Solving the Emitter-Observer Problem

Calculating light signals between two curves requires

• curve data,

• spacetime metric.

In the previous section, curves were either loaded from H5-files or calculated with information stored in a configuration dictionary. The spacetime metric was already provided in the latter case.

In the former case, a configuration dictionary containing information on the desired spacetime metric needs to be created, either directly in Python or saved in a TOML document. Refer to the config dictionary subsection for more information. An example TOML-file looks like this, if curves were not calculated with GREOPy:

[Metric]
name = 'Schwarzschild'
params.multipole_moments = [0]  # no central mass example

Let emission_curve_data and receiver_curve_data be the DataFrames containing all the data on the emitter’s and receiver’s curve, respectively.

The eop_solver function calculates a light signal for each step along the emission curve. If not every step requires a light signal, the number of emission events can be reduced by declaring start, stop and step_size when counting through the rows:

emission_curve_reduced = emission_curve_data[start:stop:step_size]

The light signals are then calculated via

from greopy.emitter_observer_problem import eop_solver

light_rays = eop_solver(
    config,
    emission_curve_reduced,
    receiver_curve_data,
)

providing the curves’ and config data.

The resulting light_rays lists indexed DataFrames. Each DataFrame in turn contains a light signal curve that connects the emitter and receiver curve at one emission and reception event.

Optionally save the light rays for later data analysis:

import pandas

for light_ray in light_rays:
    light_ray_index, light_ray_solution = light_ray
    light_ray_solution.to_hdf(
        'light_file',
        key="light_ray_" + f"{light_ray_index}".rjust(3, '0'),
        mode="a",
    )

This saves all light ray datasets in an H5-file named light_file, each with a different key: light_ray_*, where * indexes the light ray according to their respective emission event along the emitter curve. In this case a maximum number of 1000 light rays was assumed, so the index always consists of three digits, e.g. 003 or 010, to preserve the light ray sequence within the H5-file.

The data can be loaded again via the load_dataset function:

from greopy.common import load_dataset

light_rays_loaded = load_dataset('path/to/light_file')

Note that the variables light_rays and light_rays_loaded slightly differ in form:

• light_rays contains a list, each entry a tuple (index, DataFrame),

• light_rays_loaded constains a Generator, whose values are DataFrame objects.