Second Class Of Solutions Research Articles

Understanding solutions of the angular Teukolsky equation in the prolate asymptotic limit

Solutions to the Angular Teukolsky Equation have been used to solve various applied problems in physics and are extremely important to black-hole physics, particularly in computing quasinormal modes and in the extreme-mass-ratio inspiral problem. The eigenfunctions of this equation, known as spin-weighted spheroidal functions, are essentially generalizations of both the spin-weighted spherical harmonics and the scalar spheroidal harmonics. While the latter functions are quite well understood analytically, the spin-weighted spheroidal harmonics are only known analytically in the spherical and oblate asymptotic limits. Attempts to understand them in the prolate asymptotic limit have met limited success. Here, we make use of a high-accuracy numerical solution scheme to extensively explore the space of possible prolate solutions and extract analytic asymptotic expansions for the eigenvalues in the prolate asymptotic limit. Somewhat surprisingly, we find two classes of asymptotic behavior. The behavior of one class, referred to as "normal", is in agreement with the leading-order behavior derived analytically in prior work. The second class of solutions was not previously predicted, but solutions in this class are responsible for unexplained behavior seen in previous numerical prolate solutions during the transition to asymptotic behavior. The behavior of solutions in this "anomalous" class is more complicated than that of solutions in the normal class, with the anomalous class separating into different types based on the behavior of the eigenvalues at different asymptotic orders. We explore the question of when anomalous solutions appear and find necessary, but not sufficient conditions for their existence. It is our hope that this extensive numerical investigation of the prolate solutions will inspire and inform new analytic investigations into these important functions.

Black holes with spindles at the horizon

We construct AdS4 × Σ and AdS2 × Σ × {Sigma}_{mathfrak{g}} solutions in F(4) gauged supergravity in six dimensions, where Σ is a two dimensional manifold of non-constant curvature with conical singularities at its two poles, called a spindle, and {Sigma}_{mathfrak{g}} is a constant curvature Riemann surface of genus mathfrak{g} . We find that the first solution realizes a “topologically topological twist”, while the second class of solutions gives rise to an “anti twist”. We compute the holographic free energy of the AdS4 × Σ solution and find that it matches the entropy computed by extremizing an entropy functional that is constructed by gluing gravitational blocks. For the AdS2 × Σ × {Sigma}_{mathfrak{g}} solution, we find that the Bekenstein-Hawking entropy is reproduced by extremizing an appropriately defined entropy functional, which leads us to conjecture that this solution is dual to a three dimensional SCFT on a spindle. A class of the AdS2 × Σ × {Sigma}_{mathfrak{g}} solutions can be embedded in four dimensional T3 gauged supergravity, which is a subtruncation of the six dimensional theory.

Minimal surfaces and generalized Einstein–Maxwell-dilaton theory

We present novel classes of nonstationary solutions to the five-dimensional generalized Einstein–Maxwell-dilaton theory with cosmological constant, in which the Maxwell’s field and the cosmological constant couple to the dilaton field. In the first class of solutions, the two nonzero coupling constants are different, while in the second class of solutions, the two coupling constants are equal to each other. We find consistent cosmological solutions with positive, negative or zero cosmological constant, where the cosmological constant depends on the value of one coupling constant in the theory. Moreover, we discuss the physical properties of the five-dimensional solutions and the uniqueness of the solutions in five dimensions by showing the solutions with different coupling constants cannot be uplifted to any Einstein–Maxwell theory in higher dimensions.

AdS5 compactifications with punctures in massive IIA supergravity

We find AdS5 solutions holographically dual to compactifications of six- dimensional mathcal{N} = (1, 0) supersymmetric field theories on Riemann surfaces with punctures. We simplify a previous analysis of supersymmetric AdS5 IIA solutions, and with a suitable Ansatz we find explicit solutions organized in three classes, where an O8-D8 stack, D6-and D4-branes are simultaneously present, localized and partially localized. The D4-branes are smeared over the Riemann surface and this is interpreted as the presence of a uniform distribution of punctures. For the first class we identify the corresponding six-dimensional theory as an E-string theory coupled to a quiver gauge theory. The second class of solutions lacks D6-branes and its central charge scales as n5/2, suggesting a five-dimensional origin for the dual field theory. The last class has elements of the previous two.

