scholarly journals The structure and uniqueness of generalized solutions of the spherically symmetric Einstein-scalar equations

1987 ◽  
Vol 109 (4) ◽  
pp. 591-611 ◽  
Author(s):  
Demetrios Christodoulou
Keyword(s):  
Generalized Solutions ◽  
Spherically Symmetric ◽  
Scalar Equations

scholarly journals Janis–Newman–Winicour and Wyman Solutions are the Same

1997 ◽  
Vol 12 (27) ◽  
pp. 4831-4835 ◽  
Author(s):  
K. S. Virbhadra
Keyword(s):  
Exact Solution ◽  
Scalar Field ◽  
Total Energy ◽  
Space Time ◽  
Massless Scalar ◽  
Spherically Symmetric ◽  
Scalar Equations

We show that the well-known most general static and spherically symmetric exact solution to the Einstein-massless scalar equations given by Wyman is the same as one found by Janis, Newman and Winicour several years ago. We obtain the energy associated with this space–time and find that the total energy for the case of the purely scalar field is zero.

scholarly journals Nature of Singularity in Einstein-Massless Scalar Theory

1997 ◽  
Vol 06 (03) ◽  
pp. 357-361 ◽  
Author(s):  
K. S. Virbhadra ◽  
S. Jhingan ◽  
P. S. Joshi
Keyword(s):  
Exact Solution ◽  
Energy Condition ◽  
Naked Singularity ◽  
Weak Energy Condition ◽  
Massless Scalar ◽  
Spherically Symmetric ◽  
Scalar Theory ◽  
Scalar Equations

We study the static and spherically symmetric exact solution of the Einstein-massless scalar equations given by Janis, Newman and Winicour. We find that this solution satisfies the weak energy condition and has strong globally naked singularity.

BENDING OF A SUBTLE-FINISHED PLATE ON ELASTIC BASE WITH SPECIAL CONDITIONS OF ITS WORK

2019 ◽  
pp. 424-430
Author(s):  
A. T. Marufiy ◽  
A. S. Kalykov
Keyword(s):  
Analytical Solution ◽  
Working Conditions ◽  
Fourier Transforms ◽  
Infinite Plate ◽  
Elastic Base ◽  
Generalized Solutions ◽  
Middle Plane ◽  
Actual Working

In this article, an analytical solution is obtained for the problem of bending a semi-infinite plate on an elastic Winkler base, taking into account incomplete contact with the base and the influence of longitudinal forces applied in the middle plane of the plate. The analytical solution is obtained by the method of generalized solutions using integral Fourier transforms. Any analytical solution is the result, approaching the actual working conditions of the designed structures.

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.

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