arXiv subjects
Publications and source records attributed to Mustapha Azreg-Aïnou.
We show that the range of applicability of the change of representation formula derived in J. Math. Phys. \textbf{54}, 033513 (2013) [arXiv:1302.6928] is very narrow and extend it to include all physical applications, particularly, applications to black hole thermodynamics, cosmology and fluid thermodynamics.
We investigate the empirical data for the vapor pressure (154$ \leq$$T$$\leq$196 K) and heat capacity (15.52$ \leq$$T$$\leq$189.78 K) of the solid carbon dioxide. The approach is both theoretical and numerical, using a computer algebra system (CAS). From the latter point of view, we have adopted a cubic piecewise polynomial representation for the heat capacity and reached an excellent agreement between the available empirical data and the evaluated one. Furthermore, we have obtained values for the vapor pressure and heat of sublimation at temperatures below 195 right down to 0 K. The key prerequisites are the: 1) Determination of the heat of sublimation of 26250 J$\cdot$mol\textsuperscript{-1} at vanishing temperature and 2) Elaboration of a `linearized' vapor pressure equation that includes all the relevant properties of the gaseous and solid phases. It is shown that: 1) The empirical vapor pressure equation derived by Giauque & Egan remains valid below the assumed lower limit of 154 K (similar argument holds for Antoine's equation), 2) The heat of sublimation reaches its maximum value of 27211 J$\cdot$mol\textsuperscript{-1} at 58.829 K and 3) The vapor behaves as a (polyatomic) ideal gas for temperatures below 150 K.
Using a new metric for generating rotating solutions, we derive in a general fashion the solution of an imperfect fluid and that of its conformal homolog. We discuss the conditions that the stress-energy tensors and invariant scalars be regular. On classical physical grounds, it is stressed that, conformal fluids used as cores for static or rotating solutions, are exempt from any malicious behavior in that they are finite and defined everywhere.
We show that, for the scalar field cosmology with exponential potential, the set of values of the coupling parameter for which the solutions undergo a transient period of acceleration is much larger than the set discussed in the literature. The gradual inclusion of ordinary and dark matters results in an everywhere, but near the origin, smoother and right shifted (along the time axis) acceleration curve. For the 3-fluid problem, the energy density need not exhibit a plateau during the acceleration period. Much excess in the dark matter and/or ordinary matter energy densities would lead the universe to undergo an eternal deceleration expansion. For the 3-fluid problem with a single exponential potential we conclude that the Big Bang Nucleosynthesis constraint is not fulfilled if the universe is to undergo a transient period of acceleration. The 3-fluid model remains a good approximation for the description of large scale structures.
Properties pertaining to thermodynamical local stability of Reissner-Nordström black holes surrounded by quintessence as well as adiabatic invariance, adiabatic charging and a generalized Smarr formula are discussed. Limits for the entropy, temperature and electric potential ensuring stability of canonical ensembles are determined by the classical thermodynamical and Poincaré methods. By the latter approach we show that microcanonical ensembles (isolated black holes) are stable. Two geometrical approaches lead to determine the same states corresponding to second order phase transitions.
We perform a phase-space analysis of the cosmological 3-fluid problem consisting of a barotropic fluid with an equation-of-state parameter $γ-1$, a pressureless dark matter fluid, plus a scalar field $ϕ$ (representing dark energy) coupled to exponential potential $V=V_0\exp{(-κλϕ)}$. Besides the potential-kinetic-scaling solutions, which are not the unique late-time attractors whenever they exist for $λ^2\geq 3\ga$, we derive new attractors where both dark energy and dark matter coexist and the final density is shared in a way independent of the value of $γ>1$. The case of a pressureless barotropic fluid ($γ=1$) has a one-parameter family of attractors where all components coexist. New one-parameter families of matter-dark matter saddle points and kinetic-matter repellers exist. We investigate the stability of the ten critical points by linearization and/or Lyapunov's Theorems and a variant of the theorems formulated in this paper. A solution with two transient periods of acceleration and two transient periods of deceleration is derived.
Null geodesics of normal and phantom Einstein-Maxwell-dilaton black holes are determined analytically by the Weierstrass elliptic functions. The black hole parameters other than the mass enter, with the appropriate signs, the formula for the angle of deflection to the second order in the inverse of the impact parameter allowing for the identification of the nature of matter (phantom or normal). Such identification is also possible via the time delay formula and observation of relativistic images. Scattering experiencesmay favor black holes of Einstein-anti-Maxwell-dilatonic theory for their high relative discrepancy with respect to the Schwarzschild value. For the cases we restrict ourselves to, phantom black holes are characterized by the absence of many-world and two-world null geodesics.
