On axially symmetric solutions to the Higgs-Kibble-Yang-Mills field equations

The field equations for axially symmetric generalizations of the 't Hooft-Polyakov magnetic monopole are written out in a preferred coordinate system. It is argued that no soliton solutions exist when the product 2eg of the electric chargee with the magnetic chargeg is an even integer.Dedicated to Achille Papapetrou on the occasion of his retirement.     

A new class of exact hairy black hole solutions

We present a new class of black hole solutions with a minimally coupled scalar field in the presence of a negative cosmological constant. We consider an one-parameter family of self-interaction potentials parametrized by a dimensionless parameter g. When g = 0, we recover the conformally invariant solution of the Martinez–Troncoso–Zanelli (MTZ) black hole. A non-vanishing g signals the departure from conformal invariance. Thermodynamically, there is a critical temperature at vanishing black hole mass, where a higher-order phase transition occurs, as in the case of the MTZ black hole. Additionally, we obtain a branch of hairy solutions which undergo a first-order phase transition at a second critical temperature which depends on g and it is higher than the MTZ critical temperature. As g → 0, this second critical temperature diverges.     

Cosmological Post-Newtonian Expansions to Arbitrary Order

We prove the existence of a large class of one parameter families of solutions to the Einstein-Euler equations that depend on the singular parameter e = v_T/c{\epsilon=v_T/c} (0 < e < e₀){(0< \epsilon < \epsilon_0)}, where c is the speed of light, and v _T is a typical speed of the gravitating fluid. These solutions are shown to exist on a common spacetime slab M @ [0,T)×\mathbb T³{M\cong [0,T)\times \mathbb {T}^3}, and converge as e\searrow 0{\epsilon \searrow 0} to a solution of the cosmological Poisson-Euler equations of Newtonian gravity. Moreover, we establish that these solutions can be expanded in the parameter e{\epsilon} to any specified order with expansion coefficients that satisfy e{\epsilon}-independent (nonlocal) symmetric hyperbolic equations.     

Solutions of the Einstein-Maxwell equations with many black holes

In Newtonian gravitational theory a system of point charged particles can be arranged in static equilibrium under their mutual gravitational and electrostatic forces provided that for each particle the charge,e, is related to the mass,m, bye=G ^1/2 m. Corresponding static solutions of the coupled source free Einstein-Maxwell equations have been given by Majumdar and Papapetrou. We show that these solutions can be analytically extended and interpreted as a system of charged black holes in equilibrium under their gravitational and electrical forces.We also analyse some of stationary solutions of the Einstein-Maxwell equations discovered by Israel and Wilson. If space is asymptotically Euclidean we find that all of these solutions have naked singularities.Alfred P. Sloan Research Fellow, supported in part by the National Science Foundation.     

The method of virtual quanta as a probe of the equivalence principle

We consider bremsstrahlung encounters between a test body of massm, chargee, and a large fixed massM with chargeQ. We use the method of virtual quanta, and calculate the total electromagnetic and gravitational energy radiated in such encounters. We consider both the case in which the deflection is principally electromagnetic in nature, and the case in which the deflection is principally gravitational. The results are interpreted by considering the predictions of the equivalence principle, for the behavior of the test particle,and for the behavior of the virtual quanta. As expected from the equivalence principle, the total radiation produced is larger for electromagnetic deflection than for a gravitational deflection through the same angle.Dedicated to the memory of Alfred Schild, born7 September 1921; died 24 May 1977. A good man, a great scholar, the best of friends.Research supported in part by NSF grant no. PHV76-07919 and by NATO Research grant no. 1002.     

Chern-Simons solitons,Toda theories and the chiral model

The two-dimensional self-dual Chern-Simons equations are equivalent to the conditions for static, zero-energy solutions of the (2+1)-dimensional gauged nonlinear Schrödinger equation with Chern-Simons matter-gauge dynamics. In this paper we classify all finite chargeSU(N) solutions by first transforming the self-dual Chern-Simons equations into the two-dimensional chiral model (or harmonic map) equations, and then using the Uhlenbeck-Wood classification of harmonic maps into the unitary groups. This construction also leads to a new relationship between theSU(N) Toda andSU(N) chiral model solutions.This work is supported in part by funds provided by the U.S. Department of Energy (D.O.E.) under contract #DE-AC02-76ER03069, and NSF grant #87-08447     

TheC-metric withm = 0,e ≠ 0

TheC-metric with parametersm = 0,e 0 is transformed to Weyl form; the sources then appear as a spherical cap of chargee, and an uncharged semi-infinite line mass. Next, the Weyl metric is enlarged by a further transformation. The enlarged space-time has as its source two uniformly accelerated charged caps. In an appropriate approximation, the electromagnetic field components of this solution are identical to those of the Born solution of classical electrodynamics.     

