The evolution of Brown–York quasilocal energy as due to evolution of Lovelock gravity in a system of M0-branes

Abstract

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 [Formula: see text]-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, [Formula: see text]-branes join each other and form an [Formula: see text]-brane and an anti-[Formula: see text]-branes connected by an [Formula: see text]-brane. This system is named BIon. Universes and anti-universes live on [Formula: see text]-branes and [Formula: see text] plays the role of wormhole between them. By passing time, [Formula: see text] dissolves in [Formula: see text]’s and nonlinear massive gravities like Lovelock massive gravity emerges and grows. By closing [Formula: see text]-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 [Formula: see text]-branes towards each other, the square energy of their system becomes negative and some tachyonic states are produced. To remove these states, [Formula: see text]-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 [Formula: see text] between [Formula: see text]-branes. By getting away of branes from each other, Brown–York energy decreases and shrinks to zero.