### Abstract

We present effective equations to describe the four-dimensional gravity of a brane world, assuming that a five-dimensional bulk spacetime satisfies the Einstein equations and gravity is confined on the Z_{2} symmetric brane. Applying this formalism to the Randall-Sundrum brane world model, we find two new additional terms in the Einstein equations: One is the quadratic term of the energy-momentum tensor of matter field and the other is the 5-dimensional Weyl curvature term. Although the four-dimensional effective equations are not closed and further information from the bulk is required, those terms may provide us windows to search for extra dimensions. We discuss some effects of those terms on cosmology and compact objects. Since those additional terms appear naturally from the present reduction, we apply it to other brane models. We study three models; the model with a bulk dilaton field motivated by Hořava-Witten model, the induced gravity brane model of Dvali, Gabadadze and Porrati, and the R^{2} inflationary model proposed by Starobinsky.

Original language | English |
---|---|

Pages (from-to) | 59-90 |

Number of pages | 32 |

Journal | Progress of Theoretical Physics Supplement |

Volume | 148 |

Issue number | 2 |

Publication status | Published - 2002 |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*Progress of Theoretical Physics Supplement*,

*148*(2), 59-90.

**The Einstein equations on a brane world.** / Maeda, Keiichi.

Research output: Contribution to journal › Article

*Progress of Theoretical Physics Supplement*, vol. 148, no. 2, pp. 59-90.

}

TY - JOUR

T1 - The Einstein equations on a brane world

AU - Maeda, Keiichi

PY - 2002

Y1 - 2002

N2 - We present effective equations to describe the four-dimensional gravity of a brane world, assuming that a five-dimensional bulk spacetime satisfies the Einstein equations and gravity is confined on the Z2 symmetric brane. Applying this formalism to the Randall-Sundrum brane world model, we find two new additional terms in the Einstein equations: One is the quadratic term of the energy-momentum tensor of matter field and the other is the 5-dimensional Weyl curvature term. Although the four-dimensional effective equations are not closed and further information from the bulk is required, those terms may provide us windows to search for extra dimensions. We discuss some effects of those terms on cosmology and compact objects. Since those additional terms appear naturally from the present reduction, we apply it to other brane models. We study three models; the model with a bulk dilaton field motivated by Hořava-Witten model, the induced gravity brane model of Dvali, Gabadadze and Porrati, and the R2 inflationary model proposed by Starobinsky.

AB - We present effective equations to describe the four-dimensional gravity of a brane world, assuming that a five-dimensional bulk spacetime satisfies the Einstein equations and gravity is confined on the Z2 symmetric brane. Applying this formalism to the Randall-Sundrum brane world model, we find two new additional terms in the Einstein equations: One is the quadratic term of the energy-momentum tensor of matter field and the other is the 5-dimensional Weyl curvature term. Although the four-dimensional effective equations are not closed and further information from the bulk is required, those terms may provide us windows to search for extra dimensions. We discuss some effects of those terms on cosmology and compact objects. Since those additional terms appear naturally from the present reduction, we apply it to other brane models. We study three models; the model with a bulk dilaton field motivated by Hořava-Witten model, the induced gravity brane model of Dvali, Gabadadze and Porrati, and the R2 inflationary model proposed by Starobinsky.

UR - http://www.scopus.com/inward/record.url?scp=0042833288&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0042833288&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0042833288

VL - 148

SP - 59

EP - 90

JO - Progress of Theoretical Physics

JF - Progress of Theoretical Physics

SN - 0033-068X

IS - 2

ER -