FORM 4.0 (Jun 30 2012) 64-bits Run: Mon Feb 4 11:47:30 2013 * Title: POINT CHARGE: * tests for energy-momentum tensor as a tempered distribution * File: energy-tensor-test.frm * Author: David N. Williams * License: Creative Commons Attribution-Share Alike * Started: September 3, 2012 * Revised: September 3-5,7,10,11, 2012 * * All parts of this program not in the public domain are: * * Copyright (C) 1987-1990, 2012 David N. Williams * * This work is licensed under the Creative Commons Attribution- * Share Alike 2.5 License. To view a copy of this license, visit * http://creativecommons.org/licenses/by-sa/2.5/ or send a letter * to Creative Commons, 543 Howard Street, 5th Floor, San * Francisco, California, 94105, USA. * * Input: energy-tensor.sav * Output: log file #if 0 The calculation in energy-tensor.frm realizes the retarded or advanced energy-momentum tensor for the electromagnetic field of a point charge as a tempered distribution. This program verifies agreement with our hand calculated Master Sheet dated October 13, 1974. #endif *** DECLARATIONS #include derivs-ra.h #- off statistics; I mu,nu,la,ro; * tensors for pretty printing CF [r,u],[r,a],[rr],[{r,u}],[{r,a}],[uu],[{u,a}],[aa]; Load energy-tensor.sav; dr loaded du loaded da loaded dj loaded [d(r.u)] loaded [d(r.a)] loaded [d.r] loaded [d.u] loaded [d.a] loaded [d.j] loaded [r.dr] loaded [r.du] loaded [r.da] loaded [r.dj] loaded [u.dr] loaded [u.du] loaded [u.da] loaded [a.dr] loaded [a.du] loaded [a.da] loaded df loaded df1 loaded [r.d(r.u)] loaded [r.d(r.a)] loaded [u.d(r.u)] loaded [u.d(r.a)] loaded [a.d(r.u)] loaded [a.d(r.a)] loaded [r.df] loaded [u.df] loaded dfr loaded dfu loaded dfa loaded dfj loaded df1r loaded df1u loaded df1a loaded df1j loaded drr loaded dru loaded dra loaded drj loaded duu loaded dua loaded duj loaded daa loaded daj loaded dfrr loaded dfru loaded dfra loaded dfrj loaded dfuu loaded dfua loaded dfuj loaded dfaa loaded dfaj loaded [d.fr] loaded [d.fu] loaded [d.fa] loaded [d.fj] loaded [d.frr] loaded [d.fru] loaded [d.fra] loaded [d.fur] loaded [d.fuu] loaded [d.fua] loaded [d.far] loaded [d.fau] loaded [d.faa] loaded ddf loaded ddr loaded ddu loaded dda loaded ddfr loaded ddfu loaded ddfa loaded ddrr loaded ddru loaded ddra loaded dduu loaded ddua loaded ddaa loaded ddfrr loaded ddfru loaded ddfra loaded ddfuu loaded ddfua loaded ddfaa loaded dddfr loaded A loaded F loaded t1 loaded t2 