# Light propagation through black-hole lattices

## Abstract

The apparent properties of distant objects encode information about the way the light they emit propagates to an observer, and therefore about the curvature of the underlying spacetime. Measuring the relationship between the redshift z and the luminosity distance D {sub L} of a standard candle, for example, yields information on the Universe's matter content. In practice, however, in order to decode this information the observer needs to make an assumption about the functional form of the D {sub L}( z ) relation; in other words, a cosmological model needs to be assumed. In this work, we use numerical-relativity simulations, equipped with a new ray-tracing module, to numerically obtain this relation for a few black-hole-lattice cosmologies and compare it to the well-known Friedmann-Lema(ȋtre-Robertson-Walker case, as well as to other relevant cosmologies and to the Empty-Beam Approximation. We find that the latter provides the best estimate of the luminosity distance and formulate a simple argument to account for this agreement. We also find that a Friedmann-Lema(ȋtre-Robertson-Walker model can reproduce this observable exactly, as long as a time-dependent cosmological constant is included in the fit. Finally, the dependence of these results on the lattice mass-to-spacing ratio μ is discussed: we discover that,more »

- Authors:

- Dipartimento di Fisica e Astronomia, Università degli Studi di Catania, Via S. Sofia 64, 95123 Catania (Italy)
- Center for Theoretical Physics, Polish Academy of Sciences, Al. Lotników 32/46, 02-668 Warsaw (Poland)
- Max-Planck-Institut für Gravitationsphysik, Albert-Einstein-Institut, Am Mühlenberg 1, D-14476 Golm (Germany)

- Publication Date:

- OSTI Identifier:
- 22679989

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Cosmology and Astroparticle Physics; Journal Volume: 2017; Journal Issue: 03; Other Information: Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; APPROXIMATIONS; BLACK HOLES; COMPARATIVE EVALUATIONS; COSMOLOGICAL CONSTANT; COSMOLOGICAL MODELS; COSMOLOGY; DISTANCE; EMISSION; EXPANSION; LIGHT TRANSMISSION; LUMINOSITY; MASS; RED SHIFT; SIMULATION; SPACE-TIME; TIME DEPENDENCE; UNIVERSE

### Citation Formats

```
Bentivegna, Eloisa, Korzyński, Mikołaj, Hinder, Ian, and Gerlicher, Daniel, E-mail: eloisa.bentivegna@unict.it, E-mail: korzynski@cft.edu.pl, E-mail: ian.hinder@aei.mpg.de, E-mail: daniel.gerlicher@tum.de.
```*Light propagation through black-hole lattices*. United States: N. p., 2017.
Web. doi:10.1088/1475-7516/2017/03/014.

```
Bentivegna, Eloisa, Korzyński, Mikołaj, Hinder, Ian, & Gerlicher, Daniel, E-mail: eloisa.bentivegna@unict.it, E-mail: korzynski@cft.edu.pl, E-mail: ian.hinder@aei.mpg.de, E-mail: daniel.gerlicher@tum.de.
```*Light propagation through black-hole lattices*. United States. doi:10.1088/1475-7516/2017/03/014.

```
Bentivegna, Eloisa, Korzyński, Mikołaj, Hinder, Ian, and Gerlicher, Daniel, E-mail: eloisa.bentivegna@unict.it, E-mail: korzynski@cft.edu.pl, E-mail: ian.hinder@aei.mpg.de, E-mail: daniel.gerlicher@tum.de. Wed .
"Light propagation through black-hole lattices". United States.
doi:10.1088/1475-7516/2017/03/014.
```

```
@article{osti_22679989,
```

title = {Light propagation through black-hole lattices},

author = {Bentivegna, Eloisa and Korzyński, Mikołaj and Hinder, Ian and Gerlicher, Daniel, E-mail: eloisa.bentivegna@unict.it, E-mail: korzynski@cft.edu.pl, E-mail: ian.hinder@aei.mpg.de, E-mail: daniel.gerlicher@tum.de},

abstractNote = {The apparent properties of distant objects encode information about the way the light they emit propagates to an observer, and therefore about the curvature of the underlying spacetime. Measuring the relationship between the redshift z and the luminosity distance D {sub L} of a standard candle, for example, yields information on the Universe's matter content. In practice, however, in order to decode this information the observer needs to make an assumption about the functional form of the D {sub L}( z ) relation; in other words, a cosmological model needs to be assumed. In this work, we use numerical-relativity simulations, equipped with a new ray-tracing module, to numerically obtain this relation for a few black-hole-lattice cosmologies and compare it to the well-known Friedmann-Lema(ȋtre-Robertson-Walker case, as well as to other relevant cosmologies and to the Empty-Beam Approximation. We find that the latter provides the best estimate of the luminosity distance and formulate a simple argument to account for this agreement. We also find that a Friedmann-Lema(ȋtre-Robertson-Walker model can reproduce this observable exactly, as long as a time-dependent cosmological constant is included in the fit. Finally, the dependence of these results on the lattice mass-to-spacing ratio μ is discussed: we discover that, unlike the expansion rate, the D {sub L}( z ) relation in a black-hole lattice does not tend to that measured in the corresponding continuum spacetime as 0μ → .},

doi = {10.1088/1475-7516/2017/03/014},

journal = {Journal of Cosmology and Astroparticle Physics},

number = 03,

volume = 2017,

place = {United States},

year = {Wed Mar 01 00:00:00 EST 2017},

month = {Wed Mar 01 00:00:00 EST 2017}

}