Domain-theoretic Solution of Differential Equations (Scalar Fields)

We deal with the presence of topological defects in models for two real scalar fields. We comment on defects hosting topological defects and search for explicit defect solutions using the trial orbit method. As we know, under certain circumstances the second-order equations of motion can be solved by solutions of first-order differential equations. In this case we show that the trial orbit method can be used very efficiently to obtain explicit solutions.

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Conserved Currents in Supersymmetric Quantum Cosmology?

International Journal of Modern Physics D ◽

10.1142/s0218271897000388 ◽

1997 ◽

Vol 06 (05) ◽

pp. 625-641 ◽

Cited By ~ 11

Author(s):

P. V. Moniz

Keyword(s):

Differential Equations ◽

Quantum Cosmology ◽

Scalar Fields ◽

Square Root ◽

Root Structure ◽

Complex Scalar ◽

First Order ◽

Class A ◽

Conserved Currents ◽

First Order Differential Equations

In this paper we investigate whether conserved currents can be sensibly defined in super-symmetric minisuperspaces. Our analysis deals with k = +1 FRW and Bianchi class-A models. Supermatter in the form of scalar supermultiplets is included in the former. Moreover, we restrict ourselves to the first-order differential equations derived from the Lorentz and supersymmetry constraints. The "square-root" structure of N = 1 super-gravity was our motivation to contemplate this interesting research. We show that conserved currents cannot be adequately established except for some very simple scenarios. Otherwise, equations of the type ∇a Ja = 0 may only be obtained from Wheeler–DeWittlike equations, which are derived from the supersymmetric algebra of constraints. Two appendices are included. In Appendix A we describe some interesting features of quantum FRW cosmologies with complex scalar fields when supersymmetry is present. In particular, we explain how the Hartle–Hawking state can now be satisfactorily identified. In Appendix B we initiate a discussion about the retrieval of classical properties from supersymmetric quantum cosmologies.

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Black holes with scalar hair in Einstein–Gauss–Bonnet gravity

International Journal of Modern Physics D ◽

10.1142/s021827181650084x ◽

2016 ◽

Vol 25 (07) ◽

pp. 1650084 ◽

Cited By ~ 2

Author(s):

Y. Brihaye ◽

L. Ducobu

Keyword(s):

Black Holes ◽

Angular Velocity ◽

Differential Equations ◽

Nonlinear Differential Equations ◽

Large Family ◽

Scalar Fields ◽

Regular Solutions ◽

Five Dimensions ◽

Bonnet Gravity ◽

Scalar Hair

The Einstein–Gauss–Bonnet gravity in five dimensions is extended by scalar fields and the corresponding equations are reduced to a system of nonlinear differential equations. A large family of regular solutions of these equations is shown to exist. Generically, these solutions are spinning black holes with scalar hairs. They can be characterized (but not uniquely) by an horizon and an angular velocity on this horizon. Taking particular limits, the black holes approach boson star or become extremal, in any case the limiting configurations remain hairy.

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Spherically symmetric differential equations, the rotation group, and tensor spherical functions

Mathematical Proceedings of the Cambridge Philosophical Society ◽

10.1017/s0305004100044170 ◽

1969 ◽

Vol 65 (1) ◽

pp. 157-175 ◽

Cited By ~ 27

Author(s):

R. Burridge

Keyword(s):

Quantum Theory ◽

Irreducible Representation ◽

Differential Equations ◽

Spherical Symmetry ◽

Symmetric Tensor ◽

Scalar Fields ◽

Rotation Group ◽

Spherically Symmetric ◽

Tensor Fields ◽

Covariant Differentiation

AbstractIn this paper a scheme is developed for handling tensor partial differential equations having spherical symmetry. The basic technique is that of Gelfand and Shapiro ((2), §8) by which tensor fields defined on a sphere give rise to scalar fields defined on the rotation group. These fields may be expanded as series of functions, where,mis fixed and the matricesTl(g) form a 21+ 1 dimensional irreducible representation of.Spherically symmetric operations, such as covariant differentiation of tensors and the contraction of tensors with other spherically symmetric tensor fields, are shown to act in a particularly simple way on the terms of the series mentioned above: terms with givenl, nare transformed into others with the same values ofl, n. That this must be so follows from Schur's Lemma and the fact that for eachmandlthe functionsform a basis for an invariant subspace of functions onof dimension 2l+ 1 in which an irreducible representation ofacts. Explicit formulae for the results of such operations are presented.The results are used to show the existence of scalar potentials for tensors of all ranks and the results for tensors of the second rank are shown to be closely related to those recently obtained by Backus(1).This work is intended for application in geophysics and other fields where spherical symmetry plays an important role. Since workers in these fields may not be familiar with quantum theory, some matter in sections 2–5 has been included in spite of the fact that it is well known in the quantum theory of angular momentum.

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Tolman–Oppenheimer–Volkoff equations in nonlocal f(R) gravity

International Journal of Modern Physics A ◽

10.1142/s0217751x15500931 ◽

2015 ◽

Vol 30 (16) ◽

pp. 1550093 ◽

Cited By ~ 26

Author(s):

Davood Momeni ◽

H. Gholizade ◽

Muhammad Raza ◽

Ratbay Myrzakulov

Keyword(s):

Differential Equations ◽

Compact Star ◽

Gaussian Quadrature ◽

Scalar Fields ◽

Compact Stars ◽

Dynamical Equations ◽

Physically Based ◽

State Formula ◽

User Friendly ◽

Adaptive Gaussian Quadrature

Nonlocal f(R) gravity was proposed as a powerful alternative to general relativity (GR). This theory has potentially adverse implications for infrared (IR) regime as well as ultraviolet (UV) early epochs. However, there are a lot of powerful features, making it really user-friendly. A scalar–tensor frame comprising two auxiliary scalar fields is used to reduce complex action. However, this is not the case for the modification complex which plays a distinct role in modified theories for gravity. In this work, we study the dynamics of a static, spherically symmetric object. The interior region of space–time had rapidly filled the perfect fluid. However, it is possible to derive a physically based model which relates interior metric to nonlocal f(R). The Tolman–Oppenheimer–Volkoff (TOV) equations would be a set of first-order differential equations from which we can deduce all mathematical (physical) truths and derive all dynamical objects. This set of dynamical equations govern pressure p, density ρ, mass m and auxiliary fields {ψ, ξ}. The full conditional solutions are evaluated and inverted numerically to obtain exact forms of the compact stars Her X-1, SAX J 1808.4-3658 and 4U 1820-30 for nonlocal Starobinsky model of f(◻-1 R) = ◻-1 R+α(◻-1 R)2. The program solves the differential equations numerically using adaptive Gaussian quadrature. An ascription of correctness is supposed to be an empirical equation of state [Formula: see text] for star which is informative in so far as it excludes an alternative nonlocal approach to compact star formation. This model is most suited for astrophysical observation.

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