#include <stdio.h> #include <math.h> #include "tyh.h" d rs=1e-2; /*d nu trab z = log(mrs); rz*/ d nu trab z = log(1 - 1/(r*r*x[0])); rz /*d lamda trab z = log(1/mrs); rz*/ d lamda trab z = log(1 - 1/(r*t)); rz d ro trab z = x[1]/(t*t); rz /*Used symbols t,r,a,b,rs,mrs,mrs2,trab,sa,sb,ca,cb,x[],V[][],g00*/ /*g11,g22,g33,g[],W00,..,W[][],V00,..,VB00,..,VB200,..,V[][],VB[][],VB2[][]*/ /*VRab00,..,VRab[][],XYtrabLB00,..,LB200,..,LB[][],LB2[][],LRab00,..,LRab[][]*/ /*Lor,LorB1R1,fjk,Lp1,Lp2,ggNN,gg[],d,rz,fz,PI,A,B,K,GN,gr*/ d Lp1 = 0; /* Lorentz parameter - Boosts*/ d Lp2 = 0; d Lp3 = 0; d Lp4 = 0;/*Rotations*/ d Lp5 = 0; d Lp6 = 0; int ETA[4] = {1,-1,-1,-1}; d x[4]={7.00, 1.00, 1.5707963 , 0.00}; d dx[4]={0.0001, 0.0001, 0.0001, 0.0001}; /*Covariant metric*/ d g00 trab z= exp(nu(x)); rz d g11 trab z= -exp(lamda(x)); rz d g22 trab z= - (ro(x) * ro(x)); rz d g33 trab z= -(ro(x) * ro(x) * sa * sa); rz d (*g[4])() = { g00, g11, g22, g33}; d dg(d x[]){d z; z = g00(x) * g11(x) * g22(x) * g33(x); rz /*Contravariant metric*/ d gg00 trab z = exp(-nu(x)); rz d gg11 trab z = -exp(-lamda(x)); rz d gg22 trab z = -1/(ro(x) * ro(x)); rz d gg33 trab z = - 1/(ro(x) * ro(x) * sa * sa); rz d (*gg[4])() = {gg00,gg11,gg22,gg33}; /*Christoffel Symbols*/ d deriv(d (*f)(d x[]), d x[], d dx[], int i); d G000 trab z = 0.5 * deriv(nu, x, dx, 0); rz d G001 trab z = 0.5 * deriv(nu, x, dx, 1); rz d G011 trab z = 0.5 * deriv(lamda, x, dx, 0) * exp(lamda(x)-nu(x)); rz d G022 trab z = ro(x) * deriv(ro, x, dx, 0); rz d G033 trab z = ro(x) * deriv(ro, x, dx, 0) * sa*sa; rz d G100 trab z = 0.5 * deriv(nu, x, dx, 1) * exp(nu(x)-lamda(x)); rz d G101 trab z = 0.5 * deriv(lamda, x, dx, 0); rz d G111 trab z = 0.5 * deriv(lamda, x, dx, 1); rz d G122 trab z = - ro(x) * deriv(ro, x, dx, 1) * exp(-lamda(x)); rz d G133 trab z = - ro(x) * deriv(ro, x, dx, 1)*exp(-lamda(x))*sa*sa; rz d G212 trab z = deriv(ro, x, dx, 1)/ro(x); rz d G233 trab z = -sa * ca; rz d G323 trab z = ca / sa; rz d (*G[4][4][4])() = {G000,G001,F0,F0,G001,G011,F0,F0,F0,F0,G022,F0,F0,F0,F0, G033,G100,G101,F0,F0,G101,G111,F0,F0,F0,F0,G122,F0, F0,F0,F0,G133,F0,F0,F0,F0,F0,F0,G212,F0,F0,G221,F0,F0,F0, F0,F0,G233,F0,F0,F0,F0,F0,F0,F0,G313,F0, F0,F0,G323,F0,G331,G323,F0}; /* W or W1 is the original tetrad TX.C*/ d W00 trab z= exp(-nu(x)/2) * ch; rz d W01 trab z= exp(-lamda(x)/2) * sh; rz d W10 trab z= exp(-nu(x)/2) * sh * sa * cb; rz d W11 trab z= exp(-lamda(x)/2) * sa * cb * ch; rz d W12 trab z= 1/ro(x) * ca * cb; rz d W13 trab z= -(1/(ro(x) * sa) * sb); rz d W20 trab z= exp(-nu(x)/2) * sa * sb * sh; rz