Minisuperspace Models in M-theory

We derive the full canonical formulation of the bosonic sector of 11-dimensional supergravity, and explicitly present the constraint algebra. We then compactify M-theory on a warped product of homogeneous spaces of constant curvature, and construct a minisuperspace of scale factors. First classical behaviour of the minisuperspace system is analysed, and then a quantum theory is constructed. It turns out that there similarities with the "pre-Big Bang" scenario in String Theory.Comment: 35 pages, 2 figures, added additional discussion of gauge fixing and self-adjointness of the Hamiltonian, added reference

Nonmetricity and torsion induced by dilaton gravity in two dimension

We develop a theory in which there are couplings amongst Dirac spinor, dilaton and non-Riemannian gravity and explore the nature of connection-induced dilaton couplings to gravity and Dirac spinor when the theory is reformulated in terms of the Levi-Civita connection. After presenting some exact solutions without spinors, we investigate the minimal spinor couplings to the model and in conclusion we can not find any nontrivial dilaton couplings to spinor.Comment: Added references, Accepted for publication in GR

Competing PT potentials and re-entrant PT symmetric phase for a particle in a box

We investigate the effects of competition between two complex, $\mathcal{PT}$-symmetric potentials on the $\mathcal{PT}$-symmetric phase of a "particle in a box". These potentials, given by $V_Z(x)=iZ\mathrm{sign}(x)$ and $V_\xi(x)=i\xi[\delta(x-a)-\delta(x+a)]$, represent long-range and localized gain/loss regions respectively. We obtain the $\mathcal{PT}$-symmetric phase in the $(Z,\xi)$ plane, and find that for locations $\pm a$ near the edge of the box, the $\mathcal{PT}$-symmetric phase is strengthened by additional losses to the loss region. We also predict that a broken $\mathcal{PT}$-symmetry will be restored by increasing the strength $\xi$ of the localized potential. By comparing the results for this problem and its lattice counterpart, we show that a robust $\mathcal{PT}$-symmetric phase in the continuum is consistent with the fragile phase on the lattice. Our results demonstrate that systems with multiple, $\mathcal{PT}$-symmetric potentials show unique, unexpected properties.Comment: 7 pages, 3 figure

Complex solitons with real energies

Using Hirota’s direct method and Bäcklund transformations we construct explicit complex one and two-soliton solutions to the complex Korteweg-de Vries equation, the complex modified Korteweg-de Vries equation and the complex sine-Gordon equation. The one-soliton solutions of trigonometric and elliptic type turn out to be PT -symmetric when a constant of integration is chosen to be purely imaginary with one special choice corresponding to solutions recently found by Khare and Saxena. We show that alternatively complex PT -symmetric solutions to the Korteweg-de Vries equation may also be constructed alternatively from real solutions to the modified Korteweg-de Vries by means of Miura transformations. The multi-soliton solutions obtained from Hirota’s method break the PT -symmetric, whereas those obtained from Bäcklund transformations are PT -invariant under certain conditions. Despite the fact that some of the Hamiltonian densities are non-Hermitian, the total energy is found to be positive in all cases, that is irrespective of whether they are PT -symmetric or not. The reason is that the symmetry can be restored by suitable shifts in space-time and the fact that any of our N-soliton solutions may be decomposed into N separate PT -symmetrizable one-soliton solutions

Entropic corrections to Newton's law

In this short letter we calculate separately the generalized uncertainty principle (GUP) and self gravitational corrections to the Newton's gravitational formula. We show that for a complete description of the GUP and self-gravity effects, both temperature and the entropy must be modified.Comment: 4 pages, Accepted for publication in "Physica Scripta",Title changed, Major revisio

Using the gibbs function as a measure of human brain development trends from fetal stage to advanced age

We propose to use a Gibbs free energy function as a measure of the human brain development. We adopt this approach to the development of the human brain over the human lifespan: from a prenatal stage to advanced age. We used proteomic expression data with the Gibbs free energy to quantify human brain’s protein–protein interaction networks. The data, obtained from BioGRID, comprised tissue samples from the 16 main brain areas, at different ages, of 57 post-mortem human brains. We found a consistent functional dependence of the Gibbs free energies on age for most of the areas and both sexes. A significant upward trend in the Gibbs function was found during the fetal stages, which is followed by a sharp drop at birth with a subsequent period of relative stability and a final upward trend toward advanced age. We interpret these data in terms of structure formation followed by its stabilization and eventual deterioration. Furthermore, gender data analysis has uncovered the existence of functional differences, showing male Gibbs function values lower than female at prenatal and neonatal ages, which become higher at ages 8 to 40 and finally converging at late adulthood with the corresponding female Gibbs functions

Brane decay of a (4+n)-dimensional rotating black hole: spin-0 particles

In this work, we study the `scalar channel' of the emission of Hawking radiation from a (4+n)-dimensional, rotating black hole on the brane. We numerically solve both the radial and angular part of the equation of motion for the scalar field, and determine the exact values of the absorption probability and of the spheroidal harmonics, respectively. With these, we calculate the particle, energy and angular momentum emission rates, as well as the angular variation in the flux and power spectra -- a distinctive feature of emission during the spin-down phase of the life of the produced black hole. Our analysis is free from any approximations, with our results being valid for arbitrarily large values of the energy of the emitted particle, angular momentum of the black hole and dimensionality of spacetime. We finally compute the total emissivities for the number of particles, energy and angular momentum and compare their relative behaviour for different values of the parameters of the theory.Comment: 24 pages, 13 figure

Horizon Formation in High-Energy Particles Collision

We investigate a classical formation of a trapped surface in 4-dimensional flat space-time in a process of a non-head-on collision of two high-energy particles which are treated as Aichelburg-Sexl shock waves. From the condition of the horizon volume local maximality an equation for the trapped surface is deduced. Using a known solution on the shocks we find a time-dependent solution describing the trapped surface between the shocks. We analyze the horizon appearance and evolution. Obtained results may describe qualitatively the horizon formation in higher dimensional space-time.Comment: Latex2e, 8 pages, 6 figures, references adde

A Fermi Gamma-Ray Burst Monitor Search for Electromagnetic Signals Coincident with Gravitational-Wave Candidates in Advanced LIGO\u27s First Observing Run

We present a search for prompt gamma-ray counterparts to compact binary coalescence gravitational wave (GW) candidates from Advanced LIGO\u27s first observing run (O1). As demonstrated by the multimessenger observations of GW170817/GRB 170817A, electromagnetic and GW observations provide complementary information about the astrophysical source, and in the case of weaker candidates, may strengthen the case for an astrophysical origin. Here we investigate low-significance GW candidates from the O1 compact binary coalescence searches using the Fermi Gamma-Ray Burst Monitor (GBM), leveraging its all sky and broad energy coverage. Candidates are ranked and compared to background to measure the significance. Those with false alarm rates (FARs) of less than 10-55 Hz (about one per day, yielding a total of 81 candidates) are used as the search sample for gamma-ray follow-up. No GW candidates were found to be coincident with gamma-ray transients independently identified by blind searches of the GBM data. In addition, GW candidate event times were followed up by a separate targeted search of GBM data. Among the resulting GBM events, the two with the lowest FARs were the gamma-ray transient GW150914-GBM presented in Connaughton et al. and a solar flare in chance coincidence with a GW candidate