The Massive Black Hole Bias: A Potential Origin for the Cosmological Redshift-Distance Relation without Universal Expansion

The Massive Black Hole Bias: A Potential Origin for the Cosmological Redshift-Distance Relation without Universal Expansion Gerasimos D Danilatos Version 4: 12 December 2025 https://doi.org/10.5281/zenodo.17855884 ESEM Research Laboratory 28 Wallis Parade North Bondi, NSW 2026 Australia [email protected] Abstract The inference of universal expansion rests primarily on the observed redshiftdistance relation for galaxies. We propose that this relation may arise not from expanding space but from systematic observational biases inherent in deepeld astronomy. At increasing distances, detection limits permit the observation of only the most luminousand thus the most massive and compactastrophysical systems. If the gravitational redshift of these objects is larger than traditionally estimated, a natural correlation arises: objects detected at greater distances will on average exhibit higher intrinsic gravitational redshift. This mimics the functional form of Hubble's law without invoking cosmic expansion. Furthermore, a reassessment of the concept of mass in Push Gravity (PG)a theoretical framework that resolves longstanding inconsistencies in standard mass determination and gravitational couplingsuggests that the gravitational inuence of compact bodies has been substantially underestimated. PG distinguishes between eective mass , the gravitationally active component, and black mass , the inert interior; the former is distributed within a thin, highly absorbing Total Absorption Layer (TAL) surrounding the latter. This reinterpretation alters the relation between luminosity, radius, and mass, and leads to Malmquist-like selection eects that systematically bias high-redshift observations. If correct, these eects imply that the cosmological redshift may be of gravitational rather than kinematic origin, and that the case for universal expansion requires re-examination. The present work develops this thesis and lays the foundation for a cosmology based on PG rather than on spacetime expansion. 1 Introduction The commonly accepted evidence for universal expansion stems from the observed correlation between redshift and distance in galaxies. This correlation is canonically interpreted as a Doppler-like eect resulting from the recession of galaxies embedded in an expanding spacetime. We examine an alternative possibility: the redshiftdistance relation may arise from selection biases connected with mass, radius, and luminosity measurements of distant astrophysical bodies. At large distances, only the most luminous systems remain above detection thresholds. Such systems are associated with the most massive objects or collections of objects: massive black holes, dense stellar populations, compact galactic nuclei, and gravitationally intense environments. This observational ltering introduces several Malmquist-type biases: 1. Only the most massive and luminous systems are detectable near the instrumental limits. 2. Their eective radii, gravitational elds, and distances are systematically underestimated under conventional assumptions. 3. Mischaracterization of their luminosity and gravitational environment propagates into distance and mass estimates, compounding the bias. 1 For a detailed treatment of Malmquist and selection biases in astronomical samples, see Malmquist (1920) and Teerikorpi (1984). Recent discoveries have intensied these concerns. JWST observations demonstrate the existence of galaxies at redshifts z > 10 with stellar masses exceeding 1010M (Labbe et al. , 2023). These challenge formation timescales in the standard Λ CDM picture. Simultaneously, the Hubble tensiona persistent discrepancy between earlyand late-universe measurements of the Hubble constant (Riess et al. , 2024)suggests that the interpretation of redshift as universal expansion may be incomplete or misleading. In a series of works , Push Gravity (PG) proposes a new conceptualization of mass, radius, and gravitational interaction. PG distinguishes between the eective mass responsible for gravitational coupling and the black mass that constitutes an inert core. The eective mass resides in an extremely thin Total Absorption Layer (TAL) surrounding the black mass. As mass increases, the TAL becomes thinner while the radius increases, leading to signicant deviations from conventional density and radius estimates. This reinterpretation of mass distribution implies that many very massive objectsincluding those observed by JWSTare far larger than conventionally estimated. Their gravitational redshift may therefore be substantially higher than expected under standard GR assumptions. Because only such objects are visible at greatest distances, their enhanced gravitational redshift creates a built-in bias: the further we observe, the higher the redshift. An adequate understanding for the proposed Malmquist biases should extend beyond those analyzed by Butkevich et al. (2005) Thus, the observed redshiftdistance relation may be an artifact of Malmquist-type selection rather than evidence of cosmic expansion. Whereas a qualitative report entitled  Is the Big Bang an artifact? was previously made by Danilatos (2024), the aim of current paper is to explore this possibility quantitatively. 