A class that defines the geodesic evolution equations for a particle moving in a Schwarzschild spacetime.
For this system nvars=7. The quantities stored in var_data are 1: , 2: , 3: , 4: , 5: , 6: , 7: , where is the radial coordinate in Schwarzschild coordinates, is the azimuthal angle, and are the time, radial and components of the 4-velocity, is the mass of the scalar charge and s a variable defined in the osculating orbits framework that varies from to over a full radial cycle. Note that is stricly constant for all other cases than a scalar charge and should stricly not be included in a generic geodesic evolution. Also is included for convenience as it is useful to control the turn on of the back-reaction in terms of timescales related to the radial cycle.
| Type | Visibility | Attributes | Name | Initial | |||
|---|---|---|---|---|---|---|---|
| integer(kind=ip), | public | :: | ntmp | The number of temporary storage variables to allocate. |
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| character(len=:), | public, | allocatable | :: | ename | The name of the system of equations |
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| integer(kind=ip), | public | :: | nvars | The number of variables in the ODE system. |
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| real(kind=wp), | public, | dimension(:), allocatable | :: | var_data | A 1d array of reals that contains the data variables. |
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| real(kind=wp), | public, | dimension(:), allocatable | :: | rhs_data | A 1d array of reals that contains the RHS variables. |
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| real(kind=wp), | public, | dimension(:,:), allocatable | :: | tmp_data | A 2d array of reals that contains the temporary variables needed by the time integrator. |
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| integer(kind=ip), | public | :: | io_id | The file unit id used for output for this system of ODE's. |
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| real(kind=wp), | public | :: | En | The orbital energy per unit mass. |
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| real(kind=wp), | public | :: | Lz | The orbital angular momentum per unit mass. |
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| real(kind=wp), | public | :: | e | The orbital eccentricity. |
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| real(kind=wp), | public | :: | p | The orbital semi-latus rectum. |
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| real(kind=wp), | public | :: | w | The value of at periapsis. |
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| real(kind=wp), | public | :: | d2rdt2 | The second time derivative of the radial coordinate. Needed for the time dependent coordinate transformation. |
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| real(kind=wp), | public, | dimension(4) | :: | force | The self-force or any external force . |
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| real(kind=wp), | public, | dimension(4) | :: | accel | The acceleration . |
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| real(kind=wp), | public | :: | udota | The dot-product of the 4-velocity and the force . |
The set_to_zero routine is provided by ode_set_to_zero.
The interface for the ODE version of set_to_zero. This interface is consistent with eq_set_to_zero_interface.
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| class(ode_equation), | intent(inout) | :: | this | The routine is called on this equation. |
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| integer(kind=ip), | intent(in) | :: | dest | Can be either -1 (RHS), 0 (main) or between 1 and ntmp (temporary). |
The update_vars routine is provided by ode_update_vars.
The interface for the ODE version of update_vars. This interface is consistent with eq_update_vars_interface.
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| class(ode_equation), | intent(inout), | target | :: | this | The routine is called on this equation. |
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| integer(kind=ip), | intent(in) | :: | source | The first source for the update. Can be either -1 (RHS), 0 (main) or between 1 and ntmp (temporary). |
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| integer(kind=ip), | intent(in) | :: | dest | The destination for the update. Can be either -1 (RHS), 0 (main) or between 1 and ntmp (temporary). |
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| integer(kind=ip), | intent(in), | optional | :: | source2 | The second source for the update. Can be either -1 (RHS), 0 (main) or between 1 and ntmp (temporary). |
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| real(kind=wp), | intent(in), | optional | :: | scalar | The scalar multiplying the first source. |
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| real(kind=wp), | intent(in), | optional | :: | scalar2 | The scalar multiplying the second source. |
The print_data routine is provided by ode_print_data.
The interface for the ODE version of print_data. This interface is consistent with eq_print_data.
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| class(ode_equation), | intent(inout) | :: | this | The routine is called on this equation. |
The init routine is provided by geod_schw_init.
The interface for the geod_schw version of init. This interface is consistent with eq_init_interface.
