homework10.pdf?? Done Phys/Math 479: Special and General Relativity Homework 10
ID: 2304801 • Letter: H
Question
homework10.pdf?? Done Phys/Math 479: Special and General Relativity Homework 10 due: April 11, 2018 Problem 1 Consider a space-time with line element ds2--dt2 + e2"dr2 + dr + da (i) Show that the 4-vectors e, (1.0, 0.0), ei (0,e-r,0,0), = = ei = (0,0, 1, 0) and e (0,0,0,1) form an orthonormal basis. the components po =-p e, and pi = p-ei of the 4-momentum What is the mass of a particle with this 4-momentum? moving along a worldline given by (ii) Using the basis given in part (i) as a local inertial frame, compute (ii) Using a global frame (t,r), compute the 4-momentum of a particle t(r) = a-i sinh(ar) ?(r) = log(a-1 cosh(ar)) , and y(T)-0 with a constant a Compute the components p of the same particle, using the orthonor- mal basis of part () 1 of 1Explanation / Answer
%Part1
x=0:0.2:10;
y=sin(x);
h=.2;
forw=(y(2:end)-y(1:end-1))/h;
back=(y(2:end)-y(1:end-1))/h;
cen=(y(3:end)-y(1:end-2))/(2*h);
act=cos(x);
plot(x(1:end-1),forw,'b',x(2:end),back,'g',x(2:end-1),cen,'r',x,act,'k:','linewidth',2)
xlabel('x')
ylabel('dy/dx')
title('x vs dydx')
legend('Forward difference','Backward difference','Central Difference','Actual Derivative')
%
%PARTB
f=@(x)x.*sin(x.^2)+1;
x=0:.01:10;
act=sin(x.^2)+2*x.^2.*cos(x.^2);
h=.01;
y=f(x);
cen1=(y(3:end)-y(1:end-2))/(2*h);
h=.1;x1=0:h:10;
y=f(x1);
cen2=(y(3:end)-y(1:end-2))/(2*h);
h=.5;x2=0:h:10;
y=f(x2);
cen3=(y(3:end)-y(1:end-2))/(2*h);
figure
plot(x,act,'r',x(2:end-1),cen1,'k:',x1(2:end-1),cen2,'b:',x2(2:end-1),cen3,'g:','linewidth',2)
xlabel('x')
ylabel('dy/dx')
title('x vs dydx')
legend('Actual Derivation','Central difference (h=.01)','Central difference (h=.1)','Central difference (h=.5)')
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.