My Science & Epistemology Researches
Astrophysics encompasses the study of everything related to cosmic topics. We could say ‘how it works’, while Cosmology focuses on general evolutionary and interpretative aspects. This category therefore highlights insights into ‘details’.
A short paper, in english, on a fascinating development of General Relativity.
Abstract
Extended Theories of Gravity (ETG) represent a prominent framework in modern theoretical physics and cosmology, aimed at modifying or extending Albert Einstein’s General Relativity to address open phenomenological questions at both ultraviolet (early universe) and infrared (galactic and cosmological) scales.
Brussi 2026 Mathematical and historical foundations of ETG (305 KB)
Galactic Energy Profiles: GEP II. In-System and Background Energy Densities
Update: I decided to publish this work, part of the GEP series, on Zenodo without peer review and to use it as a basic tool for building a subsequent dataset (GEP III). Note: This work is version 2.0 of the previous NAGE II work, which has been superseded.
Abstract
Standard galactic energy inventories typically focus on virialized components, namely kinetic and gravitational potential energy derived from baryonic mass distributions, together with energy inferred from bolometric luminosities. In the first paper of the Galactic Energy Profiles (GEP) series, we introduced a reproducible geometric framework for the radiant and relativistic fluxes of galactic origin, accounting for their finite escape time across the Halo. In this second work, we extend the framework toward a volumetric energy inventory, where bolometric luminosity is complemented by energy densities persistently present within the galactic volume. We consider the thermal and kinetic energy of baryonic matter—including bulk motions, turbulence, and rotational degrees of freedom from large-scale dynamics down to the intrinsic angular momentum of bound systems—together with cosmic rays confined by magnetic fields and extragalactic backgrounds (photons, neutrinos, and diffuse fields) permeating the Halo. This approach distinguishes between flux-based contributions and volume-based reservoirs, providing a complementary description of the total galactic energy budget. Crucially, by resolving these volumetric reservoirs into local radial profiles, we characterize the multi-component pressure support (including thermal, magnetic, cosmic ray, and radiant pressures) available to sustain the circumgalactic medium (CGM) in hydrostatic equilibrium. Although these components vary with morphology and evolutionary state, this study is purely theoretical and simplifies the extreme variability of galactic systems to derive reference estimates and ‘standard cases’. The resulting parametrized framework, supported by publicly available Python scripts, is intended as a further methodological baseline for the sample-wide application planned in later work.
Keywords
galactic energy inventory; galactic energy density; galactic Halo energy; energy distribution based on galactic morphology
Here is the Zenodo version of the paper (1.1 MB):
Galactic Energy Profiles: GEP I. Radiant and Relativistic Fluxes
Update: I decided to publish this work, part of the GEP series, on Zenodo without peer review and to use it as a basic tool for building a subsequent dataset (GEP III). Note: This work is version 2.0 of the previous NAGE I work, which has been superseded.
Abstract
Standard galactic energy inventories typically focus on the virialized components of the system, namely the kinetic and gravitational potential energy, derived from baryonic mass distributions and stellar luminosity. This paper, the first in the Galactic Energy Profiles series, introduces a reproducible geometric framework for accounting radiant and relativistic fluxes as a standing energy reservoir. By considering the photon and neutrino escape time τ across the galactic Halo, we quantify the energy density of radiation currently in transit as a component of the total galactic budget, complementary to the standard flux-based description. The resulting closed-form expressions, together with the accompanying open-source Python implementation, are intended as a calibrated methodological baseline for the subsequent application of this framework to observed galactic samples.
Keywords
galactic energy inventory; energy residence time; galactic radiant fluxes; galactic Halo energy; galaxy morphology
Here is the Zenodo version of the paper (1.1 MB):
The URD Framework: Cosmological Distances from Redshift in a Non-Standard Context
While I am still developing the project —including through parallel studies on the Tolman test and the quality of indirect data obtained from recent galaxy surveys— I am making my work public as a preprint. I always hope that someone might be interested in my conjectures or perhaps even willing to collaborate with me to address the critical issues of the URD Framework.
Abstract
A phenomenological framework for determining cosmological distances is proposed, based on a non-expanding spacetime interpretation consistent with current observational datasets. The model introduces a redshift mechanism associated with cumulative photon energy attenuation along the line of sight, formulated in a way that is not equivalent to standard tired light scenarios. The approach is constructed to remain compatible with established relativistic principles whereas adopting boundary conditions distinct from the metric expansion paradigm. Distance estimation is achieved through the URD equation (U energy density, Redshift, Distance), which incorporates two phenomenological parameters that describe conformal geometric dissipation in extended gravity and an effective relativistic path-length correction. Within this formulation, the model addresses the primary shortcomings traditionally associated with energy dissipation effects, specifically reconciling time dilation in supernova light curves and the Tolman surface brightness relation. The model is calibrated using the Pantheon+ supernova sample by comparing and cross-validating distances inferred from the proposed redshift mapping with redshift-independent indicators, with additional comparison performed against baryon acoustic oscillations, radio galaxy samples, and high-energy quasars. Across these datasets, the framework reproduces observational constraints over a wide redshift range within a phenomenological, non-standard cosmological setting. The results indicate that alternative, non-expansion-based mappings between redshift and distance can be constructed that remain consistent within the observational range considered, suggesting a phenomenological alternative worth further study.
