Generic Three-Parameter Wormhole Solution in Einstein-Scalar Field Theory

An exact analytical, spherically symmetric, three-parametric wormhole solution has been found in the Einstein-scalar field theory, which covers the several well-known wormhole solutions. It is assumed that the scalar field is massless and depends on the radial coordinate only. The relation between the full contraction of the Ricci tensor and Ricci scalar has been found as RαβRαβ=R2. The derivation of the Einstein field equations have been explicitly shown, and the exact analytical solution has been found in terms of the three constants of integration. The several wormhole solutions have been extracted for the specific values of the parameters. In order to explore the physical meaning of the integration constants, the solution has been compared with the previously obtained results. The curvature scalar has been determined for all particular solutions. Finally, it is shown that the general solution describes naked singularity characterized by the mass, the scalar quantity and the throat.

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Black hole and naked singularity geometries supported by three-form fields

The European Physical Journal C ◽

10.1140/epjc/s10052-020-8178-1 ◽

2020 ◽

Vol 80 (7) ◽

Author(s):

Bruno J. Barros ◽

Bogdan Dǎnilǎ ◽

Tiberiu Harko ◽

Francisco S. N. Lobo

Keyword(s):

Black Hole ◽

Killing Vector ◽

Field Potential ◽

Naked Singularity ◽

Radial Coordinate ◽

Spherically Symmetric ◽

Field Equations ◽

Metric Tensor ◽

Killing Horizon ◽

Form Field

Abstract We investigate static and spherically symmetric solutions in a gravity theory that extends the standard Hilbert–Einstein action with a Lagrangian constructed from a three-form field $$A_{\alpha \beta \gamma }$$Aαβγ, which is related to the field strength and a potential term. The field equations are obtained explicitly for a static and spherically symmetric geometry in vacuum. For a vanishing three-form field potential the gravitational field equations can be solved exactly. For arbitrary potentials numerical approaches are adopted in studying the behavior of the metric functions and of the three-form field. To this effect, the field equations are reformulated in a dimensionless form and are solved numerically by introducing a suitable independent radial coordinate. We detect the formation of a black hole from the presence of a Killing horizon for the timelike Killing vector in the metric tensor components. Several models, corresponding to different functional forms of the three-field potential, namely, the Higgs and exponential type, are considered. In particular, naked singularity solutions are also obtained for the exponential potential case. Finally, the thermodynamic properties of these black hole solutions, such as the horizon temperature, specific heat, entropy and evaporation time due to the Hawking luminosity, are studied in detail.

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A NOTE ON SCALAR FIELD THEORY IN AdS3/CFT2

International Journal of Modern Physics A ◽

10.1142/s0217751x10048500 ◽

2010 ◽

Vol 25 (14) ◽

pp. 2815-2836

Author(s):

PABLO MINCES

Keyword(s):

Field Theory ◽

Scalar Field ◽

Central Charge ◽

Virasoro Algebra ◽

Radial Coordinate ◽

Poisson Brackets ◽

Scalar Field Theory ◽

Classical Level ◽

Conjugate Momentum ◽

Conformal Fields

We consider a scalar field theory in AdS d+1, and introduce a formalism on surfaces at equal values of the radial coordinate. In particular, we define the corresponding conjugate momentum. We compute the Noether currents for isometries in the bulk, and perform the asymptotic limit on the corresponding charges. We then introduce Poisson brackets at the border, and show that the asymptotic values of the bulk scalar field and the conjugate momentum transform as conformal fields of scaling dimensions Δ- and Δ+, respectively, where Δ± are the standard parameters giving the asymptotic behavior of the scalar field in AdS. Then we consider the case d = 2, where we obtain two copies of the Virasoro algebra, with vanishing central charge at the classical level. An AdS3/CFT2 prescription, giving the commutators of the boundary CFT in terms of the Poisson brackets at the border, arises in a natural way. We find that the boundary CFT is similar to a generalized ghost system. We introduce two different ground states, and then compute the normal ordering constants and quantum central charges, which depend on the mass of the scalar field and the AdS radius. We discuss certain implications of the results.

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Field Equations and Lagrangian for the Kaluza Metric Evaluated with Tensor Algebra Software

Journal of Gravity ◽

10.1155/2015/901870 ◽

2015 ◽

Vol 2015 ◽

pp. 1-6 ◽

Cited By ~ 5

Author(s):

L. L. Williams

Keyword(s):

Field Theory ◽

Scalar Field ◽

Computer Algebra ◽

Data File ◽

The Other ◽

Tensor Algebra ◽

Field Equations ◽

Scalar Field Theory ◽

Computer Package ◽

Self Consistency

This paper calculates the Kaluza field equations with the aid of a computer package for tensor algebra, xAct. The xAct file is provided with this paper. We find that Thiry’s field equations are correct, but only under limited circumstances. The full five-dimensional field equations under the cylinder condition are provided here, and we see that most of the other references miss at least some terms from them. We go on to establish the remarkable Kaluza Lagrangian, and verify that the field equations calculated from it match those calculated with xAct, thereby demonstrating self-consistency of these results. Many of these results can be found scattered throughout the literature, and we provide some pointers for historical purposes. But our intent is to provide a definitive exposition of the field equations of the classical, five-dimensional metric ansatz of Kaluza, along with the computer algebra data file to verify them, and then to recover the unique Lagrangian for the theory. In common terms, the Kaluza theory is an “ω=0” scalar field theory, but with unique electrodynamic couplings.

