### Related

ct_coords:[t,r,theta,...

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A;

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lg:matrix([-exp(2*A(...

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### christof

Run Example
```(%i1)load(ctensor);
(%o1)          /usr/share/maxima/5.21.1/share/tensor/ctensor.mac
(%i2) ct_coords:[t,r,theta,phi];
(%o2)                         [t, r, theta, phi]
(%i3) lg:matrix([-exp(-2*A/r),0,0,0],[0,1,0,0],[0,0,exp(-2*A/r)*r^2,0],[0,0,0,exp(-2*A/r)*r^2*sin(theta)^2]);
[       2 A                                        ]
[     - ---                                        ]
[        r                                         ]
[ - %e       0      0                 0            ]
[                                                  ]
[     0      1      0                 0            ]
[                                                  ]
(%o3)        [                      2 A                         ]
[                    - ---                         ]
[                2      r                          ]
[     0      0  r  %e                 0            ]
[                                                  ]
[                                              2 A ]
[                                            - --- ]
[                            2    2             r  ]
[     0      0      0       r  sin (theta) %e      ]
(%i4) ug:matrix([-exp(2*A/r),0,0,0],[0,1,0,0],[0,0,exp(2*A/r)/r^2,0],[0,0,0,exp(2*A/r)/(r^2*sin(theta)^2)]);
[     2 A                           ]
[     ---                           ]
[      r                            ]
[ - %e     0    0          0        ]
[                                   ]
[    0     1    0          0        ]
[                                   ]
[               2 A                 ]
[               ---                 ]
[                r                  ]
(%o4)                [             %e                    ]
[    0     0  -----        0        ]
[               2                   ]
[              r                    ]
[                                   ]
[                          2 A      ]
[                          ---      ]
[                           r       ]
[                        %e         ]
[    0     0    0    -------------- ]
[                     2    2        ]
[                    r  sin (theta) ]
(%i5) christof(mcs);
2 A
- ---
r
A %e
(%t5)                       mcs        = ---------
1, 1, 2       2
r

A
(%t6)                           mcs        = --
1, 2, 1    2
r

A + r
(%t7)                         mcs        = -----
2, 3, 3     2
r

A + r
(%t8)                         mcs        = -----
2, 4, 4     2
r

2 A
- ---
r
(%t9)                   mcs        = - (A + r) %e
3, 3, 2

cos(theta)
(%t10)                      mcs        = ----------
3, 4, 4   sin(theta)

2 A
- ---
2                 2              r
(%t11)      mcs        = - (sin (theta) A + r sin (theta)) %e
4, 4, 2

(%t12)               mcs        = - cos(theta) sin(theta)
4, 4, 3

(%o12)                               done
(%i13) riemann(true);
2 A          2 A
- ---        - ---
r     2      r
2 A %e        A  %e
(%t13)             riem           = ----------- - ----------
1, 2, 1, 2        3             4
r             r

2 A
- ---
r
A (A + r) %e
(%t14)               riem           = - -----------------
1, 3, 1, 3             4
r

2 A
- ---
r
A (A + r) %e
(%t15)               riem           = - -----------------
1, 4, 1, 4             4
r

2
A  - 2 r A
(%t16)                   riem           = - ----------
2, 2, 1, 1          4
r

2
(A + r)    2 (A + r)   1
(%t17)            riem           = -------- - --------- + --
2, 3, 2, 3       4          3        2
r          r        r

2
(A + r)    2 (A + r)   1
(%t18)            riem           = -------- - --------- + --
2, 4, 2, 4       4          3        2
r          r        r

2 A
- ---
2             r
(A  + r A) %e
(%t19)               riem           = - ------------------
3, 3, 1, 1              2
r

2 A
- ---
2      r
A  %e
(%t20)                   riem           = - ----------
3, 3, 2, 2          2
r

2 A
- ---
2      r
(A + r)  %e
(%t21)               riem           = ---------------- - 1
3, 4, 3, 4           2
r

2 A
- ---
2         2        2                r
(sin (theta) A  + r sin (theta) A) %e
(%t22)   riem           = - ------------------------------------------
4, 4, 1, 1                          2
r

2 A
- ---
2         2      r
sin (theta) A  %e
(%t23)             riem           = - ----------------------
4, 4, 2, 2                2
r

2 A                   2 A
- ---                   ---
r    2    2           r       2         2
(%t24) riem           = (%e      (r  sin (theta) %e    - sin (theta) A
4, 4, 3, 3
2             2    2           2
- 2 r sin (theta) A - r  sin (theta)))/r

(%o24)                               done
(%i25) ricci(true);
2 A                   2 A           2 A
- ---                 - ---         - ---
2      r                     r             r
A  %e        2 A (A + r) %e        2 A %e
(%t25)     ric     = ---------- + ------------------- - -----------
1, 1        4                4                 3
r                r                 r

2    2
2 (A + r)    A    4 (A + r)   2 A   2
(%t26)        ric     = - ---------- - -- + --------- + --- - --
2, 2          4        4       3        3     2
r        r       r        r     r

2 A
- ---       2 A
r      - ---
3 A (A + r) %e             r
(%t27)           ric     = - ------------------- - %e      + 1
3, 3              2
r

2 A
- ---
2                 2              r
3 A (sin (theta) A + r sin (theta)) %e
(%t28) ric     = - -------------------------------------------
4, 4                          2
r
2 A
- ---
2             r       2
- sin (theta) %e      + sin (theta)

(%o28)                               done
(%i29) R:scurvature();
2 A                   2 A           2 A
- ---                 - ---         - ---    2 A
2      r                     r             r     ---
A  %e        2 A (A + r) %e        2 A %e          r
(%o29) - (---------- + ------------------- - -----------) %e
4                4                 3
r                r                 r
2 A
- ---                   2 A
2                 2              r                  - ---
3 A (sin (theta) A + r sin (theta)) %e           2             r
+ ((- ------------------------------------------- - sin (theta) %e
2
r
2 A
---
2            r     2    2
+ sin (theta)) %e   )/(r  sin (theta))
2 A
- ---       2 A        2 A
r      - ---        ---
3 A (A + r) %e             r          r
(- ------------------- - %e      + 1) %e
2                                          2    2
r                                  2 (A + r)    A    4 (A + r)
+ ------------------------------------------- - ---------- - -- + ---------
2                             4        4       3
r                             r        r       r
2 A   2
+ --- - --
3     2
r     r
(%i30) einstein(true);
2 A
---
2    r       2            2
r  %e    - 3 A  - 2 r A - r
(%t30)             ein     = - ----------------------------
1, 1                   4
r

2 A
---
2    r       2            2
r  %e    - 3 A  - 4 r A - r
(%t31)             ein     = - ----------------------------
2, 2                   4
r

2
3 A  - r A
(%t32)                       ein     = ----------
3, 3        4
r

2
3 A  - r A
(%t33)                       ein     = ----------
4, 4        4
r

(%o33)                               done
(%i34) ```
Run Example
```load(ctensor);
(%o1)          /usr/share/maxima/5.21.1/share/tensor/ctensor.mac
(%i2) (cframe_flag:false,gcd:spmod,ctrgsimp:true,ratfac:true);
(%o2)                                true
(%i3) lg:diag_matrix(1,-r^2,-r^2,-r^2);
[ 1   0     0     0   ]
[                     ]
[       2             ]
[ 0  - r    0     0   ]
(%o3)                       [                     ]
[             2       ]
[ 0   0    - r    0   ]
[                     ]
[                   2 ]
[ 0   0     0    - r  ]
(%i4) ct_coords:[t,r,th,ph];
(%o4)                           [t, r, th, ph]
(%i5) cmetric(false);
(%o5)                                done
(%i6) christof(mcs);
1
(%t6)                           mcs        = -
2, 2, 2   r