Statistical errors and systematic biases in the calibration of the convective core overshooting with eclipsing binaries

We attempt to constrain the initial helium abundance, the age and the efficiency of the convective core overshooting of the binary system TZ Fornacis. Our main aim is in pointing out the biases in the results due to not accounting for some sources of uncertainty. We adopt the SCEPtER pipeline, relying on stellar models computed with two stellar evolutionary codes (FRANEC and MESA). We found multiple independent groups of solutions. The best one suggests a system of age 1.10 $\pm$ 0.07 Gyr (primary star in the central helium burning stage, secondary in the sub-giant branch), with a helium-to-metal enrichment ratio of $\Delta Y/\Delta Z = 1$ and core overshooting parameter $\beta = 0.15 \pm 0.01$ (FRANEC) and $f_{\rm ov}= 0.013 \pm 0.001 $ (MESA). The second class of solutions, characterised by a worse goodness-of-fit, still suggest a primary star in the central helium-burning stage but a secondary in the overall contraction phase, at the end of the main sequence. The FRANEC grid provides an age of $1.16_{-0.02}^{+0.03}$ Gyr and $\beta = 0.25_{-0.01}^{+0.005}$, while the MESA grid gives $1.23 \pm 0.03$ Gyr and $f_{\rm ov} = 0.025 \pm 0.003$. We also show that very precise mass determinations with uncertainty of a few thousandths of solar mass are required to obtain reliable determinations of stellar parameters, as mass errors larger than approximately 1% lead to estimates that are not only less precise but also biased. Moreover, we show that a fit obtained with a grid of models computed at a fixed $\Delta Y/\Delta Z$ can provide biased age and overshooting estimates. The possibility of independent overshooting efficiencies for the two stars of the system is also explored. This work confirms that to constrain the core overshooting parameter by means of binary systems is a very difficult task that requires an observational precision still rarely achieved and robust statistical methods.

Stability of the Einstein static universe in f(R,\xa0T) gravity

The Einstein static (ES) universe has played a major role in various emergent scenarios recently proposed in order to cure the problem of the initial singularity of the standard model of cosmology. In the model we address, we study the existence and stability of an ES universe in the context of f(R, T) modified theories of gravity. Considering specific forms of the f(R, T) function, we seek for the existence of solutions representing ES state. Using dynamical system techniques along with numerical analysis, we find two classes of solutions: the first one is always unstable of the saddle type, while the second is always stable so that its dynamical behavior corresponds to a center equilibrium point. The importance of the second class of solutions is due to the significant role they play in constructing non-singular emergent models in which the universe could have experienced past-eternally a series of infinite oscillations about such an initial static state after which it enters, through a suitable physical mechanism, to an inflationary era. Considering specific forms for the functionality of f(R, T), we show that this theory is capable of providing cosmological solutions which admit emergent universe (EU) scenarios. We also investigate homogeneous scalar perturbations for the mentioned models. The stability regions of the solutions are parametrized by a linear equation of state (EoS) parameter and other free parameters that will be introduced for the models. Our results suggest that modifications in f(R, T) gravity would lead to stable solutions which are unstable in f(R) gravity model.

New Analytical Solutions for Quark Stars with Charged Anisotropic Matter

In this paper, we found new exact solutions to the Einstein- Maxwell system of equations within the framework of MIT Bag Model considering a particular form for the measure of anisotropy and a gravitational potential which depends on an adjustable parameter α. The first class of solutions has a singularity in the center. The second class of solutions is regular in the stellar interior. Variables as the energy density, radial pressure, tangential pressure, electric field intensity and the metric functions are written in terms of elementary and polinominal functions. We show that the form chosen for the gravitational potential and the anisotropy allows obtain physically acceptable solutions with any value of the adjustable parameter.

Topological black holes for Einstein-Gauss-Bonnet gravity with a nonminimal scalar field

We consider the Einstein-Gauss-Bonnet gravity with a negative cosmological constant together with a source given by a scalar field nonminimally coupled in arbitrary dimension D. For a certain election of the cosmological and Gauss-Bonnet coupling constants, we derive two classes of AdS black hole solutions whose horizon is planar. The first family of black holes obtained for a particular value of the nonminimal coupling parameter only depends on a constant M, and the scalar field vanishes as M=0. The second class of solutions corresponds to a two-parametric (with constants M and A) black hole stealth configuration, that is a nontrivial scalar field with a black hole metric such that both side (gravity and matter parts) of the Einstein equations vanishes. In this case, in the vanishing M, the solution reduces to a stealth scalar field on the pure AdS metric. We note that the existence of these two classes of solutions is inherent of the particular choice of the coupling constants and, they can not be promoted to spherical or hyperboloid black hole solutions in a standard fashion. In the last part, we add to the original action some exacts (D-1)-forms coupled to the scalar field. The direct benefit of introducing such extra fields is to obtain black hole solutions with planar horizon for arbitrary value of the nonminimal coupling parameter.

