamics theory was developed in the19century, following by which people developed the statistics theory, and unltimately discovered the atomic structure. Many people expected the thermodynamics aspects of gravity will also lead a break through in quantum gravity. In this background, the thermodynamics aspects of gravity can be categorised into2classes. One of them is to obtain thermodynamics prop-erties, laws from gravity systems by semi-classical method, or re-explain a gravitational process into a thermodynamics one. The other class reverses the logic. It starts from ther-modynamics and some necessary ansatz, and it leads them to gravity.In this thesis, we introduce the fundamental lore and recent progress about the2classes. Some of them are resolved in this thesis, and others are still open questions.First, we investigate the tunneling method of black hole thermodynamics. Banerjee et al. found that the tunneling method beyond semi-classical approximation would lead to the quantum corrected Hawking temperature. By using the first law of black hole ther-modynamics, they obtained the quantum corrections of black hole entropy. We find that this method has some drawbacks, that the procedures among various black hole models contradict each other, and the quantum corrections of entropy of the AdS black hole and Gauss-Bennet Schwarzschild black hole are erroneous. It is caused by that they made a wrong ansatz, that the undetermined function H is polynomial, and they did not apply the Maxwell relation in black hole thermodynamics in a good manner. We improve this method, and obtain the correct quantum correction of black hole entropy via tunneling method. The leading order of corrected black hole entropy is logarithmic, which is irrelevant to the black hole model. By using the improved tunneling method, we first calculate the quantum correc-tion of the neutral black ring, of which the leading order of the entropy is also logarithmic.Second, we study the possibility of gravity originating from thermodynamics. Ver- linde proposed that, gravity might be an entropic force. As a test particle comes close to a holographic screen, of which the number of degrees of freedom proportional to its area, the entropy stored on holographic screen varies, and an effective interaction will be emer-gent, i. e. Gravity. Following the spirit of Verlinde, we give a mathematical definition of holographic screen-which is an extension of the black hole horizon. Then we deduce the holographic screen thermodynamics analogously to black hole thermodynamics. Further-more, we develop the idea of that the space is also emergent from thermodynamics. We propose that the holographic principle has a new interpretation in entropic force frame, i. e. the area of a system is dependent on its numbers of degrees of freedom. When the numbers of degrees of freedom increase, its boundary area also increases, and then the3rd dimen-sional space is emergent between various holographic screens. These works provide more evidences for the similarity between gravity and thermodynamics vastly.Finally, we discuss some problems in the present achievement of thermodynamics aspects of gravity. People use the Kodama vector to define the conserved charges in time-dependent spherical metrics, and the conserved energy of the Kodama vector is Misner-Sharp energy. We find that the "first law of black hole thermodynamics " corresponding to Misner-Sharp energy violates the Maxwell relation. It indicates that Misner-Sharp energy might not be a pragmatic physical quantity for thermodynamics. There are various quasi-local energies in gravity theory. Should we apply all of them into thermodynamics? It is still under investivation.