Exact solutions to Einstein–Maxwell theory on Eguchi–Hanson space

Ghezelbash, A. M.; Kumar, Vinit

doi:10.1142/s0217751x17500981

Cited by 3 publications

(1 citation statement)

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“…The exact solutions for the metric function H(r, x) in D-dimensional Einstein-Maxwell theory with an embedded four-dimensional Eguchi-Hanson type II geometry (6.18) in the spatial section of the space-time, is given by [22] (6.21) We also verify that our numerical solutions to the differential equation (3.10), where k = 1, represent exactly the profile of the Heun-C functions in equations (6.20) and (6.21)…”

Section: K =mentioning

confidence: 99%

Bianchi IX geometry and the Einstein-Maxwell theory

Ghezelbash

2021

Preprint

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We construct numerical solutions to the higher-dimensional Einstein-Maxwell theory. The solutions are based on embedding the four dimensional Bianchi type IX space in the theory. We find the solutions as superposition of two functions, which one of them can be found numerically. We show that the solutions in any dimensions, are almost regular everywhere, except a singular point. We find that the solutions interpolate between the two exact analytical solutions to the higher dimensional Einstein-Maxwell theory, which are based on Eguchi-Hanson type I and II geometries. Moreover, we construct the exact cosmological solutions to the theory, and study the properties of the solutions.

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Section: K =mentioning

confidence: 99%

Bianchi IX geometry and the Einstein-Maxwell theory

Ghezelbash

2021

Preprint

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Bianchi IX geometry and the Einstein–Maxwell theory

Ghezelbash

2022

Class. Quantum Grav.

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We construct numerical solutions to the higher-dimensional Einstein-Maxwell theory. The solutions are based on embedding the four dimensional Bianchi type IX space in the theory. We ﬁnd the solutions as superposition of two functions, which one of them can be found numerically. We show that the solutions in any dimensions, are almost regular everywhere, except a singular point. We ﬁnd that the solutions interpolate between the two exact analytical solutions to the higher dimensional Einstein-Maxwell theory, which are based on Eguchi-Hanson type I and II geometries. Moreover, we construct the exact cosmological solutions to the theory, and study the properties of the solutions.

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Minimal surfaces and generalized Einstein–Maxwell-dilaton theory

Butler

Ghezelbash

2019

Int. J. Mod. Phys. A

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We present novel classes of non-stationary solutions to the five-dimensional generalized Einstein-Maxwell-dilaton theory with cosmological constant, in which the Maxwell's filed and the cosmological constant couple to the dilaton field. In the first class of solutions, the two non-zero 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, can't be uplifted to any Einstein-Maxwell theory in higher dimensions.1

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Exact solutions to Einstein–Maxwell theory on Eguchi–Hanson space

Cited by 3 publications

References 48 publications

Bianchi IX geometry and the Einstein-Maxwell theory

Bianchi IX geometry and the Einstein-Maxwell theory

Bianchi IX geometry and the Einstein–Maxwell theory

Minimal surfaces and generalized Einstein–Maxwell-dilaton theory

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