Trial Equation Method Based on Symmetry and Applications to Nonlinear Equations Arising in Mathematical Physics

To find exact traveling wave solutions to nonlinear evolution equations, we propose a method combining symmetry properties with trial polynomial solution to nonlinear ordinary differential equations. By the method, we obtain some exact traveling wave solutions to the Burgers-KdV equations and a kind of reaction-diffusion equations with high order nonlinear terms. As a result, we prove that the Burgers-KdV equation does not have the real solution in the form a ₀+a ₁tan ξ+a ₂tan ² ξ, which indicates that some types of the solutions to the Burgers-KdV equation are very limited, that is, there exists no new solution to the Burgers-KdV equation if the degree of the corresponding polynomial increases. For the second equation, we obtain some new solutions. In particular, some interesting structures in those solutions maybe imply some physical meanings. Finally, we discuss some classifications of the reaction-diffusion equations which can be solved by trial equation method.     

Mikhailov's experiments on detection of magnetic charge

In a reanalysis of Mikhailov's experiments, it is argued that observations of magnetic chargeg=(1/2)(1/137)(1/3)e on ferromagnetic aerosols are incorrect. Future experiments of the type conducted by Mikhailov must take into an account the component of particle velocity orthogonal toE andH. It is shown that Mikhailov's data are consistent with the existence of a Dirac unit of magnetic chargeg=(137/2)e found in meson spectroscopy.     

Static and stationary axially symmetric gravitational fields of bounded sources. I. Solutions obtainable from the van Stockum metric

This paper shows that a new class of axially symmetric static electrovacuum solutions and the Kerr solution are obtainable from the van Stockum metric. The new class contains an infinite set of asymptotically flat solutions (in closed form), each of which involves an arbitrary set of parameters. The parameters have to be interpreted as functions of massm, chargee, and higher electric multipole moments _i of the particle. The casee= _i =0 leads to the Darmois metric. Well-known and new examples are given.     

Hairy Black Hole Solutions¶to SU(3) Einstein–Yang–Mills Equations

We give a rigorous proof of existence of infinitely many black hole solutions to the Einstein–Yang–Mills equations with gauge group SU(3). In the case that the radius of event horizon is not too small, we show that there is a black hole solution for any possible numbers of zeros of the two field variables. Received: 23 October 2000 / Accepted: 30 January 2001     

The Analytical Solution of Charged Black Hole and Calculation of Quantities (<Emphasis Type="Italic">T</Emphasis>,<Emphasis Type="Italic">s</Emphasis>,<Emphasis Type="Italic">f</Emphasis>)

One of the most remarkable features of black hole is the connection between properties of the classical solutions and thermodynamics. We include the electric and magnetic charges and this lead us to resolve Einstein equations. We obtain thermodynamic properties, such as temperature, entropy density and speed of sound with analytical solution. In that case we characterize equation of state in to V(φ) language.     

Supersymmetric coloured/hairy black holes

We discuss all possible spherically symmetric black hole type solutions to an N=2 supergravity model with SO(3) gauging. The solutions consist of a one parameter family of black hole solutions evading the no-hair theorem and an isolated solution that is a supersymmetric analogue of a coloured black hole.     

Fractionally charged non-leaking dyons and fermions in a bag

We consider a fermion of chargee confined to a spherical bag with a Dirac monopole of strengthg at its centre. We find that the boundary conditions making the lowest angular momentum hamiltonian self-adjoint are characterized by a unitary matrixU, and the corresponding vacuum charge has a fractional part 2|eg|α/π where detU = -exp (2iα). Boundary conditions for conservation of helicity,CP, CT andPT are displayed. We demonstrate the possibility of a fractionally charged dyon whose interaction with a fermion conserves helicity. We also show thatthe simultaneous validity of helicity, CP, CT and PT requires integer vacuum charge.     

