The Massive Black Hole Bias: A Gravitational Origin of the Cosmological Redshift–Distance Relation

The Massive Black Hole Bias: A Gravitational Origin of the Cosmological RedshiftDistance Relation Gerasimos D Danilatos Version 01: 24 December 2025 https://doi ESEM Research Laboratory 28 Wallis Parade North Bondi, NSW 2026 Australia [email protected] Abstract Recent observations, most notably by the James Webb Space Telescope (JWST), have revealed galaxies at redshifts far higher and with inferred masses far larger than expected within the standard Λ CDM cosmological framework. These ndings have intensied longstanding tensions in observational cosmology, including the Hubble tension and the apparent early emergence of massive, luminous structures. In this work we develop a cosmological reinterpretation based on Push Gravity (PG), a physical framework in which gravitation arises from momentum transfer by an omnipresent ux of discrete push particles ( gravions ), rather than from spacetime curvature. Within PG, gravitational redshift remains nite for any nite mass, but can become extremely large for suciently massive and compact systems whose eective gravitational mass is concentrated within a thin Total Absorption Layer (TAL). We show that PG naturally permits gravitational redshifts comparable to those commonly attributed to cosmic expansion, without requiring metric expansion of space. A revised massradius relation is derived, leading to a nite minimum mass for a true black hole, dened operationally as an object from which no electromagnetic radiation of any wavelength can escape. By combining PG gravitational redshift with luminosityradius scaling for maximally compact bodies, we derive a direct relation between observed ux, redshift, and distance that does not rely on standard candles or cosmological distance ladders. This framework introduces a novel Malmquist-type selection eect: at increasing observational distances, only the most massive and compact systems remain detectable, producing an apparent redshiftdistance relation that closely mimics Hubble's law. We discuss observational implications for JWST high-redshift galaxies, gravitational-wave detections by LIGO/Virgo/KAGRA, horizon-scale imaging by the Event Horizon Telescope, and the possible reinterpretation of the Cosmic Microwave Background (CMB). The results suggest that large observed redshifts need not imply cosmic expansion, but may instead reect gravitational redshift associated with compact absorption-layer structures in a static universe. 1 Introduction The interpretation of astronomical redshift as evidence for universal expansion has been a cornerstone of modern cosmology for nearly a century. Within the framework of General Relativity (GR), redshift is predominantly understood as a kinematic or geometric eect arising from the expansion of spacetime itself. This interpretation underpins the Big Bang paradigm and the standard Λ CDM cosmological model. However, recent high-precision observations have exposed growing tensions within this framework. Chief among these are the persistent discrepancy between earlyand late-universe measurements of the Hubble constant (the Hubble tension) and the discovery by JWST of galaxies at redshifts z&10 whose inferred stellar masses, luminosities, and apparent maturity challenge conventional structure-formation timelines. These observations have revived interest in whether unrecognized systematic eects or alternative physical mechanisms may contribute to the observed redshiftdistance relation. While kinematic interpretations dominate current cosmology, redshift is, in principle, a composite observable that may include gravitational, environmental, and propagation-related contributions in addition to any Doppler component. Gravitational redshift is well established experimentally in both Newtonian gravity and GR, yet it is conventionally regarded as negligible outside the immediate vicinity of extremely compact objects. In GR, 1 the massradius relation severely restricts the magnitude of gravitational redshift unless an event horizon is approached, at which point light escape is forbidden, or becomes extremly weak and undetectable at close range. As a consequence, gravitational redshift is typically excluded as a viable contributor to cosmological redshifts. Push Gravity (PG) oers a fundamentally dierent perspective. In PG, gravitation is not a manifestation of spacetime geometry but arises from momentum transfer by an omnipresent ux of discrete particles termed gravions . The interaction of gravions with matter gives rise to an eective gravitational mass that depends on absorptivity and geometry, rather than directly on classical rest mass alone. A central feature of PG is the distinction between real mass (hyle) and eective mass , the latter being the component that actively participates in gravitational interaction. For suciently compact systems, PG predicts that eective mass becomes concentrated within a thin outer region termed the Total Absorption Layer (TAL). As compactness increases, gravitational redshift grows monotonically but remains nite for any nite mass, allowing extremely large redshifts without invoking horizons, singularities, or divergent spacetime curvature. The purpose of this paper is to explore the cosmological consequences of these properties. We show that PG permits