Symbolic and numerical analysis in general relativity with open source computer algebra systems

Tolga Birkandan; Ceren Güzelgün; Elif Şirin; Mustafa Can Uslu

doi:10.1007/s10714-018-2486-x

Symbolic and numerical analysis in general relativity with open source computer algebra systems

Tolga Birkandan^*
, Ceren Güzelgün
, Elif Şirin
, Mustafa Can Uslu

^*Bu çalışma için yazışmadan sorumlu yazar

Fizik Mühendisliği Bölümü

Istanbul Technical University

Araştırma sonucu: Dergiye katkı › Makale › bilirkişi

6 Atıf (Scopus)

Özet

We study three computer algebra systems, namely SageMath (with SageManifolds package), Maxima (with ctensor package) and Python language (with GraviPy module), which allow tensor manipulation for general relativity calculations along with general algebraic calculations. We present a benchmark of these systems using simple examples. After the general analysis, we focus on the SageMath and SageManifolds system to derive, analyze and visualize the solutions of the massless Klein–Gordon equation and geodesic motion with Hamilton–Jacobi formalism. We compare our numerical result of the Klein–Gordon equation with the asymptotic form of the analytical solution to see that they agree.

Orijinal dil	İngilizce
Makale numarası	4
Dergi	General Relativity and Gravitation
Hacim	51
Basın numarası	1
DOI'lar	https://doi.org/10.1007/s10714-018-2486-x
Yayın durumu	Yayınlandı - 1 Oca 2019

Bibliyografik not

Publisher Copyright:
© 2018, Springer Science+Business Media, LLC, part of Springer Nature.

Finansman

Acknowledgements WewouldliketothankProfs.Nes¸eÖzdemir,Durmus¸AliDemirandÉricGourgoulhon for stimulating discussions. We also thank our anonymous referee for the constructive comments which helped us to improve the manuscript. This work is partially supported by TÜB˙TAK, the Scientific and Technological Council of Turkey.

Finansörler
Scientific and Technological Council of Turkey

Belgeye Erişim

10.1007/s10714-018-2486-x

Diğer Dosyalar ve Linkler

Link to publication in Scopus

Alıntı Yap

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title = "Symbolic and numerical analysis in general relativity with open source computer algebra systems",

abstract = "We study three computer algebra systems, namely SageMath (with SageManifolds package), Maxima (with ctensor package) and Python language (with GraviPy module), which allow tensor manipulation for general relativity calculations along with general algebraic calculations. We present a benchmark of these systems using simple examples. After the general analysis, we focus on the SageMath and SageManifolds system to derive, analyze and visualize the solutions of the massless Klein–Gordon equation and geodesic motion with Hamilton–Jacobi formalism. We compare our numerical result of the Klein–Gordon equation with the asymptotic form of the analytical solution to see that they agree.",

keywords = "Geodesic motion, Numerical analysis, Symbolic analysis, Wave equations",

author = "Tolga Birkandan and Ceren G{\"u}zelg{\"u}n and Elif {\c S}irin and Uslu, \{Mustafa Can\}",

note = "Publisher Copyright: {\textcopyright} 2018, Springer Science+Business Media, LLC, part of Springer Nature.",

year = "2019",

month = jan,

day = "1",

doi = "10.1007/s10714-018-2486-x",

language = "English",

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journal = "General Relativity and Gravitation",

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T1 - Symbolic and numerical analysis in general relativity with open source computer algebra systems

AU - Birkandan, Tolga

AU - Güzelgün, Ceren

AU - Şirin, Elif

AU - Uslu, Mustafa Can

PY - 2019/1/1

Y1 - 2019/1/1

N2 - We study three computer algebra systems, namely SageMath (with SageManifolds package), Maxima (with ctensor package) and Python language (with GraviPy module), which allow tensor manipulation for general relativity calculations along with general algebraic calculations. We present a benchmark of these systems using simple examples. After the general analysis, we focus on the SageMath and SageManifolds system to derive, analyze and visualize the solutions of the massless Klein–Gordon equation and geodesic motion with Hamilton–Jacobi formalism. We compare our numerical result of the Klein–Gordon equation with the asymptotic form of the analytical solution to see that they agree.

AB - We study three computer algebra systems, namely SageMath (with SageManifolds package), Maxima (with ctensor package) and Python language (with GraviPy module), which allow tensor manipulation for general relativity calculations along with general algebraic calculations. We present a benchmark of these systems using simple examples. After the general analysis, we focus on the SageMath and SageManifolds system to derive, analyze and visualize the solutions of the massless Klein–Gordon equation and geodesic motion with Hamilton–Jacobi formalism. We compare our numerical result of the Klein–Gordon equation with the asymptotic form of the analytical solution to see that they agree.

KW - Geodesic motion

KW - Numerical analysis

KW - Symbolic analysis

KW - Wave equations

UR - https://www.scopus.com/pages/publications/85057557208

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DO - 10.1007/s10714-018-2486-x

M3 - Article

AN - SCOPUS:85057557208

SN - 0001-7701

VL - 51

JO - General Relativity and Gravitation

JF - General Relativity and Gravitation

IS - 1

M1 - 4

ER -

Symbolic and numerical analysis in general relativity with open source computer algebra systems

Özet

Bibliyografik not

Finansman

Belgeye Erişim

Diğer Dosyalar ve Linkler

Parmak izi

Alıntı Yap