Evaluating Quasilocal Energy and Solving Optimal Embedding Equation at Null Infinity

We study the limit of quasilocal energy defined in Wang and Yau (Phys Rev Lett 102(2):021101, 2009; Commun Math Phys 288(3):919–942, 2009) for a family of spacelike 2-surfaces approaching null infinity of an asymptotically flat spacetime. It is shown that Lorentzian symmetry is recovered and an energy-momentum 4-vector is obtained. In particular, the result is consistent with the Bondi–Sachs energy-momentum at a retarded time. The quasilocal mass in Wang and Yau (Phys Rev Lett 102(2):021101, 2009; Commun Math Phys 288(3):919–942, 2009) is defined by minimizing quasilocal energy among admissible isometric embeddings and observers. The solvability of the Euler-Lagrange equation for this variational problem is also discussed in both the asymptotically flat and asymptotically null cases. Assuming analyticity, the equation can be solved and the solution is locally minimizing in all orders. In particular, this produces an optimal reference hypersurface in the Minkowski space for the spatial or null exterior region of an asymptotically flat spacetime.     

Probability of inflation in loop quantum cosmology

Inflationary models of the early universe provide a natural mechanism for the formation of large scale structure. This success brings to forefront the question of naturalness: Does a sufficiently long slow roll inflation occur generically or does it require a careful fine tuning of initial parameters? In recent years there has been considerable controversy on this issue (Hollands and Wald in Gen Relativ Gravit, 34:2043, 2002; Kofman et al. in J High Energy Phys 10:057, 2002); (Gibbons and Turok in Phys Rev D 77:063516, 2008). In particular, for a quadratic potential, Kofman et al. (J High Energy Phys 10:057, 2002) have argued that the probability of inflation with at least 65 e-foldings is close to one, while Gibbons and Turok (Phys Rev D 77:063516, 2008) have argued that this probability is suppressed by a factor of ~10⁻⁸⁵. We first clarify that such dramatically different predictions can arise because the required measure on the space of solutions is intrinsically ambiguous in general relativity. We then show that this ambiguity can be naturally resolved in loop quantum cosmology (LQC) because the big bang is replaced by a big bounce and the bounce surface can be used to introduce the structure necessary to specify a satisfactory measure. The second goal of the paper is to present a detailed analysis of the inflationary dynamics of LQC using analytical and numerical methods. By combining this information with the measure on the space of solutions, we address a sharper question than those investigated in Kofman et al. (J High Energy Phys 10:057, 2002), Gibbons and Turok (Phys Rev D 77:063516, 2008), Ashtekar and Sloan (Phys Lett B 694:108, 2010): What is the probability of a sufficiently long slow roll inflation which is compatible with the seven year WMAP data? We show that the probability is very close to 1. The material is so organized that cosmologists who may be more interested in the inflationary dynamics in LQC than in the subtleties associated with measures can skip that material without loss of continuity.     

Black Hole Entropy: From Shannon to Bekenstein

In this note we have applied directly the Shannon formula for information theory entropy to derive the Black Hole (Bekenstein-Hawking) entropy. Our analysis is semi-classical in nature since we use the (recently proposed Banerjee in Int. J. Mod. Phys. D 19:2365–2369, 2010 and Banerjee and Majhi in Phys. Rev. D 81:124006, 2010; Phys. Rev. D 79:064024, 2009; Phys. Lett. B 675:243, 2009) quantum mechanical near horizon mode functions to compute the tunneling probability that goes in to the Shannon formula, following the general idea of Brillouin (Science and Information Theory, Dover, New York, 2004). Our framework conforms to the information theoretic origin of Black Hole entropy, as originally proposed by Bekenstein.     

Plane Symmetric Vacuum Bianchi Type-III Cosmological Model in Brans-Dicke Theory

We have obtained an exact solution of the vacuum Brans-Dicke (Phys. Rev. 124:925, 1961) field equations for the metric tensor of a spatially homogeneous and anisotropic model. Some physical properties of the model are also studied.     

Stabilizer Notation for Spekkens’ Toy Theory

Spekkens has introduced a toy theory (Spekkens in Phys. Rev. A 75(3):032110, 2007) in order to argue for an epistemic view of quantum states. I describe a notation for the theory (excluding certain joint measurements) which makes its similarities and differences with the quantum mechanics of stabilizer states clear. Given an application of the qubit stabilizer formalism, it is often entirely straightforward to construct an analogous application of the notation to the toy theory. This assists calculations within the toy theory, for example of the number of possible states and transformations, and enables superpositions to be defined for composite systems.     

Cylindrically Symmetric Scalar Field and it’s Lyapunov stability in General Relativity

In this paper we found an Exact solution for massless scalar field with cosmological constant. This exact solution generalized the Levi-Civita vacuum solution Levi-Civita (Rend. Acc. Lincei 27:183, 1917) to a massless scalar field, with a cosmological constant term.This solution in the absence of the Cosmological constant recovers the spacetime of a massless scalar field with cylindrical symmetry (Buchdahl metric (Buchdahl in Phys. Rev. 115:1325, 1959)). Also if the scalar field disappears, the spacetime will be a representation of de-Sitter space.We prove that the form of the metric’s function which was purposed in Momeni and Miraghaei (Int. J. Mod. Phys. A 24(31):5991, 2009) is valid even if we assume a general form. Furthermore we show that in which conditions this solution satisfies energy conditions. Finally the credibility of focusing theorem is proved.     

A Generalization of Scaling Models of Turbulence

We report on some implications of the theory of turbulence developed by V. Yakhot (Phys. Rev. E 57(2):1737, 1998). In particular we focus on the expression for the scaling exponents ζ _n . We show that Yakhot’s result contains three well known scaling models as special cases, namely K41, K62 and the theory by V. L’vov and I. Procaccia (Phys. Rev. E 62(6):8037, 2000). The model furthermore yields a theoretical justification for the method of extended self-similarity (ESS).     

Unconventional Geometric Quantum Computation in?a?Dissipative Cavity QED System Without the Heating

We improve the scheme of geometric quantum phase gate (Chen et al. in Phys. Rev. A 74:032328, 2006) by using double-Hamiltonian evolution technique to remove the photon fluctuation in the cavity mode during the gating. We also shows that when the classical laser intensity is fixed, our gating time may be shorter than that in the ideal case due to the introduction of the cavity mode decay, although the dissipation decreases the corresponding fidelity and the success probability of the gate.     

Triangle Percolation in Mean Field Random Graphs—with PDE

We apply a PDE-based method to deduce the critical time and the size of the giant component of the “triangle percolation” on the Erdős-Rényi random graph process investigated by Derényi, Palla and Vicsek in (Phys. Rev. Lett. 94:160202, [2005]; J. Stat. Phys. 128:219–227, [2007]).     

A Higher Dimensional Cosmic Domain Wall in Brans-Dicke Theory of Gravitation

Five dimensional Kaluza-Klein Space-time is considered in the presence of thick domain walls in the scalar-tensor theory formulated by Brans and Dicke (Phys. Rev. 124:925, 1961). Exact cosmological model, in this theory, is presented with the help of special law of variation proposed by Berman (Nuovo Cim. B 74:182, 1983) for Hubble’s parameter. Some physical and kinematical properties of the model are also discussed.