A parameter-independent notion of stationary slow motion is formulated then applied to the case of stationary rotation of massless trapped ghosts. The excitations correspond to a rotation mode with angular momentum $J\neq 0$ and twist modes. It is found that the rotation mode, which has no parity, causes excess in the angular velocity of dragged distant coordinate frames in one sheet of the wormhole while in the other sheet the angular velocity of the ghosts is that of rotating stars: $2J/r^3$. As to the twist modes, which all have parity, they cause excess in the angular velocity of one of the throat's poles with respect to the other.
We construct explicitly all extremal instanton solutions to $\mathcal{N}=4,\, D=4$ supergravity truncated to one vector field (Einstein-Maxwell-dilaton-axion (EMDA) theory). These correspond to null geodesics of the target space of the sigma-model $G/H=Sp(4,\mathbb{R})/GL(2,\mathbb{R})$ obtained by compactification of four-dimensional Euclidean EMDA on a circle. They satisfy a no-force condition in terms of the asymptotic charges and part of them (corresponding to nilpotent orbits of the $Sp(4,\mathbb{R})$ U-duality) are presumably supersymmetric. The space of finite action solutions is found to be unexpectedly large and includes, besides the Euclidean versions of known Lorentzian solutions, a number of new asymptotically locally flat (ALF) instantons endowed with electric, magnetic, dilaton and axion charges. We also describe new classes of charged asymptotically locally Euclidean (ALE) instantons as well as some exceptional solutions. Our classification scheme is based on the algebraic classification of matrix generators according to their rank, according to the nature of the charge vectors and according to the number of independent harmonic functions with unequal charges. Besides the nilpotent orbits of $G$, we find solutions which satisfy the asymptotic no-force condition, but are not supersymmetric. The renormalized on-shell action for instantons is calculated using the method of matched background subtraction.
We review the derivations and conclusions made in Caravelli and Modesto (2010 \textit{Class. Quantum Grav.} \textbf{27} 245022, arXiv:1006.0232) and show that most of the analysis performed there is not valid.
We construct static multicenter solutions of phantom Einstein-Maxwell-dilaton theory from null geodesics of the target space, leading to regular black holes without spatial symmetry for certain discrete values of the dilaton coupling constant. We also discuss the three-dimensional gravitating sigma models obtained by reduction of phantom Einstein-Maxwell, phantom Kaluza-Klein and phantom Einstein-Maxwell-dilaton-axion theories. In each case, we generate by group transformations phantom charged black hole solutions from a neutral seed.
We develop and modify the Adomian decomposition method (ADecM) to work for a new type of nonlinear matrix differential equations (MDE's) which arise in general relativity (GR) and possibly in other applications. The approach consists in modifying both the ADecM linear operator with highest order derivative and ADecM polynomials. We specialize in the case of a 4$\times$4 nonlinear MDE along with a scalar one describing stationary cylindrically symmetric metrics in quadratic 5-dimensional GR, derive some of their properties using ADecM and construct the \textit{most general unique power series solutions}. However, because of the constraint imposed on the MDE by the scalar one, the series solutions terminate in closed forms exhausting all possible solutions.
We make a systematic investigation of the generic properties of static, spherically symmetric, asymptotically flat solutions to the field equations describing gravity minimally coupled to a nonlinear self-gravitating real scalar field. Seven corollaries and a theorem on selection criteria for two- and one-parametric solutions are proven and conditions for obtaining particle-like solution, black holes or naked singularities are derived. A series of exact solutions in closed forms describing different black holes, naked singularities and particle-like solutions are provided.
It has been shown that 5-dimensional general relativity action extended by appropriate quadratic terms admits a singular superconducting cosmic string solution. We search for cosmic strings endowed with similar and extended physical properties by directly integrating the non-linear matrix field equations thus avoiding the perturbative approach by which we constructed the above-mentioned \textsl{exact} solution. The most general superconducting cosmic string, subject to some constraints, will be derived and shown to be mathematically \textsl{unique} up to linear coordinate transformations mixing its Killing vectors. The most general solution, however, is not globally equivalent to the old one due to the existence of Killing vectors with closed orbits.