gravitational redshifts comparable to those observed in the highz systems, derive a nite minimum mass for a true black hole, and develop a PG-based distanceredshift relation that eliminates the need for universal expansion. We further demonstrate that an observational selection eect, arising from the combined dependence of detectability on mass, compactness, and gravitational redshift, can naturally reproduce an apparent Hubble-like law in a static universe. The structure of the paper is as follows. Section 2 establishes the conceptual foundations of Push Gravity, including the role of absorptivity and the Total Absorption Layer. Section 3 summarizes the assumptions, denitions, and notation. Section 4 derives the gravitational redshift in PG and compares it explicitly with Newtonian and GR limits. Section 5 develops luminosity, ux, and distance relations and introduces the massive black hole selection bias. Section 6 derives the minimum mass for a true black hole. Section 7 discusses observational implications for EHT, gravitational waves, JWST, and the Cosmic Microwave Background. Section 8 summarizes the results and outlines future directions. 2 Conceptual Foundations of Push Gravity PG belongs to a class of physical theories in which gravitational interaction is attributed to momentum transfer from an omnipresent and omnidirectional owing medium, rather than to action at a distance or to the curvature of spacetime. Early variants of push-based gravity can be traced to the work of Fatio de Duillier (de Duillier, 1929; Gagnebin, 1949) and Le Sage (Le Sage, 1784; Gillies, 1997), with later historical analyses and critiques summarized by subsequent authors. There have also been more recent attempts to revisit and modernize push-based gravitational ideas. Notably, Fedosin (2015) developed a corpuscular graviton-eld model within a modernized Le Sage framework, providing a detailed and systematic treatment of momentum-transfer gravity in weak-interaction regimes. Such approaches typically assume very low absorptivity, eectively restricting their applicability to dilute matter distributions and weak-eld conditions. By contrast, the present Push Gravity framework explicitly incorporates absorptivity as a fundamental parameter across its full physical range, from weak interaction to complete (100%) absorption. This extension allows PG to address not only ordinary gravitational phenomena but also the extreme compactness regimes relevant to black-hole physics and cosmology. Push Gravity is formulated as a self-contained physical framework based on rst principles, without reliance on geometric spacetime curvature or on auxiliary gravitational theories. Its dening feature is the role of absorptivity in governing eective mass, gravitational redshift, and the emergence of Total Absorption Layers, providing a unied description across weakand strong-eld regimes. A comprehensive review of these and related approaches lies beyond the scope of the present article and is provided in the broader treatment by Danilatos (2025b). In the following subsections, we introduce the core concepts of Push Gravity required for the quantitative developments that follow. 2.1 Eective Mass, Black Mass, and Hyle A dening feature of PG is the distinction between the total substance content of a body and the portion that actively participates in gravitational interaction. We denote the total real mass (or hyle ) by M , and decompose it as M=Me+Mb, (1) where Me is the eective mass and Mb is the remaining black mass . 2 The eective mass Me represents the fraction of the real mass that interacts with the gravion ux and therefore contributes to gravitational and inertial eects. The black mass Mb , by contrast, is gravitationally passive: it neither contributes directly to gravion absorption nor to the external gravitational eld. For ordinary-density bodies such as planets and main-sequence stars, MbMe and PG reduces eectively to Newtonian gravity. However, as density and compactness increase, the black-mass fraction grows, leading to qualitative departures from standard gravitational descriptions. This decomposition becomes central in the analysis of compact astrophysical objects. 2.2 Absorptivity and the Total Absorption Layer The interaction between gravions and matter is characterized by a dimensionless absorptivity parameter AR , which depends on the physical radius R of the body and on its microscopic interaction properties through an absorption coecient k being the number of absorption events per unit length. These quantities enter the absorptivity function through the product kR , yielding AR= 1 −1 2k2R2+e−2kR(2kR + 1) 2k2R2. (2) The function AR(kR) has a sigmoid-like form. For very small values of kR , absorptivity is weak and the theory reduces to the Newtonian regime. For very large values of kR , absorptivity approaches unity, 0< AR<1, AR→1, (3) corresponding to maximal gravion absorption and extreme compactness. Between these limits lies a smooth transition region encompassing a large subset of astrophysical bodies. This explicit formulation allows absorptivity to be treated quantitatively across all regimes, from dilute matter to maximally compact systems, a feature absent from earlier push-gravity models. For suciently compact bodies, PG predicts that the eective mass becomes concentrated within a thin outer region termed the Total Absorption Layer (TAL). As compactness increases, the TAL becomes progressively thinner, while the interior becomes increasingly dominated by black (passive) mass. At extreme compactness, the TAL is concentrated very close to a physical surface at radius R0 from which gravitational interaction, radiation emission, and gravitational redshift predominantly originate. A conceptual illustration of the emergence and evolution of the TAL for the Sun, a white dwarf, a neutron star, and a maximally compact object (like a black hole) is shown in Fig. 1 . This surface-based mass distribution replaces both the point-mass idealization of Newtonian gravity and the horizon-based description of General Relativity. Importantly, the TAL is a physical structure rather than a coordinate artifact. 