2 Prevailing Theory In the conventional framework, three principal mechanisms contribute to observed redshift: 1. Cosmological redshift arising from the expansion of space. 2. Gravitational redshift predicted by General Relativity (GR). 3. Doppler redshift due to peculiar velocities. Of these, only cosmological redshift accounts for the dominant component in the standard interpretation. Gravitational redshift is generally considered negligible in comparison. We review these mechanisms briey below. 2.1 Cosmological Redshift: Cosmological redshift is understood as the stretching of photon wavelength induced by the expansion of the universe. In the FriedmannLemaîtreRobertsonWalker framework, the redshift parameter z relates to the scale factor a(t) via 1 + z=a(tobs) a(temit). (1) Empirically, for nearby galaxies, this leads to the HubbleLemaître law υ=H0D, (2) where υ is interpreted as recessional velocity, D is the comoving distance, and H0 is the present Hubble constant. The tension between earlyand late-universe determinations of H0 (Riess et al. , 2024), and the unexpected abundance of massive, evolved galaxies at high redshift revealed by JWST (Labbe et al. , 2023) (Naidu et al. , 2022; Kokorev et al. , 2023; Gottumukkala et al. , 2024; Giulietti et al. , 2024) suggest that the interpretation of z purely as expansion may require revision. 2.2 Gravitational Redshift in General Relativity In GR, photons lose energy as they climb out of a gravitational potential well. For a static, spherically symmetric Schwarzschild eld, the exact gravitational redshift of a photon emitted at radius r is zgGR =1 r1−2GM rc2 −1. (3) 2 Dene the compactness parameter x≡2GM rc2=RS r, (4) where RS is the Schwarzschild radius. Then Eq. (3) takes the form 1 + zgGR = (1 −x)−1/2. (5) As x→1 , the redshift diverges, which corresponds to the approach toward the event horizon. However, all observed astrophysical objects have x1 , even neutron stars where typically x∼0.4 . Thus the gravitational redshifts actually observed in nature are very small, with measured values typically ranging from z∼10−6 (solar surface) to z∼0.3 (extreme neutron star conditions). This is vastly smaller than cosmological redshifts ( z= 1  15 ). Figure 1 illustrates this behavior in the GR curve (red line). The additional curves in this gure result from and are explained by the continued work next. Consequently, within the observable universe so far, large redshifts cannot be attributed to gravitational elds under GR. The general-relativistic expression for gravitational redshift used here follows standard derivations in modern expositions (Carroll, 2004). 2.3 Newtonian Gravitational Redshift Before comparing with PG theory, it is useful to revisit the Newtonian derivation of gravitational redshift using the eective-mass concept for photons. This derivation extends beyond the classical escape-velocity argument of Michell (1784) and produces a closed-form, exact Newtonian expression for gravitational redshift. Because this derivation forms the basis for a subsequent extension, and for good measure, we present all the detailed steps for reference when needed: Let a photon of initial wavelength λr be emitted at radius r from a spherical body of mass M . Its local energy is Er=hc λr . (6) Assuming the photon carries an eective mass meff =E c2=h λc, (7) the innitesimal work done against gravity when the photon climbs by d r is d E=−GMmeff r2dr =−GM c2 E r2 d r. (8) Thus d E E=−GM c2 d r r2. (9) Integrate from r to ∞ : lnE∞ Er=−GM rc2. (10) Exponentiate: E∞=Erexp−GM rc2. (11) Convert to wavelengths: λ∞ λr = expGM rc2. (12) Therefore, the Newtonian gravitational redshift is zgN= expGM rc2−1. (13) To compare with GR, retain the compactness denition x≡2GM rc2, (14) 3 so that GM rc2=x 2 . Then Eq. (13) becomes zgN= expx 2−1. (15) As shown in Fig .1 (orange curve for Newton), even at the limiting case x= 1 the Newtonian redshift saturates at zgN(x= 1) = e1/2−1≈0.6487, (16) which is far smaller than typical cosmological redshifts. Therefore Newtonian gravity, like GR, cannot account for large observed cosmological redshifts under conventional interpretations. So far, both GR and Newtonian predictions do not support our claim stated at the outset. The GR curve diverges as x→1 , while the Newtonian curve approaches a nite value. In both cases, for realistic astrophysical objects, x stays well below unity, yielding redshifts far smaller than those observed in cosmology. The above derivation follows treatments that interpret photon frequency loss via energy conservation in a Newtonian potential (Catto, 2014; Okun, 2006). 