d W21 trab z= exp(-lamda(x)/2) * sa * sb * ch; rz d W22 trab z= 1/ro(x) *ca * sb; rz d W23 trab z= 1/(ro(x) * sa) * cb; rz d W30 trab z= exp(-nu(x)/2) * ca * sh; rz d W31 trab z= exp(-lamda(x)/2) * ca * ch; rz d W32 trab z= -(1/ro(x) * sa); rz d (*W[4][4])() = {W00,W01,F0,F0,W10,W11,W12,W13,W20,W21,W22,W23,W30,W31,W32 ,F0}; d AnaliticGG00(void){d z; z = (1 - mrs2) * (1 - mrs2)/(r * r); rz d AnaliticGG11(void){d z; z = (1 - mrs2) * (1 - mrs2)/(r * r) + (1 - 1/mrs2) * r s/(r*r*r); rz d AnaliticGG22(void){d z; z = 0.5 * (1 - 1/mrs2) * rs/(r*r*r); rz d (*AnaliticGG[4][4])(void)={AnaliticGG00,F0,F0,F0,F0,AnaliticGG11,F0,F0,F0,F0,A naliticGG22,F0,F0,F0,F0,AnaliticGG22}; /*W2 is the tetrad oriented as the spherical coordinates*/ d W200 trab z= exp(-nu(x)/2); rz d W211 trab z= exp(-lamda(x)/2); rz d W223 trab z= 1/(ro(x) * sa); rz d W232 trab z= -1/ro(x); rz d (*W2[4][4])() = {W200,F0,F0,F0,F0,W211,F0,F0,F0,F0,F0,W223,F0,F0,W232,F0}; d (*Lor)(); void NoLor(void){fputs("No Lorentz Transformation Defined\n",stdout);} /*V is the tetrad W after Lorentz transformation*/ d V00 fz Lor(x,0,i) * W[i][0](x);} rz d V01 fz Lor(x,0,i) * W[i][1](x);} rz d V02 fz Lor(x,0,i) * W[i][2](x);} rz d V03 fz Lor(x,0,i) * W[i][3](x);} rz d V10 fz Lor(x,1,i) * W[i][0](x);} rz d V11 fz Lor(x,1,i) * W[i][1](x);} rz d V12 fz Lor(x,1,i) * W[i][2](x);} rz d V13 fz Lor(x,1,i) * W[i][3](x);} rz d V20 fz Lor(x,2,i) * W[i][0](x);} rz d V21 fz Lor(x,2,i) * W[i][1](x);} rz d V22 fz Lor(x,2,i) * W[i][2](x);} rz d V23 fz Lor(x,2,i) * W[i][3](x);} rz d V30 fz Lor(x,3,i) * W[i][0](x);} rz d V31 fz Lor(x,3,i) * W[i][1](x);} rz d V32 fz Lor(x,3,i) * W[i][2](x);} rz d V33 fz Lor(x,3,i) * W[i][3](x);} rz d (*V[4][4])()={V00,V01,V02,V03,V10,V11,V12,V13,V20,V21,V22,V23,V30,V31,V32,V33} ; d iAnaliticGG00(d x[]){d z; z = (1 - mrs2) * (1 - mrs2)/(r * r); rz /*d iTG00(d x[]){d z; z = - 4*PI*r*r*gg00(x) * iAnaliticGG00(x) / K ; rz*/ d iEG(d x[]){d z; z = - 4*PI* V00(x) * (1 - mrs2) * (1 - mrs2) / K ; rz void main (void) { extern d (*LB1[4][4])();extern d (*LB2[4][4])();extern d (*LB3[4][4])(); extern d (*LR1[4][4])();extern d (*LR2[4][4])();extern d (*LR3[4][4])(); int c; int i; int j; int k; int m; int n; d z = 0; d y = 0; d GM[4][4]; d G1[4][4]; /*FOUR COMPONENTS of the EINSTEIN Tensor*/ d G2[4][4]; d G3[4][4]; d G4[4][4]; d TG1; /* Auxiliar for Gx[4][4]*/ d TG2; d TG3; d TG4; static char buf[30]; char *buf2 = "?"; char *buf3 = "W1 enabled"; d GG[4][4]; d L1 = 7e10; d L2 = 1e12; d idx = 1e-15; d zz[4]; /*Save original tetrads*/ d (*W1[4][4])() ; d (*Vx[4][4])() ; fjk