(* Components of the stress-energy tensor of the quantized massive
fields in the spacetime of the static, spherically-symmetric 
Reissner-Nordstrom black hole in (anti-)de Sitter unverse. The first 
index of the tensor is contravariant whereas the second is covariant.

All components are to be divided by 96 Pi^2 m^2.
eps can take two values: 1 for positive cosmological constant (l^2) and
-1 for negative. 


The coefficients cc1...cc10 are spin-dependent and are listed in the files:
scalar.m  ---- coefficients cc1...cc10 (xi is the curvature coupling)
spinor.m  ---- coefficients cc1...cc10
vector.m  ---- coefficients cc1...cc10 *)

(* A natural system of units is used and
cnventions are those of MTW *)

(* If you find the code useful please cite the papers: 

Jerzy Matyjasek, Stress energy tensor of neutral massive fields
in the Reissner-Nordstrom space-time, 
Physical Review D 61, 124019 (2000).

Jerzy Matyjasek, Vacuum polarization of massive scalar fields
in the space-time of the electrically charged nonlinear black hole
Physical Review  D 63,  084004 (2001).
*)

Print["Ttt, Trr, Tang --- components of the stress-energy
tensor of the general field in RN(a)dS geometry. "]
Print["To calculate the components for a scalar field"]
Print["use <<scalar.m and similarly use <<spinor.m for spinor
field and <<vector.m  for vector field"]





Ttt = (-702*cc10*Q^6 + 13248*cc2*Q^6 - 2268*cc4*Q^6 - 31752*cc5*Q^6 - 
      1701*cc6*Q^6 - 4689*cc7*Q^6 - 16182*cc8*Q^6 - 46548*cc9*Q^6 + 
      1944*cc10*M*Q^4*r - 40752*cc2*M*Q^4*r + 4320*cc4*M*Q^4*r + 
      101952*cc5*M*Q^4*r + 3240*cc6*M*Q^4*r + 11376*cc7*M*Q^4*r + 
      46080*cc8*M*Q^4*r + 135648*cc9*M*Q^4*r - 1026*cc10*M^2*Q^2*r^2 + 
      29232*cc2*M^2*Q^2*r^2 - 93744*cc5*M^2*Q^2*r^2 - 4536*cc7*M^2*Q^2*r^2 - 
      32508*cc8*M^2*Q^2*r^2 - 99576*cc9*M^2*Q^2*r^2 - 756*cc10*Q^4*r^2 + 