3 Gravitational Redshift in Push Gravity Theory Push Gravity (PG) revises the understanding of mass and its distribution within a gravitationally active body. The key PG insight is the distinction between: • eective mass Me  the gravitationally active component generally for all bodies variously distributed, but particularly concentrated in an extremely thin Total Absorption Layer (TAL) for very compact bodies, and • black mass  the gravitationally inert component generally for all bodies variously distributed in the interior that does not participate directly in gravitational absorption. Both are components of real mass, or hyle . In PG, the standard gravitational parameter µ=GM is replaced by µP G =GMe=ARg0R2, (17) where •AR is the absorptivity (dimensionless), •g0 is the universal maximum gravitational acceleration, •R is the physical radius of the compact body. This relation arises from the absorption dynamics in the TAL and replaces the conventional GM term throughout Newtonian-style gravitational interactions. Crucially, Me is not concentrated at a point, nor does it correspond to the total rest mass. Instead, it describes the eective action of the absorption layer. To compute the gravitational redshift in PG, one repeats exactly the same steps used in the Newtonian derivationbut replaces GM by the PG gravitational parameter from Eq. (17). This yields the exact PG redshift: zgPG = expARg0R2 rc2−1. (18) Maximum Compactness in PG In PG, a maximally compact object is dened not by a singularity or coordinate pathology but by the saturation of absorptivity and surface acceleration: AR= 1, g(R) = g0. (19) Such bodies possess a limiting radius R0 for a given eective mass Me , determined through Eq. (17). The TAL becomes extremely thin, fully absorbing incident gravions mediating gravity. The interior mass becomes gravitationally opaque (no inertia, inert, gravitationally inactive) but not singular. Substituting AR= 1 and R=R0 into Eq. (18) yields zgPG = expg0R2 0 rc2−1. (20) 4 Figure 1: Comparison of gravitational redshift predicted by GR (red curve), the exact Newtonian eectivemass model (orange curve), and PG plotted against compactness values x . The PG model produces a family of curves corresponding to dierent eective masses, here shown as labeled powers En , n= 1 →7 , representing compact objects with total mass n M . PG allows large gravitational redshifts even at moderate compactness, owing to its dependence on the physical radius R0 of the compact body rather than on the theoretical Schwarzschild radius alone. 5 Dene p=g0 c2, (21) so that zgPG = exppR0 R0 r−1. (22) This reveals that PG redshift depends sensitively on both the radius R0 and the emission radius r . In contrast with GR and Newtonian gravity, PG allows substantial gravitational redshifts even far from r=R0 , provided R0 is large enough. For a direct comparison, we can now dene the compactness factor by x=R0 r (23) and re-write the PG gravitational redshift as zgPG = exp(pR0x)−1. (24) Numerical Estimates Using a preliminary PG nding g0= 1.331942797 ×109m s−2, (25) we obtain p=g0 c2≈1.4819862273 ×10−8m−1. (26) Compact bodies of increasing mass yield increasing values of R0 in PG. We can now complement Fig .1 by illustrating the PG redshift in comparison to GR and Newtonian models. The PG redshift of Eq. (20) is shown against R0/r for a sequence of values of R0 corresponding to eective masses ranging from 1M to 7M . The resulting PG redshifts can exceed unity by large factors, reaching and surpassing the observed redshifts of JWST highz galaxies. In this framework, extremely large redshift values arise not from cosmic expansion but from intense gravitational elds associated with very massive objects whose radii have been underestimated in standard and prevailing analysis. These results challenge the interpretation that large observed redshifts necessarily imply cosmic expansion. 4 A Re-appraisal of Luminosity and Distance by PG Theory Given the distribution of eective mass in PG, especially for compact objects whose gravitationally active mass resides within a thin TAL, the conventional relation between luminosity, mass, and radius requires a fundamental revision. In standard astronomy, the intrinsic luminosity of an object is treated independently of its gravitational structure. In PG, however, the geometry and mass distribution of the TAL directly inuence both the emergent luminosity and the inferred distance. 