We investigate the cosmological solutions of the f (T ) gravity theory using the method of dynamical systems. For this purpose a general form of the f (T ) function is considered and three conditions are defined that they have to satisfy in order to describe the standard cosmological history. We examine five specific models of f (T ) gravity and obtained the valid range of their parameters.
We investigate equations of motion and future singularities of f (R, T ) gravity where R is the Ricci scalar and T is the trace of stress-energy tensor. Future singularities for two kinds of equation of state (barotropic perfect fluid and generalized form of equation of state) are studied. While no future singularity is found for the first case, some kind of singularity is found to be possible for the second. We also investigate f (R, T ) gravity by the method of dynamical systems and obtain some fixed points. Finally, the effect of the Noether symmetry on f (R, T ) is studied and the consistent form of f (R, T ) function is found using the symmetry and the conserved charge.
We formulate mimetic theory in f (T ) teleparallel gravity where T is torsion scalar. It is shown that the construction of the mimetic theory in the teleparallel gravity requires the vierbeins to be left unchanged and the conformal transformation performed on the Minkowski metric of the tangent space. It is further argued that the conformal degree of freedom in this teleparallel mimetic theory becomes dynamical and mimics the behavior of cold dark matter. We also show that it is possible to employ the Lagrange multipliers method to formulate the mimetic theory in an f (T ) theory without any auxiliary metric. The mimetic f (T ) theory is examined by the method of dynamical system and it is found that there are five fixed points representing inflation, radiation, matter, mimetic dark matter and dark energy dominated eras in the theory if some conditions are satisfied. We examined the power-law model and its phase trajectories with these conditions.
It is known that the emission rate of entropy from a Schwarzschild black hole is exactly the same as that of a one dimensional quantum channel [1]. We calculate the dimension of entropy emission from a D dimensional pure Lovelock black holes. Our results indicate that the dimension of transmission for odd D dimensional space-times is equal to D and for even D dimensional spacetimes, the dimension of quantum channel becomes 1 + ǫ(Λ), where Λ is cosmological constant. It is interesting that cosmological constant may put some constraint on dimension of quantum channel in even dimensional space-times. The effect of Generalized Uncertainty Principle (GUP) on the dimension of transmission of entropy for a Schwarzschild black hole is also investigated.
In this paper, we generalize Ehrenfest's equations to systems having two work terms, i.e. systems with three degrees of freedom. For black holes with two work terms we obtain nine equations instead of two to be satisfied at the critical point of a second-order phase transition. We finally generalize this method to a system with an arbitrary number of degrees of freedom and found there is N(N+1) 2 2 equations to be satisfied at the point of a second-order phase transition where N is number of work terms in the first law of thermodynamics.
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