      15768*cc2*Q^4*r^2 - 2016*cc4*Q^4*r^2 - 28224*cc5*Q^4*r^2 - 
      1512*cc6*Q^4*r^2 - 4284*cc7*Q^4*r^2 - 14616*cc8*Q^4*r^2 - 
      42336*cc9*Q^4*r^2 - 108*cc10*M^3*r^3 + 28512*cc5*M^3*r^3 + 
      7128*cc8*M^3*r^3 + 21168*cc9*M^3*r^3 + 648*cc10*M*Q^2*r^3 - 
      20736*cc2*M*Q^2*r^3 + 36288*cc5*M*Q^2*r^3 + 2160*cc7*M*Q^2*r^3 + 
      13392*cc8*M*Q^2*r^3 + 41472*cc9*M*Q^2*r^3 - 12960*cc5*M^2*r^4 - 
      3240*cc8*M^2*r^4 - 9720*cc9*M^2*r^4 + 3240*cc2*Q^2*r^4 + 
      162*cc10*eps*l^2*Q^4*r^4 - 3480*cc2*eps*l^2*Q^4*r^4 + 
      972*cc4*eps*l^2*Q^4*r^4 + 9288*cc5*eps*l^2*Q^4*r^4 + 
      729*cc6*eps*l^2*Q^4*r^4 + 1365*cc7*eps*l^2*Q^4*r^4 + 
      4566*cc8*eps*l^2*Q^4*r^4 + 12564*cc9*eps*l^2*Q^4*r^4 - 
      72*cc10*eps*l^2*M*Q^2*r^5 + 3840*cc2*eps*l^2*M*Q^2*r^5 - 
      864*cc4*eps*l^2*M*Q^2*r^5 - 12672*cc5*eps*l^2*M*Q^2*r^5 - 
      648*cc6*eps*l^2*M*Q^2*r^5 - 936*cc7*eps*l^2*M*Q^2*r^5 - 
      4608*cc8*eps*l^2*M*Q^2*r^5 - 12672*cc9*eps*l^2*M*Q^2*r^5 + 
      54*cc10*eps*l^2*M^2*r^6 + 3024*cc5*eps*l^2*M^2*r^6 + 
      756*cc8*eps*l^2*M^2*r^6 + 2376*cc9*eps*l^2*M^2*r^6 - 
      108*cc10*eps*l^2*Q^2*r^6 - 864*cc2*eps*l^2*Q^2*r^6 + 
      432*cc4*eps*l^2*Q^2*r^6 + 1728*cc5*eps*l^2*Q^2*r^6 + 
      324*cc6*eps*l^2*Q^2*r^6 + 180*cc7*eps*l^2*Q^2*r^6 + 
      576*cc8*eps*l^2*Q^2*r^6 + 864*cc9*eps*l^2*Q^2*r^6 + 
      30*cc10*eps^2*l^4*Q^2*r^8 + 8*cc2*eps^2*l^4*Q^2*r^8 + 
      432*cc3*eps^2*l^4*Q^2*r^8 + 36*cc4*eps^2*l^4*Q^2*r^8 - 
      264*cc5*eps^2*l^4*Q^2*r^8 - 27*cc6*eps^2*l^4*Q^2*r^8 - 
      3*cc7*eps^2*l^4*Q^2*r^8 - 90*cc8*eps^2*l^4*Q^2*r^8 - 
      156*cc9*eps^2*l^4*Q^2*r^8 - 2*cc10*eps^3*l^6*r^12 - 
      144*cc3*eps^3*l^6*r^12 - 36*cc4*eps^3*l^6*r^12 - 
      24*cc5*eps^3*l^6*r^12 - 9*cc6*eps^3*l^6*r^12 - 9*cc7*eps^3*l^6*r^12 - 
      6*cc8*eps^3*l^6*r^12 - 4*cc9*eps^3*l^6*r^12)/(9*r^12)
 