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| class(geod_schw), | intent(inout), | target | :: | this | The equation that is being initialized. |
The rhs routine is provided by geod_schw_rhs.
The interface for the geod_schw version of rhs. This interface is consistent with eq_rhs_interface.
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| class(geod_schw), | intent(inout) | :: | this | The equation for which the RHS is calculated. |
The output routine is provided by geod_schw_output.
The save_globals_1 routine is provided by geod_schw_save_globals_1.
The interface for the geod_schw version of save_globals_1. This interface is consistent with eq_save_globals_1.
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| class(geod_schw), | intent(inout) | :: | this | The routine is called on this equation. |
The save_globals_2 routine is provided by geod_schw_save_globals_2.
The interface for the geod_schw version of save_globals_2. This interface is consistent with eq_save_globals_2.
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| class(geod_schw), | intent(inout) | :: | this | The routine is called on this equation. |
The load_globals routine is provided by geod_schw_load_globals.
The interface for the geod_schw version of load_globals. This interface is consistent with eq_load_globals.
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| class(geod_schw), | intent(inout) | :: | this | The routine is called on this equation. |
type, extends(ode_equation) :: geod_schw
!! A class that defines the geodesic evolution equations for a particle
!! moving in a Schwarzschild spacetime.
!!
!! For this system [[geod_schw:nvars]]=7. The quantities stored in
!! [[geod_schw:var_data]] are 1: \(r\), 2: \(\phi\), 3: \(u^t\),
!! 4: \(u^r\), 5: \(u^{\phi}\), 6: \(m_q\), 7: \(\chi\), where
!! \(r\) is the radial coordinate in Schwarzschild coordinates, \(\phi\)
!! is the azimuthal angle,
!! \(u^t, u^r\) and \(u^{\phi}\) are the time, radial and \(\phi\)
!! components of the 4-velocity, \(m_q\) is the mass of the scalar charge
!! and \(\chi\) s a variable defined in the osculating orbits
!! framework that varies from \(0\) to \(2\pi\) over a full radial cycle.
!! Note that \(m_q\) is stricly constant for all other cases than a
!! scalar charge and should stricly not be included in a generic geodesic
!! evolution. Also \(\chi\) is included for convenience as it is useful to
!! control the turn on of the back-reaction in terms of timescales related
!! to the radial cycle.
real(wp) :: En
!! The orbital energy per unit mass.
real(wp) :: Lz
!! The orbital angular momentum per unit mass.
real(wp) :: e
!! The orbital eccentricity.
real(wp) :: p
!! The orbital semi-latus rectum.
real(wp) :: w
!! The value of \(\chi\) at periapsis.
real(wp) :: d2rdt2
!! The second time derivative of the radial coordinate. Needed for the
!! time dependent coordinate transformation.
real(wp), dimension(4) :: force
!! The self-force or any external force \(f_{\mu}\).
real(wp), dimension(4) :: accel
!! The acceleration \(a^{\mu}=
!! \frac{q}{m_q}(g^{\mu\nu}+u^{\mu}u^{\nu})f_{\nu}\).
real(wp) :: udota
!! The dot-product of the 4-velocity and the force \(q\, u^{\mu}f_{\mu}\).
contains
procedure :: init => geod_schw_init
!! The [[equation:init]] routine is provided by [[geod_schw_init]].
procedure :: rhs => geod_schw_rhs
!! The [[equation:rhs]] routine is provided by [[geod_schw_rhs]].
procedure :: output => geod_schw_output
!! The [[equation:output]] routine is provided by [[geod_schw_output]].
procedure :: save_globals_1 => geod_schw_save_globals_1
!! The [[equation:save_globals_1]] routine is provided by
!! [[geod_schw_save_globals_1]].
procedure :: save_globals_2 => geod_schw_save_globals_2
!! The [[equation:save_globals_2]] routine is provided by
!! [[geod_schw_save_globals_2]].
procedure :: load_globals => geod_schw_load_globals
!! The [[equation:load_globals]] routine is provided by
!! [[geod_schw_load_globals]].
final :: close_geod_schw
!! The finalizer.
end type geod_schw