Sparticle mass spectra from SU(5) SUSY GUT models with b − τ Yukawa coupling unification

Supersymmetric grand unified models based on the gauge group SU(5) often require in addition to gauge coupling unification, the unification of b-quark and τ -lepton Yukawa couplings. We examine SU(5) SUSY GUT parameter space under the condition of b − τ Yukawacouplingunificationusing2-loopMSSMRGEsincludingfull1-loopthreshold effects. The Yukawa-unified solutions break down into two classes. Solutions with low tan β ~ 3 − 11 are characterized by $ {m_{{\mathop{g}\limits^{\sim } }}} $ ~ 1 − 4 TeV and $ {m_{{\mathop{q}\limits^{\sim } }}} $ ~ 1 − 5 TeV. Many of these solutions would be beyond LHC reach, although they contain a light Higgs scalar with m h < 123 GeV and so may be excluded should the LHC Higgs hint persist. The second class of solutions occurs at large tan β ∼ 35 − 60, and are a subset of t − b − τ unified solutions. Constraining only b − τ unification to ∼ 5% favors a rather light gluino with $ {m_{{\mathop{g}\limits^{\sim } }}} $ ∼ 0.5 − 2 TeV, which should ultimately be accessible to LHC searches. While our b − τ unified solutions can be consistent with a picture of neutralino-only cold dark matter, invoking additional moduli or Peccei-Quinn superfields can allow for all of our Yukawa-unified solutions to be consistent with the measured dark matter abundance.

Dynamical solutions in the 3-form field background in the Nishino-Salam-Sezgin model

We investigate the dynamical 3-form flux compactifications and their implications for cosmology in our brane world in the six-dimensional Nishino-Salam-Sezgin model, which is usually referred to as the Salam-Sezgin model. We take the background of the 3-form field acting on the internal space and timelike dimensions without the U(1) gauge field strength. The first class of solutions we discuss is the dynamical generalization of the static solutions obtained recently. In this class, we find that the time evolution is restricted only in the azimuthal dimension of the internal space and not in the ordinary three-dimensional one, which does not give a cosmological evolution. The second class of solutions is obtained by exchanging the roles of the radial coordinate and the time coordinate from the assumptions in the first class. At the center of the internal space, there is a conical singularity which may be interpreted as our 3-brane world, but it is difficult to realize a warped structure in the direction of the ordinary 3-space. Except for the oscillating solutions, a dynamical evolution leads to expanding or contracting ordinary 3-space, depending on the choice of time direction. Furthermore, in the expanding solutions, there are decelerating and accelerating ones: In the latter solution, the evolution is sustained for a finite proper time and the scale factor of the 3-space diverges.

Holonomy, decomposability, and relativity1This paper was presented at the Theory CANADA 4 conference, held at Centre de recherches mathématiques, Montréal, Québec, Canada on 4–7 June 2008.

We discuss the geometrical properties of spacetimes in the context of higher dimensional theories of gravity. If the spacetime admits a covariantly constant time-like vector, the spacetime is static and (1+10)-decomposable, where the 10-dimensional transverse space is Riemannian. The second class of solutions consists of spacetimes that admit a covariantly constant light-like vector and belong to the higher dimensional Kundt class of spacetimes. These spacetimes are genuinely Lorentzian and have many mathematical properties quite different from their Riemannian counterparts, which can lead to interesting and novel physics. This paper is a review of results published elsewhere (J. Brannlund, A. Coley, and S. Hervik. Class. Quantum Grav. 25, 195007 (2008)).

