An Exact Solution of Higher Dimensional Einstein Equation in Presence of Matter

Corrections to Newton’s inverse law have been so far considered, but not clear in warped higher dimensional worlds, because of complexity of the Einstein equation. Here, we give a model of a warped 6D world with an extra 2D sphere. We take a general energy–momentum tensor, which does not depend on a special choice of bulk matter fields. The 6D Einstein equation reduces to the spheroidal differential equation, which can be easily solved. The gravitational potential in our 4D universe is calculated to be composed of infinite series of massive Yukawa potentials coming from the KK mode, together with Newton’s inverse law. The series of Yukawa type potentials converges well to behave as [Formula: see text] near [Formula: see text].

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Dimensional reduction in 6D standing waves braneworld

International Journal of Modern Physics D ◽

10.1142/s0218271815500091 ◽

2014 ◽

Vol 24 (01) ◽

pp. 1550009 ◽

Cited By ~ 1

Author(s):

Otari Sakhelashvili

Keyword(s):

Exact Solution ◽

Standing Wave ◽

Dimensional Reduction ◽

Cosmological Solution ◽

Standing Waves ◽

Massless Scalar ◽

Dynamical Mechanism ◽

Higher Dimensional ◽

Braneworld Model

We found cosmological solution of the 6D standing wave braneworld model generated by gravity coupled to a massless scalar phantom-like field. By obtaining a full exact solution of the model, we found a novel dynamical mechanism in which the anisotropic nature of the primordial metric gives rise to expansion of three spatial brane dimensions and affectively reduction of other spatial directions. This dynamical mechanism can be relevant for dimensional reduction in string and other higher-dimensional theories in the attempt of getting a 4D isotropic expanding spacetime.

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Einstein-Klein-Gordon System in Higher Dimensional

Indonesian Journal of Physics ◽

10.5614/itb.ijp.2021.32.2.4 ◽

2021 ◽

Vol 32 (2) ◽

pp. 16-19

Author(s):

Mirda Prisma Wijayanto ◽

Fiki Taufik Akbar Sobar ◽

Bobby Eka Gunara

Keyword(s):

Scalar Curvature ◽

Einstein Equation ◽

Ricci Tensor ◽

Gordon Equation ◽

Higher Dimensional ◽

Klein Gordon ◽

Klein Gordon Equation

In this present work, we study the Einstein equation coupled with the nonlinear Klein-Gordon equation. We obtain Ricci tensor, scalar curvature, and Einstein equation of the Einstein-Klein-Gordon system in higher dimensional. If we put D=4, our formulations reduce to the four dimensional Einstein-Klein-Gordon system.

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A GENERALIZED VACUOLE MODEL IN HIGHER DIMENSIONS

International Journal of Modern Physics D ◽

10.1142/s0218271803003669 ◽

2003 ◽

Vol 12 (06) ◽

pp. 1035-1045

Author(s):

A. BANERJEE ◽

S. CHATTERJEE

Keyword(s):

Exact Solution ◽

Frequency Shift ◽

Initial Conditions ◽

Dynamical Behavior ◽

Boundary Surface ◽

Blue Shift ◽

Higher Dimensions ◽

Junction Conditions ◽

Higher Dimensional ◽

Arbitrary Dimensions

We extend to higher dimensions a recent work of Bonnor, which generalizes the Einstein–Straus model utilizing the inhomogeneous Tolman–Bondi universe in place of the homogeneous Friedmann one. Following Israel's junction conditions, the criteria of matching between the higher dimensional Schwarzschild-like interior and the Tolman–Bondi-like exterior is obtained. We also give a new exact solution for a five-dimensional TB type of metric and use it to study the dynamical behavior of the vacuole boundary. Furthermore the transformation relations which transform the inhomogeneous TB metric to the homogeneous Friedmann model are explicitly given for any arbitrary dimensions. The frequency shift of radiation coming from the boundary surface is calculated and it is found that, depending on initial conditions both redshift and blue-shift are possible for an expanding vacuole. This is at variance with Bonnor's result where only redshift is possible under similar situation. It is also observed that higher dimensional models are less stable against perturbation than the usual 4D ones.

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Exact Solutions for(4+1)-Dimensional Nonlinear Fokas Equation Using ExtendedF-Expansion Method and Its Variant

Mathematical Problems in Engineering ◽

10.1155/2014/972519 ◽

2014 ◽

Vol 2014 ◽

pp. 1-11 ◽

Cited By ~ 7

Author(s):

Yinghui He

Keyword(s):

Exact Solution ◽

Exact Solutions ◽

Elliptic Function ◽

Expansion Method ◽

Trigonometric Function ◽

Hyperbolic Function ◽

Jacobi Elliptic Function ◽

Weierstrass Elliptic Function ◽

New Exact Solutions ◽

Higher Dimensional

The construction of exact solution for higher-dimensional nonlinear equation plays an important role in knowing some facts that are not simply understood through common observations. In our work,(4+1)-dimensional nonlinear Fokas equation, which is an important physical model, is discussed by using the extendedF-expansion method and its variant. And some new exact solutions expressed by Jacobi elliptic function, Weierstrass elliptic function, hyperbolic function, and trigonometric function are obtained. The related results are enriched.

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