1
(%t7)                           mcs        = -
2, 3, 3   r

1
(%t8)                           mcs        = -
2, 4, 4   r

1
(%t9)                          mcs        = - -
3, 3, 2     r

1
(%t10)                         mcs        = - -
4, 4, 2     r

(%o10)                               done
(%i11)  riemann(true);
1
(%t11)                       riem           = - --
2, 3, 2, 3      2
r

1
(%t12)                       riem           = - --
2, 4, 2, 4      2
r

1
(%t13)                        riem           = --
3, 3, 2, 2    2
r

1
(%t14)                        riem           = --
3, 4, 3, 4    2
r

1
(%t15)                        riem           = --
4, 4, 2, 2    2
r

1
(%t16)                       riem           = - --
4, 4, 3, 3      2
r

(%o16)                               done
(%i17) ricci(true);
2
(%t17)                           ric     = --
2, 2    2
r

(%o17)                               done
(%i18) ```
Run Example
```load(ctensor);
(%o1)          /usr/share/maxima/5.21.1/share/tensor/ctensor.mac
(%i2) (cframe_flag:false,gcd:spmod,ctrgsimp:true,ratfac:true);
(%o2)                                true
(%i3) lg:diag_matrix(1,-r^2,-r^2,-(r^2));
[ 1   0     0     0   ]
[                     ]
[       2             ]
[ 0  - r    0     0   ]
(%o3)                       [                     ]
[             2       ]
[ 0   0    - r    0   ]
[                     ]
[                   2 ]
[ 0   0     0    - r  ]
(%i4) ct_coords:[t,r,th,ph];
(%o4)                           [t, r, th, ph]
(%i5) cmetric(false);
(%o5)                                done
(%i6) christof(mcs);
1
(%t6)                           mcs        = -
2, 2, 2   r

1
(%t7)                           mcs        = -
2, 3, 3   r

1
(%t8)                           mcs        = -
2, 4, 4   r

1
(%t9)                          mcs        = - -
3, 3, 2     r

1
(%t10)                         mcs        = - -
4, 4, 2     r

(%o10)                               done
(%i11)  riemann(true);
1
(%t11)                       riem           = - --
2, 3, 2, 3      2
r

1
(%t12)                       riem           = - --
2, 4, 2, 4      2
r

1
(%t13)                        riem           = --
3, 3, 2, 2    2
r

1
(%t14)                        riem           = --
3, 4, 3, 4    2
r

1
(%t15)                        riem           = --
4, 4, 2, 2    2
r

1
(%t16)                       riem           = - --
4, 4, 3, 3      2
r

(%o16)                               done
(%i17) ricci(true);
2
(%t17)                           ric     = --
2, 2    2
r

(%o17)                               done
(%i18) ```

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