Trr = (-1350*cc10*Q^6 + 2448*cc2*Q^6 + 324*cc4*Q^6 + 4536*cc5*Q^6 + 
      243*cc6*Q^6 - 369*cc7*Q^6 + 234*cc8*Q^6 - 2484*cc9*Q^6 + 
      4968*cc10*M*Q^4*r - 7056*cc2*M*Q^4*r - 864*cc4*M*Q^4*r - 
      19008*cc5*M*Q^4*r - 648*cc6*M*Q^4*r + 720*cc7*M*Q^4*r - 
      2880*cc8*M*Q^4*r + 2592*cc9*M*Q^4*r - 5454*cc10*M^2*Q^2*r^2 + 
      5040*cc2*M^2*Q^2*r^2 + 21168*cc5*M^2*Q^2*r^2 - 504*cc7*M^2*Q^2*r^2 + 
      4284*cc8*M^2*Q^2*r^2 + 1944*cc9*M^2*Q^2*r^2 - 1404*cc10*Q^4*r^2 + 
      2376*cc2*Q^4*r^2 + 576*cc4*Q^4*r^2 + 8064*cc5*Q^4*r^2 + 
      432*cc6*Q^4*r^2 + 36*cc7*Q^4*r^2 + 1800*cc8*Q^4*r^2 + 
      1728*cc9*Q^4*r^2 + 1836*cc10*M^3*r^3 - 7776*cc5*M^3*r^3 - 
      1944*cc8*M^3*r^3 - 2160*cc9*M^3*r^3 + 2376*cc10*M*Q^2*r^3 - 
      3456*cc2*M*Q^2*r^3 - 12096*cc5*M*Q^2*r^3 + 144*cc7*M*Q^2*r^3 - 
      2736*cc8*M*Q^2*r^3 - 3456*cc9*M*Q^2*r^3 - 972*cc10*M^2*r^4 + 
      5184*cc5*M^2*r^4 + 1296*cc8*M^2*r^4 + 1944*cc9*M^2*r^4 + 
      648*cc2*Q^2*r^4 + 450*cc10*eps*l^2*Q^4*r^4 + 120*cc2*eps*l^2*Q^4*r^4 - 
      180*cc4*eps*l^2*Q^4*r^4 - 3960*cc5*eps*l^2*Q^4*r^4 - 
      135*cc6*eps*l^2*Q^4*r^4 - 195*cc7*eps*l^2*Q^4*r^4 - 
      1290*cc8*eps*l^2*Q^4*r^4 - 2700*cc9*eps*l^2*Q^4*r^4 - 
      792*cc10*eps*l^2*M*Q^2*r^5 - 192*cc2*eps*l^2*M*Q^2*r^5 - 
      288*cc4*eps*l^2*M*Q^2*r^5 + 5760*cc5*eps*l^2*M*Q^2*r^5 - 
      216*cc6*eps*l^2*M*Q^2*r^5 - 24*cc7*eps*l^2*M*Q^2*r^5 + 
      1536*cc8*eps*l^2*M*Q^2*r^5 + 3456*cc9*eps*l^2*M*Q^2*r^5 + 
      378*cc10*eps*l^2*M^2*r^6 - 3024*cc5*eps*l^2*M^2*r^6 - 
      756*cc8*eps*l^2*M^2*r^6 - 1512*cc9*eps*l^2*M^2*r^6 - 
      36*cc10*eps*l^2*Q^2*r^6 + 144*cc4*eps*l^2*Q^2*r^6 + 
      576*cc5*eps*l^2*Q^2*r^6 + 108*cc6*eps*l^2*Q^2*r^6 + 
      60*cc7*eps*l^2*Q^2*r^6 + 192*cc8*eps*l^2*Q^2*r^6 + 
      288*cc9*eps*l^2*Q^2*r^6 + 6*cc10*eps^2*l^4*Q^2*r^8 + 
      8*cc2*eps^2*l^4*Q^2*r^8 + 432*cc3*eps^2*l^4*Q^2*r^8 + 
      132*cc4*eps^2*l^4*Q^2*r^8 + 120*cc5*eps^2*l^4*Q^2*r^8 + 
      45*cc6*eps^2*l^4*Q^2*r^8 + 37*cc7*eps^2*l^4*Q^2*r^8 + 
      38*cc8*eps^2*l^4*Q^2*r^8 + 36*cc9*eps^2*l^4*Q^2*r^8 - 
      2*cc10*eps^3*l^6*r^12 - 144*cc3*eps^3*l^6*r^12 - 
      36*cc4*eps^3*l^6*r^12 - 24*cc5*eps^3*l^6*r^12 - 9*cc6*eps^3*l^6*r^12 - 
      9*cc7*eps^3*l^6*r^12 - 6*cc8*eps^3*l^6*r^12 - 4*cc9*eps^3*l^6*r^12)/
     (9*r^12)
 
