Narrow Results

Recently, the quantum spectrum of black holes has been considered. We will show that this spectrum depends on the shape of manifolds that form black holes. For example, black holes with heptagonal shapes have more energy and less temperature with respect to the ones with pentagonal or hexagonal shapes.

Recently, it has been suggested in [S. Chakraborty and N. Dadhich, Brown–York quasilocal energy in Lanczos–Lovelock gravity and black hole horizons, J. High Energ. Phys.12 (2015) 003.] that the Brown–York mechanism can be used to measure the quasilocal energy in Lovelock gravity. We have used this method in a system of $M0$-branes and show that the Brown–York energy evolves in the process of birth and growth of Lovelock gravity. This can help us to predict phenomenological events which are emerged as due to dynamical structure of Lovelock gravity in our universe. In this model, first, $M0$-branes join each other and form an $M3$-brane and an anti-$M3$-branes connected by an $M2$-brane. This system is named BIon. Universes and anti-universes live on $M3$-branes and $M2$ plays the role of wormhole between them. By passing time, $M2$ dissolves in $M3$’s and nonlinear massive gravities like Lovelock massive gravity emerges and grows. By closing $M3$-branes, BIon evolves and wormhole between branes makes a transition to black hole. During this stage, Brown–York energy increases and shrinks to large values at the colliding points of branes. By approaching $M3$-branes towards each other, the square energy of their system becomes negative and some tachyonic states are produced. To remove these states, $M3$-branes compact, the sign of compacted gravity changes, anti-gravity is created which leads to getting away of branes from each other. Also, the Lovelock gravity disappears and its energy forms a new $M2$ between $M3$-branes. By getting away of branes from each other, Brown–York energy decreases and shrinks to zero.

It was shown that both Lovelock gravity and Born–Infeld (BI) electrodynamics can be obtained from low effective limit of string theory. Motivated by the mentioned unique origin of the gauge-gravity theories, we are going to find a close relation between them. In this research, we start from the Lagrangian of a BI-type nonlinear electrodynamics with an exponential form to extract the action of Lovelock gravity. We investigate the origin of Lovelock gravity in a system of branes which are connected with each other by different wormholes through a BIonic system. These wormholes are produced as due to the nonlinear electrodynamics which are emerged on the interacting branes. By approaching branes, wormholes dissolve into branes and Lovelock gravity is generated. Also, throats of some wormholes become smaller than their horizons and they transit to black holes. Generalizing calculations to M-theory, it is found that by compacting Mp-branes, Lovelock gravity changes to nonlinear electrodynamics and thus both of them have the same origin. This result is consistent with the prediction of BIonic model in string theory.

Recently, the role of energy conditions in $f(R)$-cosmology has been investigated. We generalize these results to BIonic systems in accelerating systems and show that the energy conditions can be changed in this system. We show that $f(R)$-gravity produces a wormhole between two universes and forms a BIonic system. On the other hand, the acceleration creates two regions in the Rindler space-time which BIon in each region acts reverse to other in another region. This means that by the expansion of universes of the BIon in one region, universes of another BIon in other regions contract. Also, in this model, by increasing the order of curvatures in $f(R)$-gravity, the energy and the entropy of system in one region increases and in other region decreases. Amount of this growth or decrease in the energy depends on the acceleration of universes. Finally, by calculating the dark energy equation of state, we observe that one universe enters to phantom phase and goes toward the big rip singularity and another goes out of phantom state.