W1[j][k] = W[j][k];}} fjk Vx[j][k] = V[j][k];}} a1: /*Ask for parameter values*/ fputs("General Spherical Symmetric Metric gjk = { exp(nu),-exp(lamda),-ro2,-ro2s in2 (teta)}\n",stdout); fputs("Rjk=R1jk + R2jk = Rotor + Comutator\n",stdout); fputs("Lorentz Rotations are here the inverse than in Q,R and S\n", stdout); fputs("rs = ",stdout); fputs(gcvt(rs, 12, buf),stdout);fputs(" rs = ",stdout); gets(buf); if (buf[0] != '') rs = atof(buf); fputs("r = ",stdout); fputs(gcvt(r, 12, buf),stdout);fputs(" r = ",stdout); gets(buf); if (buf[0] != '') r = atof(buf); fputs("x[2] = ",stdout); fputs(gcvt(x[2], 12, buf),stdout);fputs(" x[2] = ",stdout); gets(buf); if (buf[0] != '') x[2] = atof(buf); fputs("x[3] = ",stdout); fputs(gcvt(x[3], 12, buf),stdout);fputs(" x[3] = ",stdout); gets(buf); if (buf[0] != '') x[3] = atof(buf); fputs("dr = ",stdout); fputs(gcvt(dx[1], 12, buf),stdout);fputs(" dr = ",stdout); gets(buf); if (buf[0] != '') dx[1] = atof(buf); fputs("dx[2] = ",stdout);fputs(gcvt(dx[2],12,buf),stdout); fputs(" dx[2] = ",stdout); gets(buf); if (buf[0] != '') dx[2] = atof(buf); fputs("dx[3] = ",stdout); fputs(gcvt(dx[3], 12, buf),stdout); fputs(" dx[3] = ",stdout); gets(buf); if (buf[0] != '') dx[3] = atof(buf); fputs("First Lorentz parameter = ", stdout); fputs(gcvt(Lp1, 12, buf),stdout); fputs(" Lp1 = ",stdout);gets(buf); if(buf[0] != '') Lp1 = atof(buf); fputs("Second Lorentz parameter = ", stdout); fputs(gcvt(Lp2, 12, buf),stdout); fputs(" Lp2 = ",stdout);gets(buf); if(buf[0] != '') Lp2 = atof(buf); fputs("Third Lorentz parameter = ", stdout); fputs(gcvt(Lp3, 12, buf),stdout); fputs(" Lp3 = ",stdout);gets(buf); if(buf[0] != '') Lp3 = atof(buf); fputs("Fourth Lorentz parameter = ", stdout); fputs(gcvt(Lp4, 12, buf),stdout); fputs(" Lp4 = ",stdout);gets(buf); if(buf[0] != '') Lp4 = atof(buf); fputs("Fifth Lorentz parameter = PI/2 - x[2] ; ENTER ", stdout); /*fputs(gcvt(L p5, 12, buf),stdout);*/ /*fputs(" Lp5 = ",stdout);*/ gets(buf);if(buf[0] != '') Lp5 = atof(buf); fputs("6th Lorentz parameter = -x[3] ; ENTER ", stdout); /*fputs(gcvt(Lp6, 12, buf),stdout);*/ /*fputs(" Lp6 = ",stdout);*/ gets(buf);if(buf[0] != '') Lp6 = atof(buf); fputs("Low limit of integration = ", stdout); fputs(gcvt(L1, 12, buf),stdout); fputs(" L1 = ",stdout);gets(buf); if(buf[0] != '') L1 = atof(buf); fputs("High limit of integration = ", stdout); fputs(gcvt(L2, 12, buf),stdout); fputs(" L2 = ",stdout);gets(buf); if(buf[0] != '') L2 = atof(buf); fputs("Integral increment = ", stdout); fputs(gcvt(idx, 12, buf),stdout); fputs(" idx = ",stdout);gets(buf); if(buf[0] != '') idx = atof(buf); /*Print parameter values*/ fputs("Lorentz transformation = ",stdout);fputs(buf2,stdout);fputs("\n",stdout) ; fputs("rs = ",stdout); fputs(gcvt(rs,12,buf),stdout); fputs(" r = ",stdout); fputs(gcvt(r,12,buf),stdout); fputs(" x[2] = ", stdout);fputs(gcvt(x[2],12, buf), stdout); fputs(" x[3] = ", stdout); fputs(gcvt(x[3], 12, buf), stdout);fputs("\n",stdou t); fputs(" dx[1] = ", stdout);fputs(gcvt(dx[1],12, buf), stdout); fputs(" dx[2] = ", stdout);fputs(gcvt(dx[2],12, buf), stdout); fputs(" dx[3] = ", stdout); fputs(gcvt(dx[3], 12, buf), stdout);fputs("\n",std out); fputs(" Lp1 = ",stdout); fputs(gcvt(Lp1,12,buf),stdout); fputs(" Lp2 = ",stdout); fputs(gcvt(Lp2,12,buf),stdout); fputs(" Lp3 = ",stdout); fputs(gcvt(Lp3,12,buf),stdout); fputs(" Lp4 = ",stdout); fputs(gcvt(Lp4,12,buf),stdout); fputs(" Lp5 = ",stdout); fputs(gcvt(Lp5,12,buf),stdout); fputs(" Lp6 = ",stdout); fputs(gcvt(Lp6,12,buf),stdout); fputs(" L1 = ",stdout); fputs(gcvt(L1,12,buf),stdout); fputs(" L2 = ",stdout); fputs(gcvt(L2,12,buf),stdout); fputs(" idx = ",stdout); fputs(gcvt(idx,12,buf),stdout); fputs("\n",stdout); fputs("rs = ",stdprn); fputs(gcvt(rs,12,buf),stdprn); fputs(" r = ",stdprn); fputs(gcvt(r,12,buf),stdprn); fputs(" x[2] = ", stdprn);fputs(gcvt(x[2],12, buf), stdprn); fputs(" x[3] = ", stdprn); fputs(gcvt(x[3], 12, buf), stdprn);fputs("\n",stdpr n); fputs(" dx[1] = ", stdprn);fputs(gcvt(dx[1],12, buf), stdprn); fputs(" dx[2] = ", stdprn);fputs(gcvt(dx[2],12, buf), stdprn); fputs(" dx[3] = ", stdprn); fputs(gcvt(dx[3], 12, buf), stdprn); fputs("\n",stdprn); fputs(" Lp1 = ",stdprn); fputs(gcvt(Lp1,12,buf),stdprn); fputs(" Lp2 = ",stdprn); fputs(gcvt(Lp2,12,buf),stdprn); fputs(" Lp3 = ",stdprn); fputs(gcvt(Lp3,12,buf),stdprn); fputs(" Lp4 = ",stdprn); fputs(gcvt(Lp4,12,buf),stdprn); fputs(" Lp5 = ",stdprn); fputs(gcvt(Lp5,12,buf),stdprn); fputs(" Lp6 = ",stdprn); fputs(gcvt(Lp6,12,buf),stdprn); fputs(" L1 = ",stdprn); fputs(gcvt(L1,12,buf),stdprn); fputs(" L2 = ",stdprn); fputs(gcvt(L2,12,buf),stdprn); fputs(" idx = ",stdprn); fputs(gcvt(idx,12,buf),stdprn); fputs("\n",stdprn); a0: /*Menu of Lorentz transformations*/ fputs("Lorentz transformation = ",stdprn);fputs(buf2,stdprn);fputs("\n",stdprn); fputs("Lorentz transformation = ",stdout);fputs(buf2,stdout);fputs("\n",stdout); fputs("\nN No Lorentz 1 Boost1 2 Boost2 3 Boost3 4 Rot1 5 Rot2 6 Rot3 ENT ER O.K.