International Journal of Geometric Methods in Modern Physics

In this paper, we consider interacting closed string tachyon with generalized cosmic Chaplygin gas as a cosmological model of Universe. We obtained cosmological parameters and discuss about fixed point for stability analysis. We find appropriate conditions where the theory is stable.

In its geometric form, the Maupertuis Principle states that the movement of a classical particle in an external potential V(x) can be understood as a free movement in a curved space with the metric g_μν(x) = 2M[V(x) - E]δ_μν. We extend this principle to the quantum regime by showing that the wavefunction of the particle is governed by a Schrödinger equation of a free particle moving through curved space. The kinetic operator is the Weyl-invariant Laplace–Beltrami operator. On the basis of this observation, we calculate the semiclassical expansion of the particle density.

We show that the metric (line element) is the first geometrical object to be associated to a discrete (quantum) structure of the spacetime without necessity of black hole-entropy-area arguments, in sharp contrast with other attempts in the literature. To this end, an emergent metric solution obtained previously in [ Phys. Lett. B661 (2008) 186–191] from a particular non-degenerate Riemannian superspace is introduced. This emergent metric is described by a physical coherent state belonging to the metaplectic group Mp(n) with a Poissonian distribution at lower n (number basis) restoring the classical thermal continuum behavior at large n(n → ∞), or leading to non-classical radiation states, as is conjectured in a quite general basis by means of the Bekenstein–Mukhanov effect. Group-dependent conditions that control the behavior of the macroscopic regime spectrum (thermal or not), as the relationship with the problem of area/entropy of the black hole are presented and discussed.

It has been argued that gravity acts dissipatively on quantum-mechanical systems, inducing thermal fluctuations that become indistinguishable from quantum fluctuations. This has led some authors to demand that some form of time irreversibility be incorporated into the formalism of quantum mechanics. As a tool toward this goal, we propose a thermodynamical approach to quantum mechanics, based on Onsager's classical theory of irreversible processes and Prigogine's nonunitary transformation theory. An entropy operator replaces the Hamiltonian as the generator of evolution. The canonically conjugate variable corresponding to the entropy is a dimensionless evolution parameter. Contrary to the Hamiltonian, the entropy operator is not a conserved Noether charge. Our construction succeeds in implementing gravitationally-induced irreversibility in the quantum theory.

In this paper, we extend the almost complex Poisson structures from almost complex manifolds to almost complex Lie algebroids. Examples of such structures are also given and the almost complex Poisson morphisms of almost complex Lie algebroids are studied.

We introduce the new algebraic property of Weyl compatibility for symmetric tensors and vectors. It is strictly related to Riemann compatibility, which generalizes the Codazzi condition while preserving much of its geometric implications. In particular, it is shown that the existence of a Weyl compatible vector implies that the Weyl tensor is algebraically special, and it is a necessary and sufficient condition for the magnetic part to vanish. Some theorems (Derdziński and Shen [11], Hall [15]) are extended to the broader hypothesis of Weyl or Riemann compatibility. Weyl compatibility includes conditions that were investigated in the literature of general relativity (as in McIntosh et al. [16, 17]). A simple example of Weyl compatible tensor is the Ricci tensor of an hypersurface in a manifold with constant curvature.

We investigate a general class of equations of state reproducing the dark energy effects in terms of geometric considerations on thermodynamic interaction. We infer cosmological solutions by combining thermodynamics with contact manifold and Riemannian geometry, showing that the standard ΛCDM model can be treated as a limiting case of a more general approach, providing early time departures as the universe expands. Thus, we interpret the microscopic nature of dark energy through the mathematical formalism of geometrothermodynamics (GTD). In particular, we investigate the thermodynamic nature of a class of cosmological models which reproduce how the universe is currently speeding up. To do so, we aim to describe thermodynamic equilibrium states of the universe through a particular equilibrium space, where the Riemannian metric g becomes a thermodynamical ruler between different states. The particular assumption we made is to consider the metric structure to be invariant under precise Legendre transformations. It turns out that any thermodynamic interaction is determined once the scalar curvature of the equilibrium manifold is known. The consequence of our recipe leads to a class of dark energy equations of state which relates standard pressure to the volume occupied by the fluid itself. In our picture, dark energy is thus determined from constant thermodynamic interaction on the manifold of GTD.