Keywords
cosmological distance ladder; redshift-distance relation; non-expanding spacetime; cosmic microwave background; extended gravity; Pantheon+ sample; baryon acoustic oscillations; Tolman test; time dilation; geodetic correction
Here is the last version of the preprint (5.1 MB):
Brussi 2026_URD Framework Preprint
Version uploaded to Zenodo:
The virial theorem is a fundamental analytical result in the mechanics of particle systems, as it establishes a rigorous connection between the time averages of kinetic and potential energies. Its validity extends to systems in dynamic equilibrium, where internal forces are governed by potentials that depend on distance according to a power law, as in the case of universal gravitation or electrostatics.
The work is written in italian.
Brussi 2026_Il teorema del viriale e l’equilibrio stellare
The Eddington luminosity (Lₑ) (named after Arthur Stanley Eddington, 1882-1944), also known as the Eddington limit, is the growth limit of a structure that is in hydrostatic equilibrium (see Figure 1), balancing the outward radiation pressure with the inward gravitational pull.
Figure 1 – Hydrostatic equilibrium
The relationship for the luminosity limit can be easily derived, obtaining:
[1] L ≤ 4π c G M / k = Lₑ
where G is the universal gravitational constant, M is the mass of the object, c is the speed of light, and k is the opacity (ability to absorb radiation) of the material that makes up the object.
As a function of solar parameters, in the case of the model consisting of ionized hydrogen, [1] can be expressed as:
[2] Lₑ ≈ 3.2 * 10⁴ (M/M๏) L๏
where M๏ and L๏ are the mass and luminosity of the Sun.
In the very hot core of massive stars (or in accretion disks of black holes), opacity is independent of frequency and temperature, is related to Thomson scattering (see Thomson scattering on Wikipedia for more informations) of free electrons, and can be expressed as:
[3] kₑₛ = σₜ nₑ / ρ
where σₜ is the Thomson cross section for electrons, nₑ is the number density of electrons, and ρ is the density of the medium.
To consider the more general case of models also consisting of helium and metals, the general relationship is expressed as a function of the mass fraction (X) of hydrogen, and the [3] becomes:
[4] kₑₛ = σₜ (1+X) / 2 mₚ ≈ 0.2 (1+X) cm² / gr
where mₚ is the mass of the proton.
Therefore, in the case of a model consisting only of helium, Eddington luminosity would double (with X=0 , [4] is halved and [1] is doubled).
Relationships can also be derived for cases of models that are not fully ionized or colder (for less massive stars), or for highly energetic radiation (e.g., gamma rays as in black hole accretion disks), but these are beyond the scope of this note.
What is notable is that this physical limit explains why we do not observe infinitely large stars; beyond a certain mass limit, the luminosity is such that it disrupts the star.
The Eddington luminosity also defines the maximum rate at which a black hole can grow: if matter falls too quickly, the light emitted repels it back.
In stellar astrophysics, opacity ( k ) is a measure of a material’s resistance to the flow of radiative energy. One analytical descriptions of this phenomenon is Kramers’ opacity law, a power-law relation derived from atomic physics that characterizes how stellar matter interacts with radiation under specific thermodynamic conditions.
Brussi 2026_Brief on Kramers’ Opacity Law in Stellar Astrophysics
Brief analysis of Chandrasekhar’s formula on dynamic friction in the general case of galactic encounters in the study of Galactic Dynamics.
Spoiler: we get a result for the dynamical friction timescale which means that in a time span of a few Gyr, for instance with the values of our assumptions applied to the Milky Way, the orbit of a massive satellite has substantially reduced, while the orbit of lower mass satellites (such as globular clusters) has not been significantly affected by dynamic friction.
Brussi 2026_Chandrasekhar dynamical friction formula
A little reminder about a useful function used in Astronomy: the Abel integral equation (source: Google AI)
A brief note on the dispersion of low-redshift measurements in the Pantheon+ database. This is part of my study of the alternative interpretation of redshift that does not involve the expansion of the universe.
The Pantheon+ database is one of the largest and most precise cosmological data collections in the world, consisting of 1,701 light curves from 1,550 Type Ia supernovae (SnIa).
Brussi 2026_Pantheon+ low z issue
