by : arshdeep singh bhatia as a part of ph.d. course phys 601
TRANSCRIPT
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A BRIEF INTRODUCTION TO
GRTensoron MAPLE platform
By : Arshdeep Singh BhatiaAs a part of Ph.D. course PHYS 601
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TOPICS ADDRESSED:
• HISTORY OF MAPLE
• INTRODUCTION TO INTERFACE
• OPERATIONS POSSIBLE
•BENEFITS/DRAWBACKS
• TENSORS
• INTRODUCTION TO GRTensor
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Palettes
Workspace
Status bar
Context bar
Toolbar
Menu bar
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O.D.E.
Analytic soln.
Initial cond.
Laplace mthd.
Series soln.
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Can work with undefined
constants !!
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360. view plot formatting
options
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TENSORS
• An incomplete definition
• Tensors generally used in cosmology
• How are they obtained
• Need for a package like GRTensor
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Kerr Metric
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Initialization
Loading a metric
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Calculating christoffel’s
symbols
Display the result
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Calculating Reimann tensor
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Ricci Tensor
Ricci Scalar
Einstein Tensor
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The new metric
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SYNTAX RESULT
R(dn,dn,pdn) Rab,c
R(dn,d,cdn) Rab;c
> grdef ( ‘A{a b}’ ): Creates a new vector ‘ A ab ‘
> grcalc ( A(dn,dn)):Inputs the components of ‘ A
ab ‘
> grdef ( ‘A{^a ^b}’ ): Creates a new vector ‘ A ab ‘
> grdef (‘new object:= object definition’ ) Defines a new tensor
R{^a ^b b c} Σ Rabbc
R{^a ^b}*Box[ R{ a b }] Rab Rab
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Some other jobs GRTensor can be used for :
• Defining new tensors• Modifying tensor components• Finding sum / products of tensors• Tensor Calculus• Simplifying the results• Working in multiple geometries• Many other operations Iam still unaware of……….