Low energy nuclear reaction polyplasmon postulate

An explanation is proposed for the nuclear reactions that occur in the electrolysis class of LENR processes. The proposed explanation postulates that a proton, or deuteron, dissolved in the hydrogen bearing metal cathode, absorbs its associated atomic electron to become a short lived state of the neutron with the resulting neutrino in a singular wave function centered on the neutron. The energy required to initiate this endothermic reaction is supplied either by the ion current during electrolysis type experiments, or by ion bombardment in plasma type experiments. It is the energy of this bombardment of the cathode with heavy ions that creates a coherent polyplasmon field within crystalline metallic grains that are present in the metal cathode of typical active electrolysis cells. The LENR process consists of a second order reaction mediated by a coherent plasmon field excited in the conduction electrons in a hydrogen bearing metal that is in the form of crystalline grains of the order of a few microns in dimension. The coherent plasmon field in each grain is called a polyplasmon. The metallic grains typically form during solidification of a metal, the impurities being forced to the grain surfaces. The resulting grain thus forms a resonant structure that can be filled with a number of coherent plasmons, i.e., a polyplasmon. Energy from the polyplasmon is coupled to the nucleus via electron capture by hydrogen. Because the neutrino has mass, its wave function has a second class of solutions. This description can take the form of a short lived pairing with the neutron that results from electron capture by the hydrogen nucleus. This short-lived compound particle is named the “dion” and in the case of deuterium results in a “dineutron”. Because the dion and dineutron are formed with essentially thermal kinetic energy, they can capture in nearby nuclei, either in hydrogen or in the host metal. Most of the resulting exothermic nuclear energy is absorbed in the plasmon field by a variety of mechanisms that increase the intensity of the plasmon field and hence the rate of electron capture – that then increases the rate of nuclear reactions. This stochastic chain-reaction process continues in the grain until it is terminated by the random occurrence of losses preventing the continuation of sustaining nuclear reactions before the plasmon field decays away, or until the rise in temperature of the metal grain alters the physical properties of the metallic grain sufficiently to disrupt the polyplasmon field. Multiple reported experiments confirm that most of the nuclear energy released is absorbed by the host metallic cathode and the electrolyte. Calculations from first principles are consistent with many of the reported quantitative and qualitative phenomena.

ANALYTICAL MODELS FOR QUARK STARS

We find two new classes of exact solutions to the Einstein–Maxwell system of equations. The matter content satisfies a linear equation of state consistent with quark matter; a particular form of one of the gravitational potentials is specified to generate solutions. The exact solutions can be written in terms of elementary functions, and these can be related to quark matter in the presence of an electromagnetic field. The first class of solutions generalizes the Mak–Harko model. The second class of solutions does not admit any singularities in the matter and gravitational potentials at the center.

Spacetimes with longitudinal and angular magnetic fields in third order Lovelock gravity

We obtain two new classes of magnetic solutions in third order Lovelock gravity. The first class of solutions yields an (n+1)-dimensional spacetime with a longitudinal magnetic field generated by a static source. We generalize this class of solutions to the case of spinning magnetic strings with one or more rotation parameters. These solutions have no curvature singularity and no horizons, but have a conic geometry. For the spinning string, when one or more rotation parameters are nonzero, the string has a net electric charge which is proportional to the magnitude of the rotation parameters, while the static string has no net electric charge. The second class of solutions yields a spacetime with an angular magnetic field. These solutions have no curvature singularity, no horizon, and no conical singularity. Although the second class of solutions may be made electrically charged by a boost transformation, the transformed solutions do not present new spacetimes. Finally, we use the counterterm method in third order Lovelock gravity and compute the conserved quantities of these spacetimes.

Magnetic branes in (n+1)-dimensional Einstein-Maxwell-dilaton gravity

We construct two new classes of spacetimes generated by spinning and traveling magnetic sources in ($n+1$)-dimensional Einstein-Maxwell-dilaton gravity with Liouville-type potential. These solutions are neither asymptotically flat nor (A)dS. The first class of solutions which yields a ($n+1$)-dimensional spacetime with a longitudinal magnetic field and $k$ rotation parameters have no curvature singularity and no horizons, but have a conic geometry. We show that when one or more of the rotation parameters are nonzero, the spinning branes have a net electric charge that is proportional to the magnitude of the rotation parameters. The second class of solutions yields a static spacetime with an angular magnetic field and has no curvature singularity, no horizons, and no conical singularity. Although one may add linear momentum to the second class of solutions by a boost transformation, one does not obtain a new solution. We find that the net electric charge of these traveling branes with one or more nonzero boost parameters is proportional to the magnitude of the velocity of the branes. We also use the counterterm method and calculate the conserved quantities of the solutions.

