alejandrito20

Hello

I study physics in chile. I am doing my thesis in "brane world and gauss bonnet term"...i studied randall sundrum 1 and 2 models, and some paper abaut the topic......My teacher of thesis does not help me....

I need find a topic abaut this subject that has not been done....My teacher says that my thesis has to be something new....unfortunately, i don't know another teacher to change......

¿anybody suggest me some calculus?

in a paper (hep-th/9905012)says that de (0,0) einstein tensor is

[math]G_{00}=3(\frac{\dot{a^2}}{a^2}-\frac{n^2}{b^2}[\frac{a''}{a}+\frac{a'^2}{a^2}-\frac{a'b'}{ab}])[/math] (eq1)

and [math]T_{00}=\frac{\rho\delta(y) n(t,y)^2 }{b(t,y)}[/math]

where

[math]a=a_0+(\frac{|y|}{2}-\frac{y^2}{2})[a']_0-\frac{y^2[a']_{1/2}}{2}[/math] (eq2)

and [math]a''=[a']_0 (\delta(y)-\delta(y-1/2) ) + ([a']_0 +[a']_{1/2} ) (\delta(y-1/2) - 1 ) ) [/math]

with [math] [a']_0 [/math] is the jump of a detivate of a in y=0....

other relation are:

[math] \frac{[a']_0}{a_0b_0}=-\frac{k^2 \rho}{3} [/math] (Eq 2.5)

[math]b=b_0+2|y|(b_{1/2}-b_0)[/math] (Eq3)

i don't understan why the (0,0) component of Einstein equation at y=0 is:

[math] \frac{\dot{a_0^2}}{a_0^2}=\frac{n_0^2}{b_0^2}(-\frac{[a']_{1/2}}{a_0}-\frac{b_{1/2}[a']_0}{b_0a_0}+\frac{[a']_0^2}{4a_0^2})[/math]

with [math]a_0=a(t,y=0)[/math]

i calculate [math]k^2T_{00}=-\frac{3n_0^2[a']_0\delta(y)}{b_0^2a_0}[/math]

but my mind question is that, i don't understand how i evaluate [math]a'_0[/math] end [math]b'_0[/math]...if i derivate Eq 2, the [math]\frac{d|y|}{dy}[/math] are not defined on y=0¡¡¡¡¡¡

I think it'll be the green path. Is [math]\epsilon \geq 0[/math]?

yes, [math]\epsilon[/math] is [math]>0[/math]

If the integral is [math]\int^{\pi-\epsilon}_{-\pi+\epsilon}d\theta[/math].

where [math]\theta[/math] is a angular coordinate.

In the riemman integral , i dont understand if tetha follows the path grenn in figure 1, or [math]\theta[/math] follows the path red in figure 2.

Hello.

I understand that [math]\frac{d|x|}{dx}=\theta(x)-\theta(-x)[/math] and then [math]\frac{d^2|x|}{dx^2}=2\delta(x)[/math].

But i DONT UNDERSTAND why when [math]\phi[/math] is a angular coordinate, then [math]\frac{d^2|\phi|}{d\phi^2}=2(\delta(\phi)-\delta(\pi-\phi))[/math]

in a spacetime with axial gauge fluctuation of metric component [math]h_{uv}[/math]

¿what mean the transverse traceless TT [math]h_{uv}^{TT}[/math], and non transverse traceless NT [math]h_{uv}^{NT}[/math] component??

When delta-potential is different from zero, it is f'' of f itself that compensate the potential term in the equation. So the plane wave cannot be a wave equation solution everywhere. "Inside" potential barrier the wave function is specific, zero, for example.

specifically, my problem is (u,v) component of Einstein equation:

[math]kf''(x)+k1=\frac{k2}{f(x)^2}(T\delta(x)+T1\delta(x-\pi)[/math]

with k,k1,k2 constant

with x between ([math]-\pi,\pi[/math])

i need to find, T and T1.

In (5,5) component of einstein equation (this equation don't have deltas of dirac) the solution is

[math]f(x)=C(|x|+C1)^2[/math]

with C and C1 konstant

[math]f''=2C\frac{d|x|}{dx}+2C1\frac{d^2|x|}{dx^2}[/math]

with [math]\frac{d^2|x|}{dx^2}=2(\delta(x)-\delta(x-\pi)[/math]

The original equation makes sense only if delta is a constant which is not the case.

 

For any other function you have a contradiction: (T-1)delta = k. A constant cannot be variable so the original equation has the only solution: T=1 if k = 0.

but in the delta dirac potential:

[math]\frac{-h^2}{2m}f''+\delta(x)f=Ef[/math] (eq1)

with [math]f=Ae^{ikx}[/math]

then

[math]-\frac{k^2h^2}{2m}+E=\delta(x)[/math]

but [math]\delta(x)[/math] is infinity in zero. This problem would not have sence too.

