Lovelock,-born-infeld Black Holes And Their Thermodynamic Study

As present in the Principle of Cosmology, the Universe is uniform and isotropic in the larger scalar of universe. Dark matter and dark energy are the large part of the total universal energy. The black hole, which is a theoretical model of the Dark matter, is well concern. In the study of super String/M theory, Lagrangian of Lovelock Gravity presents some useful corrections. Therefore, higher-dimensional gravity attracts physicists'attention to research deeply.In this paper, we talk about the higher-dimensional Lovelock gravity:the third order Lovelock Lagrangian coupling with non-line Born-Infeld electromagnetic field, calculating the solution and the thermodynamics of black hole, then stability of the black hole will be discussed on the different cosmological strcture k= 0,1,-1 in 7-dimensinal AdS space-time. Finally, using the correlated Hawking radiation, the correlation of two successive emissions and the information loss will be discussed.At first, inserting the metric into the Lagrangian of Lovelock-Born-Infeld gravity, the gravitational field equation and electromagnetic field equation will be obtained by varying it. Secondly, the general black hole solution will be easy to acquire and the thermodynamics of black hole are established depending on the black hole solution based on the special coefficient 3α3=α22=α2. On the different cosmological structure of 7-dimensional AdS space-time, the extremal black holes are existed in the case k=0,1. The discussions of black hole stability show that coefficients p,β,ιgive contributions to the heat capacity but do not change the trend. In the case k=0, the black hole is always stable. In the case k≠0, a black hole with a certain large horizon depending on the black hole mass will be stable in which heat capacity will be always positive. It is worthy mention that there may be small mass black hole in the case k=-1 of 7-dimensional AdS space-time. Finally, in the Hawking radiation of Lovelock-Born-Infeld black hole, the correlation of each two successive emissions is non-vanished by considering the emission is correlated. The total entropy lost in the whole evaporation just equals to the change of black hole from the beginning to the end of the evaporation. Therefore, depending on the correlated emission of the Lovelock-Born-Infeld black evaporation, the information loss paradox vanishes.