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Numerical simulation of gravitational waves from a black hole, using curvature tensors

Authors: Matsuki, Yoshio; Bidyuk, Petro I.;

Numerical simulation of gravitational waves from a black hole, using curvature tensors

Abstract

In this research we formulated the curvature tensors with the system of spherical polar coordinates, which describe the gravitational field and gravitational waves of a black hole; and then we calculated eigenvalues of the curvature tensors to estimate the relative strengths of their components to the stress-energy tensor in Einstein’s field equation. For this simulation, we assumed that the time and the distance interact with each other if we travel from Earth to the inside of the black hole, and then the result of the simulation showed that the gravitational waves carry the same components of the gravitational field of the black hole. On the other hand, when we assumed that the time and the distance are independent, which resembles the situation outside of the boundary of the black hole toward Earth, the curvature tensors are different between those of the gravitational field and the gravitational waves. Upon the results of the simulation we conclude that the gravitational waves that come from the inside of the black hole carry the information of the gravitational field inside of the black hole, if we assume that time and space are dependent each other.

Keywords

spherical polar coordinates, гравитационное поле; гравитационные волны; тензор кривизны; черная дыра; сферические полярные координаты, гравітаційне поле; гравітаційні хвилі; тензор кривизни; чорна діра; сферичні полярні координати, QA75.5-76.95, gravitational field, gravitational waves, Electronic computers. Computer science, black hole, Gravitational field; gravitational waves; curvature tensor; black hole; spherical polar coordinates, Gravitational field, curvature tensor

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
5
Top 10%
Top 10%
Top 10%
Green
gold