If [math]f=Ae^{ik|x|}[/math]

then eq 1 is

[math]-\frac{k^2h^2}{m}\delta(x)+\delta(x)=E[/math]

this problem would have sense only if E= 0, but E IS NOT ZERO.

hello

in need to find T in the follow equation:

[math]\delta(\phi-\pi)+k=T\delta(\phi-\pi)[/math]

where [math]\phi[/math] is a angular coordinate between([math]-\pi,\pi[/math])

¿is correct do:

[math]\int^{\pi-\epsilon}_{-\pi+\epsilon}\delta(\phi-\pi)d\phi+\int^{\pi-\epsilon}_{-\pi+\epsilon} k=T\int^{\pi-\epsilon}_{-\pi+\epsilon}\delta(\phi-\pi)[/math]???????????

¿ [math]\delta(\phi-\pi)[/math] with [math]\phi=-\pi+\epsilon[/math] is infinity??????

i have tried to do

[math]\int\frac{du}{\sqrt{A+Be^{2u}+C\sqrt{D+Ee^{4u}}}}=\int dy[/math]

but, this integral ........????????

chain rule is [math]2\frac{du}{dy}\frac{d^2u}{d^2y}=2Be^{2u}\frac{du}{dy}+2CE\frac{du}{dy}\frac{e^{4u}}{\sqrt{D+Ee^{4u}}}[/math]????????

[math](\frac{du}{dy})^2=A+Be^{2u}+C \sqrt{D+Ee^{4u}}[/math]

where A,B,C,D,E are nonzero

Hello. In maple:

the signum function is signum(x)=x/|x|

the derivate is d/dx {signum(x)}=signum(1,x)

what is:

signum(1,1,0)

signum(1,x,0)

signum(0,x,0)

????

you say this?

if exp(-f(t))=c(t) then

a := (-2*c(t)^3*(Diff(f(t), t))^2
+2*c(t)^3*(Diff(f(t), t, t))
+3*c(t)^2*(Diff(f(t), t))^4
+2*sqrt((-1+c(t)^(-1)*(Diff(f(t), t))^2)*c(t)^4*(-c(t))
+(Diff(f(t), t))^2*c(t)))*c(t)/((c(t)
-(Diff(f(t), t))^2)*sqrt(((-1+(Diff(f(t), t))^2)*c(t)^4)
*(-(c(t))-(Diff(f(t), t))^2)*c(t)^3)) = 0;

but

    dsolve(a,c(t)); maple says error... 

    dsolve(a,f(t)); maple shows a bas solution and extensive... 

sorry for not understanding. I'm starting to use maple

If you're solving a system of equations then they should be written as an array in the first parameter, the second parameter should be the function you're trying to solve for. (same as using the solve command for non-differential equations).

 

e.g.

ec1 := Diff(f(t),t)^2 - 4*f(t)  = 0;
ec2 := Diff(f(t),t,t) - 2  = 0;
dsolve([ec1,ec2],f(t));

i dont understand

where I place a(t) ?

For my thesis I need to solve many differential equations non linear, second order by using maple....

For example figure adjoint

using dsolve command, the solutions are very extensives and very bad.

there is a suggest for to solve the differential equations by using maple?

there is some methods in maple to find the aproximate solution?

thanks

any suggestions to solve the follows differential equations by using maple???

see adjoint figure

I want to calculate the Ricci tensor for a 5-D metric.

For example , the randall sundrum metric.

ds^2=dw^2+exp(-2A(w))*(-dt^2+dx^2+dy^2+dz^2)

there is any computer program to calculate ricci tensor in 5d spacetime?

In 4d , using grtensor for the metric:

ds^2=exp(-2A(w))*(-dt^2+dx^2+dy^2+dz^2)

but, all component are zero (figure)

any suggestions?

Hello.

I will do my thesis in " metric perturbation in the brane worlds and use of gauss bonnet term...I'm beginning to study the theory.

What is the difference between metric perturbation in the brane world and cosmological perturbation of brane world?

cosmological perturbations affect my thesis?

I do not consider string theory in my dissertation

Any suggestions for my work? I thank

which numerical methods are used for to solve the geodesic (by example)?

Any other suggestion?

What about numerically solving the geodesic equations in some interesting space-times?

hello, thanks

for example that space-times?

Hello

My name is alejandro, I study physics in Chile.

Now i have to do my thesis. My course of general relativity you were guided for the text " a firtz course of general relativity of Bernard Schutz".

Do you recommend some theme for my thesis to me?

I want a theoretic theme and very advanced no, since my knowledge are not very advanced.

I want a mathematical theme pertaining to general relativity

Thanks

post data: i dont speak english very well