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Static spherically-symmetric scalar-field theory in general relativity

Astrophysics and Space Science ◽

10.1007/bf01092715 ◽

1982 ◽

Vol 88 (2) ◽

pp. 493-499 ◽

Cited By ~ 3

Author(s):

Demetrios D. Dionysiou

Keyword(s):

Field Theory ◽

General Relativity ◽

Scalar Field ◽

Spherically Symmetric ◽

Scalar Field Theory

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ON THE EQUIVALENCE OF THE BUCHDAHL AND THE JANIS–NEWMAN–WINNICOUR SOLUTIONS

International Journal of Modern Physics A ◽

10.1142/s0217751x01005328 ◽

2001 ◽

Vol 16 (28) ◽

pp. 4543-4545 ◽

Cited By ~ 13

Author(s):

A. BHADRA ◽

K. K. NANDI

Keyword(s):

Field Theory ◽

Scalar Field ◽

Spherically Symmetric ◽

Scalar Field Theory ◽

Spherically Symmetric Solutions

We comment that the static and spherically symmetric solutions to the Einstein-minimally coupled scalar field theory as obtained independently by Buchdahl and Janis–Newman–Winicour (JNW) are the same. Since it is already known that JNW and Wyman solutions are not different,1 therefore we conclude that Buchdahl, JNW and Wyman solutions are the same.

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Olbertian Partition Function in Scalar Field Theory

Frontiers in Physics ◽

10.3389/fphy.2020.610625 ◽

2020 ◽

Vol 8 ◽

Author(s):

R. A. Treumann ◽

Wolfgang Baumjohann

Keyword(s):

Field Theory ◽

Scalar Field ◽

Partition Function ◽

Gaussian Approximation ◽

Field Equations ◽

Scalar Field Theory ◽

Abelian Fields

The Olbertian partition function is reformulated in terms of continuous (Abelian) fields described by the Landau–Ginzburg action, respectively, Hamiltonian. In order to make some progress, the Gaussian approximation to the partition function is transformed into the Olbertian prior to adding the quartic Landau–Ginzburg term in the Hamiltonian. The final result is provided in the form of an expansion suitable for application of diagrammatic techniques once the nature of the field is given, that is, once the field equations are written down such that the interactions can be formulated.

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Massive Scalar Field: Source of the Graviton and 'Strong Gravity'

Australian Journal of Physics ◽

10.1071/ph760195 ◽

1976 ◽

Vol 29 (3) ◽

pp. 195 ◽

Cited By ~ 8

Author(s):

JR Rao ◽

RN Tiwari ◽

BK Nayak

Keyword(s):

Scalar Field ◽

Spherically Symmetric ◽

Massive Scalar ◽

Massive Graviton ◽

Einstein Field Equations ◽

Field Equations ◽

Field Source ◽

Massive Scalar Field ◽

Strong Gravity ◽

Spherically Symmetric Solutions

An exact class of nonstatic spherically symmetric solutions is obtained for the Einstein field equations with a massive scalar field as source. The solutions are found to characterize the 'strong gravity' associated with elementary particles, and it is shown that Ivanenko's (1965) massive graviton possesses zero spin.

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MAPPING A MASSLESS SCALAR FIELD THEORY ON A YANG–MILLS THEORY: CLASSICAL CASE

Modern Physics Letters A ◽

10.1142/s021773230903165x ◽

2009 ◽

Vol 24 (30) ◽

pp. 2425-2432 ◽

Cited By ~ 21

Author(s):

MARCO FRASCA

Keyword(s):

Field Theory ◽

Scalar Field ◽

Massless Scalar ◽

Massless Scalar Field ◽

Field Equations ◽

Scalar Field Theory ◽

Classical Level ◽

Gradient Expansion ◽

Yang Mills ◽

Mills Field

We analyze a recent proposal to map a massless scalar field theory onto a Yang–Mills theory at classical level. It is seen that this mapping exists at a perturbative level when the expansion is a gradient expansion. In this limit the theories share the spectrum, at the leading order, that is the one of a harmonic oscillator. Gradient expansion is exploited maintaining Lorentz covariance by introducing a fifth coordinate and turning the theory to Euclidean space. These expansions give common solutions to scalar and Yang–Mills field equations that are so proved to exist by construction, confirming that the selected components of the Yang–Mills field are indeed an extremum of the corresponding action functional.

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Exact Kantowski–Sachs spacetimes in Einstein–Aether scalar field theory

The European Physical Journal C ◽

10.1140/epjc/s10052-020-08721-1 ◽

2020 ◽

Vol 80 (12) ◽

Author(s):

Genly Leon ◽

Andronikos Paliathanasis ◽

N. Dimakis

Keyword(s):

Field Theory ◽

Scalar Field ◽

Functional Form ◽

Analytic Solution ◽

Analytic Solutions ◽

Field Equations ◽

Scalar Field Theory ◽

Gravitational Field Equations ◽

Background Space ◽

Gravitational Model

AbstractExact and analytic solutions in Einstein–Aether scalar field theory with Kantowski–Sachs background space are determined. The theory of point symmetries is applied to determine the functional form of the unknown functions which defines the gravitational model. Conservation laws are applied to reduce the order of the field equations and write the analytic solution. Moreover, in order to understand the physical behaviour of the cosmological model a detailed analysis of the asymptotic behaviour for solutions of the gravitational field equations is performed.

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