loaded t3 loaded t4 loaded t5 loaded w5 loaded [d.w5] loaded t6 loaded TCEM loaded [d.wi] loaded [d.wii] loaded [d.waiii] loaded [d.wbiii] loaded [d.wiii] loaded [d.t6a] loaded [d.t6b] loaded [d.t6c] loaded t7 loaded ti loaded tii loaded taiii loaded tbiii loaded T loaded *** MODULES L diff1 = - t1(mu,nu) + g(mu,nu)*c^2*( 2*r.a - c^2 )/r.u^4 ; L diff2 = - t2(mu,nu) + g(mu,nu)*(-c^2)*2*( r.a - c^2 )/r.u^4 #if 0 + u(mu)*u(nu)*6*c^2/r.u^4 + r(mu)*r(nu)*( 8*c^2*( r.a - c^2 )^2/r.u^6 - 2*c^2*r.j/r.u^5 ) + ( r(mu)*u(nu) + u(mu)*r(nu) )*8*c^2*( r.a - c^2 )/r.u^5 + ( r(mu)*a(nu) + a(mu)*r(nu) )*(-2*c^2)/r.u^4 #else + [uu](mu,nu)*6*c^2/r.u^4 + [rr](mu,nu)*( 8*c^2*( r.a - c^2 )^2/r.u^6 - 2*c^2*r.j/r.u^5 ) + [{r,u}](mu,nu)*8*c^2*( r.a - c^2 )/r.u^5 + [{r,a}](mu,nu)*(-2*c^2)/r.u^4 #endif ; L diff3 = - t3(mu,nu) + g(mu,nu)*3/2*c^4/r.u^4 #if 0 + r(mu)*r(nu)*3*c^4*( 2*r.a + c^2 )/r.u^6 + ( r(mu)*u(nu) + u(mu)*r(nu) )*(-3*c^4)/r.u^5 #else + [rr](mu,nu)*3*c^4*( 2*r.a + c^2 )/r.u^6 + [{r,u}](mu,nu)*(-3*c^4)/r.u^5 #endif ; L diff4 = -t4(mu,nu) #if 0 + u(mu)*u(nu)*3*c^2/r.u^4 + ( r(mu)*u(nu) + u(mu)*r(nu) )*(-9/2)*c^2*r.a/u.r^5 + ( r(mu)*a(nu) + a(mu)*r(nu) )*3/2*c^2/r.u^4 #else + [uu](mu,nu)*3*c^2/r.u^4 + [{r,u}](mu,nu)*(-9/2)*c^2*r.a/u.r^5 + [{r,a}](mu,nu)*3/2*c^2/r.u^4 #endif ; L diff5 = -t5(mu,nu) + g(mu,nu)*(-3*c^4)/r.u^4 #if 0 + u(mu)*u(nu)*(-9*c^2)/r.u^4 + r(mu)*r(nu)*12*c^4*( r.a - c^2 )/r.u^6 + ( r(mu)*u(nu) + u(mu)*r(nu) )*c^2*( -9/2*r.a + 12*c^2 )/r.u^5 + ( r(mu)*a(nu) + a(mu)*r(nu) )*3/2*c^2/r.u^4 #else + [uu](mu,nu)*(-9*c^2)/r.u^4 + [rr](mu,nu)*12*c^4*( r.a - c^2 )/r.u^6 + [{r,u}](mu,nu)*c^2*( -9/2*r.a + 12*c^2 )/r.u^5 + [{r,a}](mu,nu)*3/2*c^2/r.u^4 #endif ; * CEM, p. 8 G diffT1 = -TCEM(mu,nu) - 1/2*g(mu,nu)*c^4/r.u^4 #if 0 + r(mu)*r(nu)*( -a.a - c^2*( c^2 - r.a )^2/r.u^2 )/r.u^4 + ( r(mu)*u(nu) + u(mu)*r(nu) )*c^2*( c^2 - r.a )/r.u^5 + ( r(mu)*a(nu) + a(mu)*r(nu) )*c^2/r.u^4 #else + [rr](mu,nu)*( -a.a - c^2*( c^2 - r.a )^2/r.u^2 )/r.u^4 + [{r,u}](mu,nu)*c^2*( c^2 - r.a )/r.u^5 + [{r,a}](mu,nu)*c^2/r.u^4 #endif ; * This verifies the distributional energy-momentum tensor. L diffT2 = -TCEM(mu,nu) + t1(mu,nu) + t2(mu,nu) + t3(mu,nu) + t4(mu,nu) + t5(mu,nu) + t6(mu,nu) ; L diff7 = -t7(mu,nu) - 2*t1(mu,nu) + t2(mu,nu); L diffT3 = -TCEM(mu,nu) + T(mu,nu); print +s; .end diff1 = 0; diff2 = 0; diff3 = 0; diff4 = 0; diff5 = 0; diffT1 = 0; diffT2 = 0; diff7 = 0; diffT3 = 0; 0.00 sec out of 0.00 sec