2.3 Maximum Surface Acceleration Push Gravity predicts the existence of a universal maximum gravitational acceleration g0 , attained in the limit of complete absorptivity. For any spherically symmetric body of radius R and absorptivity AR , the external gravitational eld is g(r) = g0AR R2 r2, (4) which reproduces the inverse-square law exactly for all ordinary bodies. The conventional gravitational constant G emerges in PG as a derived quantity. In the weak-absorption limit, the PG force law reduces identically to Newtonian gravity, ensuring consistency with all tested weak- eld phenomena. Details of all this and more can be found in the main report (Danilatos, 2025b). 2.4 Scope of the Present Work The present paper focuses exclusively on the gravitational and cosmological implications of Push Gravity for compact objects. While PG also admits analogous push-particle descriptions for other fundamental interactions, including electromagnetic and nuclear forces, these extensions are not required for the arguments developed here, but have been reported in the main work (Danilatos, 2025b). In the sections that follow, the PG framework is applied to derive gravitational redshift relations, luminositydistance scaling laws, and a nite minimum mass for true black holes. These results form the basis for a reappraisal of cosmological redshift and its interpretation in observational astronomy. 3 Sun TAL1>>R white dwarf TAL2 neutron star TAL3 black hole TAL4 astrophysical jet astrophysical jet Figure 1: Schematic representation of the Total Absorption Layer (TAL) for objects of increasing compactness: Sun-like star, white dwarf, neutron star, and a maximally compact PG object. As compactness increases, the TAL becomes thinner and more sharply dened, while the interior mass becomes predominantly black (gravitationally passive). 4 3 Assumptions, Denitions, and Notation Before proceeding to quantitative developments, we summarize the assumptions, denitions, and notation employed throughout this paper. This section distinguishes foundational concepts of PG from results derived within the present analysis and ensures notational consistency. 3.1 Foundational Concepts The present work is based on the following assumptions and concepts: 1. Gravitation arises from momentum transfer between hyle (matter) and an omnipresent ux of discrete particles (gravions), rather than from spacetime curvature or action at a distance. 2. Gravitational interaction depends on the eective mass of a body, which is determined by its absorptivity and geometry and is not generally equal to its total real mass (hyle). 3. A universal maximum gravitational acceleration g0 exists and is attained in the limit of complete gravion absorption. 4. All observable gravitational phenomena at ordinary densities must reduce to Newtonian behavior in the appropriate weak-eld limit. No assumption of cosmic expansion, spacetime curvature, metric dynamics, or global scale factor evolution is invoked in the derivations that follow. 3.2 Summary of Key Denitions For clarity, the principal quantities used throughout the paper are dened here: • Real mass (hyle), M : the total substance content of a body. • Eective mass, Me : the gravitationally and inertially active component of the real mass. • Black mass, Mb : the passive component of real mass that does not participate directly in gravion absorption, such that M=Me+Mb. • Absorptivity, AR : a dimensionless parameter characterizing the fraction of gravions absorbed by a body of radius R , satisfying 0< AR<1 . • Total Absorption Layer (TAL) : a thin outer region of a compact body in which gravion absorption is concentrated, dening the eective gravitational and radiative surface. • Maximum gravitational acceleration, g0 : the limiting acceleration achieved at the TAL for AR≈ 1 . 3.3 Derived Quantities Several quantities used in later sections follow directly from the above denitions: • PG gravitational parameter : µPG ≡GMe=ARg0R2, (5) which replaces the Newtonian GM in all PG gravitational relations. • Surface radius of maximally compact objects, R0 : the physical radius at which AR= 1 , identifying the location of the TAL. • Compactness ratio : x≡R0 r, (6) used for comparison with standard compactness parameters in other gravitational frameworks. 5 3.4 Redshift Convention All redshifts in this paper are dened using the standard spectroscopic convention 1 + z=λobs λemit . (7) When necessary, subscripts are used to distinguish between dierent contributions, for example: zgPG (PG gravitational redshift) , zgGR (GR gravitational redshift) . Unless otherwise stated, quoted redshifts refer to values measured by distant observers at innity. 