Magnetic strings in dilaton gravity

First, I present two new classes of magnetic rotating solutions in four-dimensional Einstein-Maxwell-dilaton gravity with Liouville-type potential. The first class of solutions yields a 4-dimensional spacetime with a longitudinal magnetic field generated by a static or spinning magnetic string. I find that these solutions have no curvature singularity and no horizons, but have a conic geometry. In these spacetimes, when the rotation parameter does not vanish, there exists an electric field, and therefore the spinning string has a net electric charge which is proportional to the rotation parameter. The second class of solutions yields a spacetime with an angular magnetic field. These solutions have no curvature singularity, no horizon, and no conical singularity. The net electric charge of the strings in these spacetimes is proportional to their velocities. Second, I obtain the ($n+1$)-dimensional rotating solutions in Einstein-dilaton gravity with Liouville-type potential. I argue that these solutions can present horizonless spacetimes with conic singularity, if one chooses the parameters of the solutions suitable. I also use the counterterm method and compute the conserved quantities of these spacetimes.

Matrix Cosmology

Exact time-dependent solutions of c=1 string theory are described using the free fermion formulation. One such class of solutions describes draining of the Fermi sea and has a spacetime interpretation as closed string tachyon condensation. A second class of solutions, corresponding to droplets of Fermi liquid orbiting in phase space, describes closed cosmologies which bounce through singularities.

Magnetic branes in Gauss-Bonnet gravity

We present two new classes of magnetic brane solutions in Einstein-Maxwell-Gauss-Bonnet gravity with a negative cosmological constant. The first class of solutions yields an $(n+1)$-dimensional spacetime with a longitudinal magnetic field generated by a static magnetic brane. We also generalize this solution to the case of spinning magnetic branes with one or more rotation parameters. We find that these solutions have no curvature singularity and no horizons, but have a conic geometry. In these spacetimes, when all the rotation parameters are zero, the electric field vanishes, and therefore the brane has no net electric charge. For the spinning brane, when one or more rotation parameters are non zero, the brane has a net electric charge which is proportional to the magnitude of the rotation parameter. The second class of solutions yields a spacetime with an angular magnetic field. These solutions have no curvature singularity, no horizon, and no conical singularity. Again we find that the net electric charge of the branes in these spacetimes is proportional to the magnitude of the velocity of the brane. Finally, we use the counterterm method in the Gauss-Bonnet gravity and compute the conserved quantities of these spacetimes.

Horizonless rotating solutions in (n+1)-dimensional Einstein-Maxwell gravity

We introduce two classes of rotating solutions of Einstein-Maxwell gravity in $n+1$ dimensions which are asymptotically anti-de Sitter type. They have no curvature singularity and no horizons. The first class of solutions, which has a conic singularity yields a spacetime with a longitudinal magnetic field and $k$ rotation parameters. We show that when one or more of the rotation parameters are non zero, the spinning brane has a net electric charge that is proportional to the magnitude of the rotation parameters. The second class of solutions yields a spacetime with an angular magnetic field and $% \kappa$ boost parameters. We find that the net electric charge of these traveling branes with one or more nonzero boost parameters is proportional to the magnitude of the velocity of the brane. We also use the counterterm method inspired by AdS/CFT correspondence and calculate the conserved quantities of the solutions. We show that the logarithmic divergencies associated to the Weyl anomalies and matter field are zero, and the $r$ divergence of the action can be removed by the counterterm method.

Self-gravitating scalar field in spherically symmetric comoving system: Solutions depending on one variable

The scalar and Einstein field equations are considered in the general symmetric comoving system. The self-gravitational interaction of the scalar field is expressed by identifying the energy momentum tensor with the one canonically associated to the scalar field. It is shown that the scalar field can depend only on the radial and time variables and that the energy momentum tensor is implicitly conserved. Two classes of solutions are then studied. A first class, that contains the static case previously considered and the complete time-dependent case, is determined by a priori assuming the unknown functions to depend on one only variable. This class is meaningful essentially for massless field. A second class of solutions refers to the a priori assumption that the scalar field alone depends on r or on t. In both cases some comments are developed for the massive scalar field and for a large class of massless fields we are able to determine the solutions.