\n",stdout); fputs("12 Rot3xRot2xBost1 14 Rot3xRot2\n",stdout); gets(buf); if(buf[0] == '1'&& buf[1] == '4') goto R3R2; if(buf[0] == '1'&& buf[1] == '2') goto BB; if(buf[0] == '1') goto b1; if(buf[0] == '2') goto b2; if(buf[0] == '3') goto b3; if(buf[0] == '4') goto r1; if(buf[0] == '5') goto r2; if(buf[0] == '6') goto r3; if(buf[0] == 'N') goto nl; if(buf[0] == '' && buf2[0] == '?') goto a0; if(buf[0] == '') goto a00; goto a0; a00: /*General Menu - The tetrads are contravariant and the tensors mixed*/ /*The Lorentz indeces are covariant*/ fputs("\n1 Paramters 2 V 3 VgV 4 Vcj,k 5 AnaliticmixR2jk/2 6 Vcj;kl 7 Rjk 8 R2jk/2 ",stdout); fputs("L Lorentz Matrix LT Lorentz Transformation W1 or W2 Tetrad 9 (VaiVbi;j );j\n",stdout); fputs("10 GGjk 11 AnaliticGGjk 12 Contravariant TG00?? 13 Integral?? 14 NULL \n15 EXIT",stdout); gets(buf); if(buf[0] == 'L' && buf[1] == 'T') goto a0; if(buf[0] == 'W' && buf[1] == '1') goto aW1; if(buf[0] == 'W' && buf[1] == '2') goto aW2; if(buf[0] == '1' && buf[1] == '0') goto a10; if(buf[0] == '1' && buf[1] == '1') goto a11; if(buf[0] == '1' && buf[1] == '2') goto a12; if(buf[0] == '1' && buf[1] == '3') goto a13; if(buf[0] == '1' && buf[1] == '4') goto a14; if(buf[0] == '1' && buf[1] == '5') goto a15; if(buf[0] == '1') goto a1; if(buf[0] == '2') goto a2; if(buf[0] == '3') goto a3; if(buf[0] == '4') goto a4; if(buf[0] == '5') goto a5; if(buf[0] == '6') goto a6; if(buf[0] == '7') goto a7; if(buf[0] == '8') goto a8; if(buf[0] == '9') goto a9; if(buf[0] == 'L') goto L; goto a00; aW1: fjk W[j][k] = W1[j][k];}} buf3 = "W1 enabled"; buf2 = "?"; fputs(buf3,stdout);fputs("\n",stdout); fputs(buf3,stdprn);fputs("\n",stdprn); fputs("The tetrad is = \n",stdout); fputs("The tetrad is = \n",stdprn); fjk z = W[j][k](x); fputs(gcvt(z, 12, buf), stdout);fputs(" ",stdout); fputs(buf, stdprn);fputs(" ",stdprn);} fputs("\n",stdout);fputs("\n",stdprn);} fputs("Please indicate Lorentz Transformation\n",stdout); goto a0; aW2: fjk W[j][k] = W2[j][k];}} buf3 = "W2 enabled"; buf2 = "?"; fputs(buf3,stdout);fputs("\n",stdout); fputs(buf3,stdprn);fputs("\n",stdprn); fputs("The tetrad is = \n",stdout); fputs("The tetrad is = \n",stdprn); fjk z = W[j][k](x); fputs(gcvt(z, 12, buf), stdout);fputs(" ",stdout); fputs(buf, stdprn);fputs(" ",stdprn);} fputs("\n",stdout);fputs("\n",stdprn);} fputs("Please indicate Lorentz Transformation\n",stdout); goto a0; R3R2: fjk V[j][k] = Vx[j][k];}}/*Return to V original value*/ Lor = LorR3R2; buf2 = "Rotation3 x Rotation2"; fputs(buf2,stdout);fputs("\n",stdout); fputs(buf2,stdprn);fputs("\n",stdprn); fputs("Lor = \n",stdout); fputs("Lor = \n",stdprn); fjk z = Lor(x,j,k); fputs(gcvt(z, 12, buf), stdout);fputs(" ",stdout); fputs(buf, stdprn);fputs(" ",stdprn);} fputs("\n",stdout);fputs("\n",stdprn);} goto