A minimal energy tracking method for non-radially symmetric solutions of coupled nonlinear Schrödinger equations

We aim at developing methods to track minimal energy solutions of time-independent m-component coupled discrete nonlinear Schrödinger (DNLS) equations. We first propose a method to find energy minimizers of the 1-component DNLS equation and use it as the initial point of the m-component DNLS equations in a continuation scheme. We then show that the change of local optimality occurs only at the bifurcation points. The fact leads to a minimal energy tracking method that guides the choice of bifurcation branch corresponding to the minimal energy solution curve. By combining all these techniques with a parameter-switching scheme, we successfully compute a non-radially symmetric energy minimizer that can not be computed by existing numerical schemes straightforwardly.     

Exact vacuum solutions of 4-dimensional metric-affine gauge theories of gravitation

We presenttwo exact spherically symmetric vacuum solutions of gauge theories of gravity on a spacetime with non metric-compatible connection. One of them is defined on a Weyl-Cartan spacetime and the other on a general metric-affine space. We consider Lagrangians which include terms quadratic in the irreducible parts of the curvature, the torsion, and the nonmetricity. The metric part of both solutions is of the Reissner-Nordström type and includes a contribution of an effectivedilatation charge. A nontrivial Weyl 1-form is also common to both solutions. It resembles a Coulomb potential originating from thedilatation charge. The torsion is closely related to the nonmetricity.Supported by the Consejo Superior de Investigaciones Científicas, Serrano 123, E-28006 Madrid, Spain     

Entropy function approach to charged BTZ black hole

We find solution to the metric function f(r) = 0 of charged BTZ black hole making use of the Lambert function. The condition of extremal charged BTZ black hole is determined by a non-linear relation of M _e (Q) = Q ²(1 − ln Q ²). Then, we study the entropy of extremal charged BTZ black hole using the entropy function approach. It is shown that this formalism works with a proper normalization of charge Q for charged BTZ black hole because AdS₂ × S¹ represents near-horizon geometry of the extremal charged BTZ black hole. Finally, we introduce the Wald’s Noether formalism to reproduce the entropy of the extremal charged BTZ black hole without normalization when using the dilaton gravity approach.     

Thermodynamics of charged Brans–Dicke AdS black holes

It is well known that in four dimensions, black hole solution of the Brans–Dicke–Maxwell equations is just the Reissner–Nordstrom solution with a constant scalar field. However, in n4 dimensions, the solution is not yet the (n+1)-dimensional Reissner–Nordstrom solution and the scalar field is not a constant in general. In this Letter, by applying a conformal transformation to the dilaton gravity theory, we derive a class of black hole solutions in (n+1)-dimensional (n4) Brans–Dicke–Maxwell theory in the background of anti-de Sitter universe. We obtain the conserved and thermodynamic quantities through the use of the Euclidean action method. We find a Smarr-type formula and perform a stability analysis in the canonical ensemble. We find that the solution is thermally stable for small α, while for large α the system has an unstable phase, where α is a coupling constant between the scalar and matter field.     

Paschen-Back effect in dyonium

A formulation of the Pashen-Back effect in dyonium is discussed to explain the recent evidence for a magnetic monopole of mass 2397 MeV and Dirac chargeg=(137/2)e. The masses for isospinI=0 mesons are estimated and compared with experiment.     

The structure of the nucleon

We assume that nucleons are made of quarks which are made of subquarks which are made of more fundamental subquarks, etc. Thus, finally, the proton and the neutron may be composed of an infinite number of pointlike quarks and antiquarks. The limit particle has quantum numbers of spinJ=1/2, isospinI=1/2, third component of isospinI ₃=1/2, and fractional electric chargeQ=(l/2)¦e¦, where ¦e¦ is the electron charge. All quantum numbers are thus just one-half and this fermion will behave as if it was lepton, since the baryon number approaches zero at an infinite sublayer level. Sum rules in lepton-nucleon scattering have been evaluated using this model. The predicted values are not incompatible with the experimental results.