Dilaton Mass Formulas in a Hairy Binary Black Hole Model

In this note an analytic integration is obtained for the differential equation governing the scalar-field-dependent mass in a hairy binary black hole model, in the context of the Einstein--Maxwell--dilation theory, which gives a closed-form formula-level description of the mass function. We also identify a particular solution which attracts all solutions of the mass-governing equation exponentially rapidly in large-dilaton-field limit.Comment: 16 pages, 5 figures, to appea

Domain Wall Equations, Hessian of Superpotential, and Bogomol'nyi Bounds

An important question concerning the classical solutions of the equations of motion arising in quantum field theories at the BPS critical coupling is whether all finite-energy solutions are necessarily BPS. In this paper we present a study of this basic question in the context of the domain wall equations whose potential is induced from a superpotential so that the ground states are the critical points of the superpotential. We prove that the definiteness of the Hessian of the superpotential suffices to ensure that all finite-energy domain-wall solutions are BPS. We give several examples to show that such a BPS property may fail such that non-BPS solutions exist when the Hessian of the superpotential is indefinite.Comment: 25 page

Cosmic strings in a generalized linear formulation of gauge field theory

In this note we construct self-dual cosmic strings from a gauge field theory with a generalized linear formation of potential energy density. By integrating the Einstein equation, we obtain a nonlinear elliptic equation which is equal with the sources. We prove the existence of a solution in the broken symmetry category on the full plane and the multiple string solutions are valid under a sufficient condition imposed only on the total string number N. The technique of upper-lower solutions and the method of regularization are employed to show the existence of a solution when there are at least two distant string centers. When all the string centers are identical, fixed point theorem are used to study the properties of the nonlinear elliptic equation. Finally, We give the sharp asymptotic estimate for the solution at infinity