a00; b1: buf2 = "Boost1"; fjk V[j][k] = Vx[j][k];}}/*Return to V original value*/ fputs(buf2,stdout);fputs("\n",stdout); fputs(buf2,stdprn);fputs("\n",stdprn); Lor = LorB1; goto a00; b2: buf2 = "Boost2"; fjk V[j][k] = Vx[j][k];}}/*Return to V original value*/ fputs(buf2,stdout);fputs("\n",stdout); fputs(buf2,stdprn);fputs("\n",stdprn); Lor = LorB2; goto a00; b3: buf2 = "Boost3"; fjk V[j][k] = Vx[j][k];}}/*Return to V original value*/ fputs(buf2,stdout);fputs("\n",stdout); fputs(buf2,stdprn);fputs("\n",stdprn); Lor = LorB3; goto a00; BB: buf2 = "R3xR2xB1"; fjk V[j][k] = Vx[j][k];}}/*Return to V original value*/ fputs(buf2,stdout);fputs("\n",stdout); fputs(buf2,stdprn);fputs("\n",stdprn); Lor = LorR3R2B1; goto a00; r1: buf2 = "Rotation on x1"; fjk V[j][k] = Vx[j][k];}}/*Return to V original value*/ fputs(buf2,stdout);fputs("\n",stdout); fputs(buf2,stdprn);fputs("\n",stdprn); Lor = LorR1; goto a00; r2: buf2 = "Rotation on x2"; fjk V[j][k] = Vx[j][k];}}/*Return to V original value*/ fputs(buf2,stdout);fputs("\n",stdout); fputs(buf2,stdprn);fputs("\n",stdprn); Lor = LorR2; goto a00; r3: fjk V[j][k] = Vx[j][k];}}/*Return to V original value*/ buf2 = "Rotation on x3"; fputs(buf2,stdout);fputs("\n",stdout); fputs(buf2,stdprn);fputs("\n",stdprn); Lor = LorR3; goto a00; nl: Lor = NoLor; fjk V[j][k] = W[j][k];}} buf2 = "Lorentz transformation disabled"; fputs(buf2,stdout);fputs("\n",stdout); fputs(buf2,stdprn);fputs("\n",stdprn); goto a00; #ifdef DEF2 /* Fuera de Servicio*/ z = mrs; fputs("mrs = ",stdout); fputs(gcvt(z, 12, buf), stdout); fputs("\n", stdout); z = mrs2; fputs("mrs2 = ", stdout); fputs(gcvt(z, 12, buf), stdout); fputs("\n",stdout); fputs("g = \n", stdout); for (j=0;j<=3;j++){ z = g[j](x); fputs(gcvt(z, 12, buf), stdout); fputs(" ", stdout); } fputs("\n\n", stdout); #endif DEF2 /*Fin de "Fuera de Servicio"*/ L: if(Lor == NoLor){NoLor(); goto a00;} fputs("L = \n",stdout); fputs("L = \n",stdprn); fjk z = Lor(x,j,k); fputs(gcvt(z, 12, buf), stdout);fputs(" ",stdout); fputs(buf, stdprn);fputs(" ",stdprn);} fputs("\n",stdout);fputs("\n",stdprn);} goto a00; a2: fputs(" k\n", stdout); fputs("V = \n", stdout); fputs(" a\n", stdout); fputs("Vak =\n",stdprn); for (j=0;j<=3;j++){ for (k=0;k<=3;k++){ fputs(gcvt(V[j][k](x), 12, buf), stdout); fputs(" ", stdout); fputs(buf, stdprn); fputs(" ", stdprn); } fputs("\n", stdout); fputs("\n", stdprn); } goto a00; a3: fputs("\n VgV =\n", stdout); for (j=0;j<=3;j++){ for (k=0;k<=3;k++){ z = VgV(V, V, x, j, k); fputs(gcvt(z, 