We adopt the Dirac–Detweiler–Whiting radiative and regular effective field in curved spacetime. Thereby, we derive straightforwardly the first order perturbative correction to the geodesic of the background in a covariant form, for the extreme mass ratio two-body problem. The correction contains the self-force contribution and a background metric-dependent term.

We will consider the least-order torsional completion of gravity for a spacetime filled with fermionic Dirac matter fields, and we study the effects of the background-induced nonlinear potentials for the matter field themselves, in terms of their effects for both standard models of physics: from the one of cosmology to that of particles, we will discuss the mechanisms of generation of the cosmological constant and particles masses as well as the phenomenology of leptonic weak-like forces and neutrino oscillations, the problem of zero-point energy, how there can be neutral massive fields as candidates for dark matter, and the avoidance of gravitationally-induced singularity formation; we will show the way in which all these different effects can nevertheless be altogether described in terms of just a single model, which will be discussed in the beginning.

In this paper, we analyze the Hawking radiation (HR) of a non-asymptotically flat (NAF) dyonic black hole (dBH) in four-dimensional (4D) Einstein–Maxwell–Dilaton (EMD) gravity by using one of the semiclassical approaches which is the so-called Hamilton–Jacobi (HJ) method. We particularly motivate on the isotropic coordinate system (ICS) of the dBH in order to highlight the ambiguity to be appeared in the derivation of the Hawking temperature (T_H) via the HJ method. Besides, it will be shown that the ICS allows us to write the metric of the dBH in form of the Fermat metric, which renders possible of identification of the refractive index (n) of the dBH. It is unraveled that the value of n and therefore the gravitational lensing effect is decisive on the tunneling rate of the HR. We also uncloak how one can resolve the discrepancy about the T_H of the dBH in spite of that lensing effect.

M2-branes couple to a 3-form potential, which suggests that their description involves a non-abelian 2-gerbe or, equivalently, a principal 3-bundle. We show that current M2-brane models fit this expectation: they can be reformulated as higher gauge theories on such categorified bundles. We thus add to the still very sparse list of physically interesting higher gauge theories.

A generalization of 8-dimensional multiply-warped product manifolds is considered as a special warped product, by allowing the fiber metric to be non-block diagonal. Motivating from the previous paper [S. Uğuz and A. H. Bilge, (3 + 3 + 2) warped-like product manifolds with Spin(7) holonomy, J. Geom. Phys.61 (2011) 1093–1103], we present a special warped product as a (4 + 3 + 1) warped-like manifold of the form M = F × B, where the base B is a 1-dimensional Riemannian manifold, and the fiber F is of the form F = F₁ × F₂ where F_i's (i = 1, 2) are Riemannian 4- and 3-manifolds, respectively. It is showed that the connection on M is entirely determined provided that the Bonan 4-form is closed. Assuming that the F_i's are complete, connected and simply connected, it is proved that the 3-dimensional fiber is isometric to S³ with constant curvature k > 0. Finally, the geometric properties of the 4-dimensional fiber of M are studied.

Motivated by the newly proposal for gravity as the effect of the torsion scalar T and trace of the energy momentum tensor 𝒯, we investigate the cosmological reconstruction of different models of the Universe. Our aim here is to show that how this modified gravity model, f(T, 𝒯) is able to reproduce different epochs of the cosmological history. We explicitly show that f(T, 𝒯) can be reconstructed for ΛCDM as the most popular and consistent model. Also we study the mathematical reconstruction of f(T, 𝒯) for a flat cosmological background filled by two fluids mixture. Such model describes phantom–non-phantom era as well as the purely phantom cosmology. We extend our investigation to more cosmological models like perfect fluid, Chaplygin gas and massless scalar field. In each case we obtain some specific forms of f(T, 𝒯). These families of f(T, 𝒯) contain arbitrary function of torsion and trace of the energy momentum.