scholarly journals Study of the geodesic equations of a spherical symmetric spacetime in conformal Weyl gravity

2017 ◽  
Vol 34 (5) ◽  
pp. 055004 ◽  
Author(s):  
Bahareh Hoseini ◽  
Reza Saffari ◽  
Saheb Soroushfar
Keyword(s):  
Geodesic Equations ◽  
Weyl Gravity ◽  
Symmetric Spacetime

The two-body problem: an effective-one-body approach

2018 ◽  
Author(s):  
Nathalie Deruelle ◽  
Jean-Philippe Uzan
Keyword(s):  
Body Problem ◽  
Equations Of Motion ◽  
Reaction Force ◽  
Kerr Black Hole ◽  
Radiation Reaction ◽  
Spherically Symmetric ◽  
Geodesic Motion ◽  
Two Body Problem ◽  
Symmetric Spacetime ◽  
Radiation Reaction Force

This chapter presents the basics of the ‘effective-one-body’ approach to the two-body problem in general relativity. It also shows that the 2PN equations of motion can be mapped. This can be done by means of an appropriate canonical transformation, to a geodesic motion in a static, spherically symmetric spacetime, thus considerably simplifying the dynamics. Then, including the 2.5PN radiation reaction force in the (resummed) equations of motion, this chapter provides the waveform during the inspiral, merger, and ringdown phases of the coalescence of two non-spinning black holes into a final Kerr black hole. The chapter also comments on the current developments of this approach, which is instrumental in building the libraries of waveform templates that are needed to analyze the data collected by the current gravitational wave detectors.

scholarly journals Exact static cylindrical solution to conformal Weyl gravity

2012 ◽  
Vol 85 (10) ◽  
Author(s):  
Jackson Levi Said ◽  
Joseph Sultana ◽  
Kristian Zarb Adami
Keyword(s):  
Weyl Gravity

scholarly journals Projective Collineations of Decomposable Spacetimes Generated by the Lie Point Symmetries of Geodesic Equations

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 1018
Author(s):  
Andronikos Paliathanasis
Keyword(s):  
Differential Equations ◽  
Riemannian Space ◽  
Dimensional Subspace ◽  
Geometric Construction ◽  
Lie Point Symmetries ◽  
Geodesic Equations ◽  
Symmetries Of Differential Equations ◽  
Projective Collineations

We investigate the relation of the Lie point symmetries for the geodesic equations with the collineations of decomposable spacetimes. We review previous results in the literature on the Lie point symmetries of the geodesic equations and we follow a previous proposed geometric construction approach for the symmetries of differential equations. In this study, we prove that the projective collineations of a n+1-dimensional decomposable Riemannian space are the Lie point symmetries for geodesic equations of the n-dimensional subspace. We demonstrate the application of our results with the presentation of applications.

scholarly journals BOUNCE OF GRAVITONS EMITTED FROM THE BRANE TO THE BULK BACK TO THE BRANE

2013 ◽  
Vol 28 (25) ◽  
pp. 1350126 ◽  
Author(s):  
MIKHAIL Z. IOFA
Keyword(s):  
Cosmological Model ◽  
Extra Dimension ◽  
Fixed Position ◽  
Geodesic Equations ◽  
Alternative Approaches ◽  
To Come ◽  
The One

Solutions of geodesic equations describing propagation of gravitons in the bulk are studied in a cosmological model with one extra dimension. Brane with matter is embedded in the bulk. It is shown that in the period of early cosmology gravitons emitted from the brane to the bulk under certain conditions can return back to the brane. The model is discussed in two alternative approaches: (i) brane with static metric moving in the AdS space, and (ii) brane located at a fixed position in extra dimension with nonstatic metric. Transformation of coordinates from the one picture to another is performed. In both approaches, conditions for gravitons emitted to the bulk to come back to the brane are found.

Some Exact Solutions to Conformal Weyl Gravity

1991 ◽  
Vol 631 (1 Nonlinear Pro) ◽  
pp. 194-211 ◽  
Author(s):  
PHILIP D. MANNHEIM
Keyword(s):  
Exact Solutions ◽  
Weyl Gravity

scholarly journals A derivation of Weyl gravity

2001 ◽  
Vol 10 (11-12) ◽  
pp. 935-964 ◽  
Author(s):  
Nicolas Boulanger ◽  
Marc Henneaux
Keyword(s):  
Weyl Gravity

scholarly journals Research Article. Geodesic equations and their numerical solutions in geodetic and Cartesian coordinates on an oblate spheroid

2017 ◽  
Vol 7 (1) ◽  
Author(s):  
G. Panou ◽  
R. Korakitis
Keyword(s):  
Initial Value Problem ◽  
Numerical Solutions ◽  
Oblate Spheroid ◽  
Initial Value ◽  
Data Set ◽  
Cartesian Coordinates ◽  
Geodesic Equations ◽  
Research Article ◽  
Fast Solution ◽  
Geodesic Problem

AbstractThe direct geodesic problem on an oblate spheroid is described as an initial value problem and is solved numerically using both geodetic and Cartesian coordinates. The geodesic equations are formulated by means of the theory of differential geometry. The initial value problem under consideration is reduced to a system of first-order ordinary differential equations, which is solved using a numerical method. The solution provides the coordinates and the azimuths at any point along the geodesic. The Clairaut constant is not used for the solution but it is computed, allowing to check the precision of the method. An extensive data set of geodesics is used, in order to evaluate the performance of the method in each coordinate system. The results for the direct geodesic problem are validated by comparison to Karney’s method. We conclude that a complete, stable, precise, accurate and fast solution of the problem in Cartesian coordinates is accomplished.

scholarly journals Vaidya solutions in general covariant Hořava–Lifshitz gravity without projectability: Infrared limit

2014 ◽  
Vol 23 (08) ◽  
pp. 1450068 ◽  
Author(s):  
O. Goldoni ◽  
M. F. A. da Silva ◽  
G. Pinheiro ◽  
R. Chan
Keyword(s):  
General Relativity ◽  
Gauge Field ◽  
Radiation Field ◽  
Relativity Theory ◽  
Covariant Theory ◽  
Spherically Symmetric ◽  
Theory U ◽  
General Relativity Theory ◽  
Infrared Limit ◽  
Symmetric Spacetime

In this paper, we have studied nonstationary radiative spherically symmetric spacetime, in general covariant theory (U(1) extension) of Hořava–Lifshitz (HL) gravity without the projectability condition and in the infrared (IR) limit. The Newtonian prepotential φ was assumed null. We have shown that there is not the analogue of the Vaidya's solution in the Hořava–Lifshitz Theory (HLT), as we know in the General Relativity Theory (GRT). Therefore, we conclude that the gauge field A should interact with the null radiation field of the Vaidya's spacetime in the HLT.

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