12, buf), stdout); fputs(" ", stdout); } fputs("\n", stdout); } goto a00; a4: fputs("derivada Vcj,k = \n", stdout); for(c=0;c<=3;c++) {fputs("c = ", stdout); fputs(itoa(c, buf, 10),stdout);fputs("\n", stdout); fjk z = deriv(V[c][j], x, dx, k); fputs(gcvt(z, 12, buf), stdout); fputs(" ",stdout);} fputs("\n",stdout);}} goto a00; a5: fputs(" j\n",stdout); fputs("AnaliticmixR2 /2 =\n",stdout); fputs(" j\n",stdout); fputs("AnaliticmixR2jj/2 = \n",stdprn); zz[0] = AnaliticmixR200/2;zz[1]=AnaliticmixR211/2;zz[2]=AnaliticmixR222/2;zz[3] =AnaliticmixR233/2; for(j=0;j<=3;j++){ fputs(gcvt(zz[j],12,buf), stdout);fputs(" ",stdout); fputs(buf, stdprn);fputs(" ",stdprn); } fputs("\n",stdout); fputs("\n",stdprn); goto a00; a6: fputs("c = ",stdout); fputs(itoa (c, buf, 10), stdout); gets(buf); if (buf[0] != '') c = atoi (buf); fputs("c = ",stdout); for(i=0;i<=3;i++) { fputs(itoa(c, buf, 10), stdout);fputs(", ",stdout); fputs(itoa(i, buf, 10), stdout); fputs(" Vcj;kl = \n", stdout); fjk z = mixderMV(contderV, V, x, dx, c, i, j, k); fputs(gcvt(z, 12, buf), stdout); fputs(" ",stdout);} fputs("\n",stdout);} } goto a00; /*Fuera de Servicio*/ #ifdef DEF2 fputs("\nGijk = \n ",stdout); for(i=0;i<=3;i++){fjk if((z=G[i][j][k](x)) != 0) {c= i*100+j*10+k;fputs(itoa(c, buf,10),stdout); fputs(" Gijk = ",stdout);fputs(gcvt(G[i][j][k](x),12,buf),stdout); fputs(" ",stdout);}}} fputs("\n",stdout);} goto a0; #endif DEF2 /*Fin de Fuera de Servicio*/ a7: fputs(" j \n", stdout); fputs("R = \n", stdout); fputs(" l \n", stdout); fputs("Rjl = \n", stdprn); for (j=0;j<=3;j++){ for (k=0;k<=3;k++){ fputs(gcvt(Rjl(mixderMV,V,x,dx,j,k), 12, buf), stdout); fputs(buf,stdprn); fputs(" ", stdout); fputs(" ", stdprn); } fputs("\n", stdout); fputs("\n", stdprn); } goto a00; a8: fputs(" j \n",stdout); fputs("R2 /2 =\n",stdout); fputs(" k\n",stdout); fputs("R2/2 =\n",stdprn); fjk fputs(gcvt(R2lm(V,x,dx,j,k)/2,12,buf),stdout); fputs(" ",stdout); fputs(buf,stdprn);fputs(" ",stdprn);} fputs("\n",stdout); fputs("\n",stdprn);} goto a00; a9: fputs("(VajVbj;k);k = \n",stdout); fputs("(VajVbj;k);k = \n",stdprn); fjk fputs(gcvt(VgVjgj(VgVj,x,dx,j,k),12,buf), stdout);fputs(" ",stdout); fputs(buf, stdprn);fputs(" ",stdprn);} fputs("\n",stdout); fputs("\n",stdprn);} fputs("(sqrt(-g)VajVbj;k),k = \n",stdout); fputs("(sqrt(-g)VajVbj;k),k = \n",stdprn); fjk fputs(gcvt(SRdgVVjj(VgVj,x,dx,j,k),12,buf), stdout);fputs(" ",stdout); fputs(buf, stdprn);fputs(" ",stdprn);} fputs("\n",stdout); fputs("\n",stdprn);} goto a00; a10: /*GGij = Gravitational part of Einstein Tensor*/ /*RGij = Pkjk;l - Pkjl;k*/ /*void