Tang = (7074*cc10*Q^6 - 6840*cc2*Q^6 - 2916*cc4*Q^6 - 40824*cc5*Q^6 - 
      2187*cc6*Q^6 - 315*cc7*Q^6 - 9378*cc8*Q^6 - 9612*cc9*Q^6 - 
      23544*cc10*M*Q^4*r + 20304*cc2*M*Q^4*r + 5184*cc4*M*Q^4*r + 
      127872*cc5*M*Q^4*r + 3888*cc6*M*Q^4*r - 72*cc7*M*Q^4*r + 
      29232*cc8*M*Q^4*r + 32832*cc9*M*Q^4*r + 23166*cc10*M^2*Q^2*r^2 - 
      14112*cc2*M^2*Q^2*r^2 - 117936*cc5*M^2*Q^2*r^2 + 1008*cc7*M^2*Q^2*r^2 - 
      27468*cc8*M^2*Q^2*r^2 - 36072*cc9*M^2*Q^2*r^2 + 5616*cc10*Q^4*r^2 - 
      8208*cc2*Q^4*r^2 - 2304*cc4*Q^4*r^2 - 32256*cc5*Q^4*r^2 - 
      1728*cc6*Q^4*r^2 - 144*cc7*Q^4*r^2 - 7200*cc8*Q^4*r^2 - 
      6912*cc9*Q^4*r^2 - 6912*cc10*M^3*r^3 + 36288*cc5*M^3*r^3 + 
      9072*cc8*M^3*r^3 + 13392*cc9*M^3*r^3 - 8316*cc10*M*Q^2*r^3 + 
      10800*cc2*M*Q^2*r^3 + 42336*cc5*M*Q^2*r^3 - 504*cc7*M*Q^2*r^3 + 
      9576*cc8*M*Q^2*r^3 + 12096*cc9*M*Q^2*r^3 + 2916*cc10*M^2*r^4 - 
      15552*cc5*M^2*r^4 - 3888*cc8*M^2*r^4 - 5832*cc9*M^2*r^4 - 
      1944*cc2*Q^2*r^4 - 1278*cc10*eps*l^2*Q^4*r^4 + 
      1440*cc2*eps*l^2*Q^4*r^4 + 252*cc4*eps*l^2*Q^4*r^4 + 
      6408*cc5*eps*l^2*Q^4*r^4 + 189*cc6*eps*l^2*Q^4*r^4 - 
      75*cc7*eps*l^2*Q^4*r^4 + 1326*cc8*eps*l^2*Q^4*r^4 + 
      1044*cc9*eps*l^2*Q^4*r^4 + 1728*cc10*eps*l^2*M*Q^2*r^5 - 
      1536*cc2*eps*l^2*M*Q^2*r^5 + 576*cc4*eps*l^2*M*Q^2*r^5 - 
      6912*cc5*eps*l^2*M*Q^2*r^5 + 432*cc6*eps*l^2*M*Q^2*r^5 + 
      336*cc7*eps*l^2*M*Q^2*r^5 - 1344*cc8*eps*l^2*M*Q^2*r^5 - 
      1440*cc9*eps*l^2*M*Q^2*r^5 - 594*cc10*eps*l^2*M^2*r^6 + 
      3024*cc5*eps*l^2*M^2*r^6 + 756*cc8*eps*l^2*M^2*r^6 + 
      1080*cc9*eps*l^2*M^2*r^6 + 72*cc10*eps*l^2*Q^2*r^6 + 
      432*cc2*eps*l^2*Q^2*r^6 - 288*cc4*eps*l^2*Q^2*r^6 - 
      1152*cc5*eps*l^2*Q^2*r^6 - 216*cc6*eps*l^2*Q^2*r^6 - 
      120*cc7*eps*l^2*Q^2*r^6 - 384*cc8*eps*l^2*Q^2*r^6 - 
      576*cc9*eps*l^2*Q^2*r^6 - 18*cc10*eps^2*l^4*Q^2*r^8 - 
      8*cc2*eps^2*l^4*Q^2*r^8 - 432*cc3*eps^2*l^4*Q^2*r^8 - 
      84*cc4*eps^2*l^4*Q^2*r^8 + 72*cc5*eps^2*l^4*Q^2*r^8 - 
      9*cc6*eps^2*l^4*Q^2*r^8 - 17*cc7*eps^2*l^4*Q^2*r^8 + 
      26*cc8*eps^2*l^4*Q^2*r^8 + 60*cc9*eps^2*l^4*Q^2*r^8 - 
      2*cc10*eps^3*l^6*r^12 - 144*cc3*eps^3*l^6*r^12 - 
      36*cc4*eps^3*l^6*r^12 - 24*cc5*eps^3*l^6*r^12 - 9*cc6*eps^3*l^6*r^12 - 
      9*cc7*eps^3*l^6*r^12 - 6*cc8*eps^3*l^6*r^12 - 4*cc9*eps^3*l^6*r^12)/
     (9*r^12)