3.5 Scope and Limitations The present analysis applies primarily to compact objects with high absorptivity ( AR≈1 ), where PG eects depart most strongly from General Relativity. For ordinary stars, planets, and diuse systems, PG reduces eectively to Newtonian gravity and no observable deviations are expected. Radiative transfer, accretion physics, and detailed stellar evolution within PG are not treated here. Where luminosity scaling relations are introduced, they are restricted to maximally compact objects whose emission originates predominantly at the TAL. These clarications establish the framework within which the subsequent derivations of gravitational redshift, luminositydistance relations, and minimum black-hole mass are to be interpreted.  Throughout this paper, Push Gravity (PG) is developed as a physically distinct gravitational framework with its own ontology, in which gravitation arises from momentum transfer via an omnipresent gravion ux and not from spacetime curvature. Comparisons with GR, including references to horizons, compactness, inspiral dynamics, or observational signatures, are made solely at the level of phenomenology and observational correspondence, and do not imply ontological equivalence, theoretical continuity, or shared foundational assumptions. Agreement with GR in certain regimes reects observational degeneracy (i.e., indistinguishabilty within current measurement precision) rather than theoretical convergence. Conversely, departures from GR in high-compactness or strong-eld regimes are expected and are intrinsic to the PG framework. All interpretations, predictions, and proposed tests in this work should therefore be understood within the independent physical ontology of Push Gravity, and not as modications, extensions, or limits of General Relativity. 4 Gravitational Redshift in Push Gravity This section derives the gravitational redshift predicted by PG using the same physical reasoning employed in Newtonian treatments of gravitational redshift, with the sole modication that the Newtonian gravitational parameter GM is replaced by the PG gravitational parameter µPG dened in Sec. 3. 4.1 Energy Balance Argument Consider a photon of frequency νemit emitted at radius r from a spherically symmetric gravitating body and received at innity. In Newtonian gravity, gravitational redshift follows from energy conservation applied to the photon climbing out of a gravitational potential. In PG, the gravitational acceleration outside the body is g(r) = ARg0R2 r2, (8) which obeys the inverse-square law exactly and reduces to Newtonian gravity in the appropriate limit. The gravitational potential dierence between radius r and innity is ∆Φ(r) = Z∞ r g(r0) dr0=ARg0R2 r. (9) 6 4.2 PG Gravitational Redshift Formula The fractional change in photon frequency is related to the gravitational potential dierence by νemit ν∞ = exp∆Φ c2, (10) which reproduces the standard Newtonian result in the weak-eld limit. Substituting the PG potential yields the exact PG gravitational redshift 1 + zgPG = expARg0R2 rc2, (11) or equivalently, zgPG = expARg0R2 rc2−1. (12) No approximation has been made beyond spherical symmetry and stationarity. 4.3 Maximally Compact Objects A maximally compact PG object is dened by the simultaneous conditions AR= 1, g(R0) = g0, (13) where R0 denotes the physical radius of the TAL. In this limit, the redshift formula becomes 1 + zgPG = expg0R2 0 rc2. (14) Introducing the constant p≡g0 c2, (15) we may write 1 + zgPG = exppR0 R0 r. (16) The exponential dependence of redshift on R0 is a dening feature of PG and underlies the cosmological implications developed in later sections. 4.4 Surface Emission For radiation emitted directly from the TAL, the emission radius is r=R0 . In this physically relevant case, 1 + zgPG = exp(pR0), (17) or equivalently, ln(1 + zgPG) = pR0. (18) This relation provides a direct link between the observed gravitational redshift and the physical radius of the compact object within PG. 4.5 Relation to Eective Mass Using the PG massradius relation with AR= 1 GMe=g0R2 0, (19) the eective mass may be written as Me=c4 Gg0 [ln(1 + zgPG)]2. (20) This expression shows that arbitrarily large gravitational redshifts are attainable for nite mass, without invoking horizons or singular behavior. 7 4.6 Newtonian and GR Limits For comparison purposes only, it is useful to contrast the PG gravitational redshift with the corresponding Newtonian and general-relativistic expressions. These comparisons are strictly phenomenological and do not imply shared physical mechanisms. The GR and Newtonian expressions are presented here solely for comparison of observable behavior, not as limiting cases from which PG is derived. In the weak-eld limit g0R2 rc21, the PG redshift given by Eq. 11 reduces to zgPG ≈ARg0R2 rc2=GMe rc2, (21) which coincides with the standard Newtonian gravitational redshift. Thus PG reproduces all tested weak- eld results while permitting qualitatively new behavior in the regime of extreme compactness. Extended Newtonian Redshift Newtonian gravity is normally presented only in the linear approximation. However, following treatments that interpret photon frequency loss via energy conservation in a Newtonian potential (Catto, 