GGij(d GG[][4], d (*V[][4])(), d x[], d dx[])*/ GGij(GG,V,x,dx); fputs(" i\n",stdout); fputs("GG = \n",stdout); fputs(" j \n",stdout); fputs("GGij = \n",stdprn); fjk fputs(gcvt(GG[j][k],12,buf), stdout);fputs(" ",stdout); fputs(buf, stdprn);fputs(" ",stdprn);} fputs("\n",stdout); fputs("\n",stdprn);} #ifndef FOUR_COMPONENTS fputs("Trace of GG = TGG = ", stdout); fputs("Trace of GG = TGG = ", stdprn); fputs(gcvt(TGG(GG, x, dx),12,buf), stdout); fputs(buf, stdprn); fputs("\n",stdout); fputs("\n",stdprn); #endif goto a00; a11: fputs(" i\n",stdout); fputs("AnaliticGG =\n",stdout); fputs(" j\n",stdout); fputs("AnaliticGGij = \n",stdprn); fjk fputs(gcvt(AnaliticGG[j][k](),12,buf), stdout);fputs(" ",stdout); fputs(buf, stdprn);fputs(" ",stdprn);} fputs("\n",stdout); fputs("\n",stdprn);} goto a00; a12: fputs("If r and rs are given in cm. TG00 results in gr/cm3\n",stdout); fputs("K = ",stdout); fputs("K = ",stdprn); fputs(gcvt(K,12,buf), stdout);fputs(" ",stdout); fputs(buf, stdprn);fputs(" ",stdprn); fputs("\n",stdout); fputs("\n",stdprn); fputs("Contravariant GG00 = ",stdout); fputs("Contravariant GG00 = ",stdprn); fputs(gcvt(gg00(x)*AnaliticGG00(),12,buf), stdout);fputs(" ",stdout); fputs(buf, stdprn);fputs(" ",stdprn); fputs("\n",stdout); fputs("\n",stdprn); fputs("Contravariant TG00 = ",stdout); fputs("Contravariant TG00 = ",stdprn); fputs(gcvt(TG00(),12,buf), stdout);fputs(" ",stdout); fputs(buf, stdprn);fputs(" ",stdprn); fputs("\n",stdout); fputs("\n",stdprn); goto a00; a13: /*Integral*/ /*d iTG00(d x[]){d z; z = - 4*PI*r*r*gg00(x) * iAnaliticGG00(x) / K ; rz*/ /*d iAnaliticGG00(d x[]){d z; z = (1 - mrs2) * (1 - mrs2)/(r * r); rz*/ /*d integral (d (*f)(), d idx, d L1, d L2){d z=0; d y[4]; d dy; int i; int n;*/ /* y[1] = L1;*/ /* while(y[1] < L2){*/ /* y[1] += dy = L1*L1*idx/2;*/ /* z+= f(y) * 2*dy;} rz*/ fputs("Integral of EG = sqrt(-g) V00 TG00 = ",stdout); fputs("Integral of EG = sqrt(-g) V00 TG00 = ",stdprn); #ifndef integral fputs("Analitical Calculation = 4PIrs/k + 8PIL1/k (sqrt(1 - rs/L1) - 1) =\n",st dout); #endif #ifdef integral fputs(gcvt(integral(iEG(),idx,L1,L2),12,buf), stdout);fputs(" ",stdout); #endif #ifndef integral fputs(gcvt(EG(rs,L1),12,buf), stdout);fputs(" ",stdout); #endif fputs(buf, stdprn);fputs(" ",stdprn); fputs("\n",stdout); fputs("\n",stdprn); fputs("E/En = ",stdout);fputs("E/En = ",stdprn); fputs(gcvt(EG(rs,L1)/En,12,buf), stdout); fputs(gcvt(EG(rs,L1)/En,12,buf), stdprn); fputs("\n",stdout); fputs("\n",stdprn); goto a00; a14: goto a00; a15:
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