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bikramphy

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4 years, 68 days
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These are questions asked by bikramphy

How to find Dirac gamma matrix?...

bikramphy 70 Maple
homework metric physics
July 24 2022
1 1

Given a diagonal metric of signature (++- -)  for example the diagonal elements are [1,1,-1,-1], then how to find the Dirac gamma matrix in the standard representation or any representation.

Define a signature of a metric...

bikramphy 70 Maple
metric physics duplicate-question
July 12 2022
1 2

How can I define an arbitrary signature of a space-time metric?

I want to define the signature of the form `++--`.

solving first order differential equatio...

bikramphy 70 Maple
ode dsolve series
November 20 2020
1 3

I am trying  to solve a first order differential equation.  But the maple is not able to solve. Please help me in finding the solutions...

Exact solution is not necessary. Solution in the series expansion is also be very helpful.

Here is the attached maple code..Please do check. Please scroll down to download the given maple file.


 

``

``

> 

restart
> 

with(Student[NumericalAnalysis])
> 

with(PDEtools)
> 

with(DEtools)
> 

with(MmaTranslator)

[FromMma, FromMmaNotebook, Mma, MmaToMaple]

 (1)

``

> 

``

``

> 

C1 := 2*M/(4*M*R^2*a-3*R^3*a)

``

> 

D1 := -M*(8*M-9*R)*(3*ln(1+2*M/(4*M-3*R))+2*ln(1-2*M/R))/(3*R^2*(-16*M^2+26*M*R-9*R^2+(16*M^2-30*M*R+11*R^2)*ln(1+2*M/(4*M-3*R))+R^2*ln(-3*R/(4*M-3*R))))

``

> 

A1 := R^2*(3*ln(1+2*M/(4*M-3*R))+2*ln(1-2*M/R))/(-32*M^2+52*M*R-18*R^2+(2*(16*M^2-30*M*R+11*R^2))*ln(1+2*M/(4*M-3*R))+2*R^2*ln(-3*R/(4*M-3*R)))

``

> 

explambda := simplify((-2*C1*a*r^2+1)/(C1*a*r^2+1))

``

> 

density := simplify(a*C1*(2*C1*a*r^2-3)/(-2*C1*a*r^2+1)^2)

``

> 

pr := simplify(-D1+3*a*A1*C1*(2*C1*a*r^2-3)/(-2*C1*a*r^2+1)^2)

``

> 

pt := simplify((D1*(-D1*r^2+4)-4*a^4*C1^4*r^6*(9*(1+A1)^2-(4*(1+3*A1))*D1*r^2+4*D1^2*r^4)+2*a*C1*(18*A1-(16+9*A1)*D1*r^2+4*D1^2*r^4)-3*a^2*C1^2*r^2*(9+16*A1+27*A1^2-(28*(1+A1))*D1*r^2+8*D1^2*r^4)+4*a^3*C1^3*r^4*(18+3*A1*(17+9*A1)-(10*(2+3*A1))*D1*r^2+8*D1^2*r^4))/((4*(C1*a*r^2+1))*(2*C1*a*r^2-1)^3))

``

> 

drhodp := simplify(1/A1)

``

> 

dptdp := (diff(pt, r))/(diff(pr, r))

``

> 

A := simplify(-(-1-explambda)/r+4*explambda*Pi*r*(pr-density))

``

> 

B := -(explambda^2+4*explambda+1)/r^2-64*explambda^2*Pi^2*r^2*pr^2-16*explambda*Pi*((-2+explambda)*pr-pt-density)-(-4*explambda*Pi*(pr+density)-4*explambda*Pi*drhodp*(pr+density))/dptdp

``

> 

sys := {r*(diff(y(r), r))+y(r)^2+(A*r-1)*y(r)+r^2*B = 0}

 

[moderator edited to remove pages of output]
 

Download CALCULATION_OF_Y_v1.mw
 

Solving the differential equation numeri...

bikramphy 70 Maple
ode dsolve numeric
November 03 2020
0 1

I am trying to solve a differential equation numerically. But I am facing some difficulties. It is saying that ODE system has a removable singularity at r = 0. How can I remove the singularity?  Please check the attached figure and try to help.

Given a lagrangian in general relativit...

bikramphy 70 Maple
affine lagrangian metric
September 19 2020
0 0

Given a lagrangian  in general relativity , how can I calculate equation of motion using euler lagrangian equation in maple software ?

the lagrangian is 

L = 1/2 g[mu,nu] diff(x[~mu], lambda) diff(x[~nu],lambda)

here lambda is the affine parameter.  and the metric is 

 

 

metric coordinate = (t,u,x,y)

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