redshift.cpp

void redshift(long double r, long double ktkp, long double& gg)
{
	/* I have to write this function new for the case of Polish doughnut model.*/
	/* Using equation 6.22 Cosimo's Book, and Ut and OMEGA from E.5 and E.6 respectively */
	long double Omega;
	long double uet;
    long double met[4][4], met_rder[4][4];
    long double th = Pi/2;
    
	
    
    metric(r, th, met);
    
    metric_rderivatives(r, th, met_rder);
    
    Omega = ( -met_rder[0][3] + sqrt( (met_rder[0][3]*met_rder[0][3]) - (met_rder[0][0]*met_rder[3][3]) ))/(met_rder[3][3]) ;
    
	//Omega  = (-rderg03 + sqrt(rderg03*rderg03 - rderg00*rderg33))/rderg33;
	
	//uet = sqrt(-g00 - 2.*g03*Omega - g33*Omega*Omega);
    
    uet = sqrt(-met[0][0] - (2*met[0][3]*Omega) - (met[3][3]*Omega*Omega));
	
	gg = uet/(1. - ktkp*Omega);
}