grg/pgt.up

% Exact soluition of the Poincare Gauge Theory
  with the Kerr-Newman in De Sitter metric;

Zero Time;
Coordinates  t,r,th,ph;
Constants  m,j,q,L;
Find Metric;
Functions f(th),Si(r,th),De(r),J(th),Q(r);

Frame
  T0 = SQRT(De)/SQRT(Si)*(d t + j*SIN(th)^2*d ph),
  T1 = SQRT(Si)/SQRT(De)*d r,
  T2 = SQRT(Si)/SQRT(f)*d th,
  T3 = SQRT(f)/SQRT(Si)*SIN(th)*(j*d t + (r^2+j^2)*d ph);

Constants L0,L1,L2,L3,L4,L5,L6;
L-Constants  LCONST1 =  L0,
             LCONST2 = -L0+2*L1,
             LCONST3 =  L0+2*L3-2*L1,
             LCONST4 =  L0+2*L5-2*L2,
             LCONST5 = -L0+2*L2,
             LCONST6 =  L0+2*L4-2*L2,
             LCONST0 = 1;

FF = SQRT(1+2/3*L*L3)/SQRT(GCONST)*q/Si^2*( (r^2-J^2)*S01
              +2*r*J*S23);

On TORSION,CCONST;

New V.n5;
V1=1/Si^2*((Q-q^2/2)*r-m*J^2);
V2=-SQRT(f)/SQRT(Si)/Si^2*Q*j*SIN(th)*J;
V3=SQRT(f)/SQRT(Si)/Si^2*Q*j*SIN(th)*r;
V4=1/Si^2*Q*J;
V5=1/Si^2*Q*r;

Torsion
  THETA0 = SQRT(Si)/SQRT(De)*(V1*S01+2*V4*S23) +
           Si/De*(-V2*(S02-S12)-V3*(S03-S13)),
  THETA2 = SQRT(Si)/SQRT(De)*(-V5*(S02-S12)-V4*(S03-S13)),
  THETA3 = SQRT(Si)/SQRT(De)*( V4*(S02-S12)-V5*(S03-S13));
  THETA1 = THETA0;

Transform Metric ( (1/SQRT(2),-1/SQRT(2),0,0),
                   (1/SQRT(2), 1/SQRT(2),0,0),
	           (0,0,1/SQRT(2), I/SQRT(2)),
                   (0,0,1/SQRT(2),-I/SQRT(2)) );

Find Maxwell Eq, TEM;
Find Curvature Components;
Show Time;

Let SIN(th)^2=1-COS(th)^2;

Let f  = 1 + L/3*j^2*COS(th)^2;
Let Si = r^2 + j^2*COS(th)^2;
Let De = r^2 + j^2 + q^2 - 2*m*r - L/3*r^2*(r^2+j^2);
Let Q  = m*r-q^2/2;
Let J  = j*COS(th);

Evaluate All;
Show Time;
Write Maxwell Eq;
Write Curvature Components;

Let CCONST=L;
Let MC1=-2-4/3*L*L3, MC2=4+8/3*L*L3;

Find and Write Gravitational Equations;
Show Time;