2014; Okun, 2006), the redshift derivation admits a natural exponential form when treated exactly. Introducing the compactness parameter x≡2GM rc2, (22) the gravitational redshift in an extended Newtonian formulation (see Danilatos (2025a)) may be written as zgN= expGM rc2−1 = expx 2−1. (23) This expression is mathematically well dened over the full range 0≤x≤1, even though Newtonian gravity has no intrinsic notion of a horizon. The exponential Newtonian redshift therefore provides a useful reference curve against which both GR and PG can be compared across the entire compactness domain, as illustrated in Fig. 2 (orange curve). It is noted that even at the limiting case x= 1 the Newtonian redshift saturates at zgN(x= 1) = e1/2−1≈0.6487, (24) which is far smaller than typical cosmological redshifts. General Relativistic Redshift In General Relativity, gravitational redshift arises from the curvature of spacetime. Following standard derivations in modern expositions (Carroll, 2004), for a static, spherically symmetric Schwarzschild eld, the exact redshift of a photon emitted at radius r and received at innity is zgGR =1 r1−2GM rc2 −1. (25) Dening the compactness parameter x≡2GM rc2=RS r, (26) where RS is the Schwarzschild radius, this expression becomes 1 + zgGR = (1 −x)−1/2. (27) In GR, as x→1 , the redshift diverges, corresponding to the approach to the event horizon. This divergence of gravitational redshift as compactness approaches unity reects the formation of a geometric event horizon. In PG, no such divergence occurs; instead, redshift increases exponentially with compactness while remaining nite for any nite mass. 8 However, all astrophysical objects with directly observable emitting surfaces occupy compactness regimes that remain bounded well below the black-hole limit. For ordinary stars and white dwarfs one has x1 , while even the most compact neutron stars are expected to satisfy x∼0.2−0.4 , depending on the equation of state. In these regimes, gravitational redshifts predicted by General Relativity are correspondingly modest, ranging from z∼10−6 at the solar surface to at most z∼0.3 under extreme neutron-star conditions. These values are many orders of magnitude smaller than the redshifts commonly observed in distant galaxies ( z∼1 15). Consequently, within the standard GR framework, large observed astronomical redshifts cannot be attributed to gravitational elds associated with material emitting surfaces, but must instead be explained by cosmological expansion or other non-gravitational mechanisms. The General Relativistic gravitational redshift as a function of compactness x is shown in Fig. 2 (red curve). For comparison, the corresponding Push Gravity predictions are also plotted in the same gure. Eq. (16) admits a sequence of TAL radii R0 associated with eective masses ranging from 1M to 7M . Over this range, the PG gravitational redshift increases rapidly with compactness and can exceed unity by large amounts, reaching and surpassing the redshifts observed in highz galaxies detected by JWST. 5 Luminosity, Flux, and Distance in Push Gravity A central element of the cosmological argument developed in this work is that the observed redshiftdistance relation can arise from intrinsic properties of compact sources rather than from metric expansion of space. To demonstrate this, we must establish how luminosity and distance are inferred within the PG framework. This section develops the luminositydistance relation appropriate to maximally compact PG objects, emphasizing where it departs from standard treatments and why a new Malmquist-type selection eect naturally emerges. 5.1 Observed Flux and Geometric Dilution Independently of any cosmological model, the observed ux f from a radiating source of intrinsic luminosity L at physical distance D satises the inverse-square law f=L 4πD2. (28) This relation is purely geometric and does not rely on assumptions about cosmic expansion, spacetime curvature, or the physical origin of redshift. 5.2 Luminosity of Maximally Compact PG Objects In Push Gravity, the gravitationally active mass of a compact object is not distributed throughout its interior but is concentrated in an extremely thin TAL at radius R0 . For maximally compact bodies with absorptivity AR= 1, the TAL is the dominant site of both gravitational interaction and radiative emission. In this limit, luminosity does not arise from volumetric interior processes but from surface phenomena occurring at the TAL. It is therefore natural to associate the intrinsic luminosity with the surface area of the absorption layer, L∝4πR2 0. (29) Using the PG massradius relation GMe=g0R2 0, (30) this scaling may be written equivalently as L∝Me. (31) No assumption about the detailed emission mechanism is required at this stage; only the geometric concentration of eective mass in the TAL is invoked. This scaling is specic to maximally compact PG objects and does not apply to ordinary stars or diuse systems in the transition regime of the absorptivity AR ; such conditions are important but pending further developmental work. 9 through the abundant production and trapping of long-wavelength radiation in highly absorptive environments. The present work represents a focused and testable extraction from a broader, continuously evolving theoretical program. 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