4.1 Conventional Relation Between Luminosity and Distance The observed ux f , intrinsic luminosity L , and physical distance D of an astronomical object are related by the inversesquare law: f=L 4πD2. (27) Here, f= apparent brightness (ux) , L = intrinsic luminosity , D = distance . 4.2 Luminosity of Compact Bodies in PG For general absorptivity values AR<1 , the connection between AR , eective mass Me , and luminosity remains an open theoretical task. However, for maximally compact bodies satisfying AR= 1 , PG provides a clear simplication: the entire eective mass is concentrated in a thin TAL at radius R0 . In such cases there is no need to model radiative transfer from an interior volume; the luminosity is set by surface processes at the TAL. 6 It is therefore plausibleand consistent with PG structureto assume that the intrinsic luminosity scales with the surface area of the absorption layer: L∝Me∝R2 0. (28) This contrasts sharply with GR-based compact objects, where luminosity is either severely suppressed or originates from accretion physics rather than a well-dened physical surface. Distance as a Function of Flux and PG Radius Substituting the proportionality L∼R2 0 into Eq. (27), we obtain D2∼R2 0 4πf ,⇒D∼R0 2√πf . (29) Thus, knowledge of R0 implies knowledge of distance. Determining the Radius R0 from PG Redshift The PG gravitational redshift for a compact body with AR= 1 is provided by Eq. 22 being rearranged as 1 + zgPG = exppR0 R0 r, (30) Taking natural logarithms: ln(1 + zgPG) = p R0 R0 r. (31) For emission from the physical surface of a maximally compact body in PG, r=R0 , hence ln(1 + zgPG) = p R0. (32) Solving for R0 , R0=1 pln(1 + zgPG). (33) Distance in Terms of Redshift and Flux Substituting Eq. (33) into the luminositydistance relation gives D∼ln (1 + zgPG) 2p√πf . (34) Thus, in PG, the distance to a remote compact object can be determined directly from its gravitational redshift and apparent ux without appealing to standard candles or cosmological distance ladders. The absolute luminosity scales with the radius of the TAL, which is itself xed by the PG redshift. This relation has major cosmological ramications 5 Toward a PG-Based Cosmology The results obtained above suggest that the Push Gravity framework may provide an alternative foundation for cosmology. In particular, PG modies the behavior of gravitational redshift, luminosity, and distance in ways that lead naturally to large observable redshifts without invoking cosmic expansion. This section integrates the key implications and outlines a PG-based reinterpretation of cosmological observations. 5.1 Immediate Implications of PG Redshift and Luminosity Scaling The preceding analysis establishes several important points: • The luminosity of maximally compact objects with AR= 1 is determined by the radius of their Total Absorption Layer (TAL), and therefore predictable from PG structure alone. Standard candles are unnecessary. • Distance estimates follow from PG-specic relations between ux, radius, and redshift, becoming independent of expansion-based cosmology. • High-redshift objects observed by JWST may not lie at extreme cosmological distances; instead, they may simply possess large PG radii and therefore large gravitational redshifts. • Observed correlations between ux and redshift may arise naturally from PG massradius relations, not from recessional velocity or metric expansion. These results already point toward a potentially transformative reinterpretation of astronomical observations. 7 5.2 Large Gravitational Redshifts Without Expansion PG allows gravitational redshifts that exceed unity and extend into the range z∼10  20 and beyond, matching the highest values reported by JWST. The masses and radii required are well within observationally plausible ranges for extremely massive compact systems. If correct, this removes the need to interpret high redshift as a consequence of cosmic expansion. Instead, the observed redshift is an intrinsic property of the compact body's TAL, linked directly to its physical radius R0 and eective mass Me . As masses increase across the observable universe, the gravitational redshift grows correspondingly. At still greater sizes of maximally compacted bodies, the redshift pushes the emitted radiation toward microwave frequencies, oering a possible reinterpretation of the cosmic microwave background (CMB) as the accumulated PG-shifted emission of remotest, most massive and compact objects. Truly light-trapping con- gurations would represent the limiting case of this progression, and only those conditions would correspond to true black holesif they exist at all. Under PG, the universe is not expanding. The large observed redshifts arise from gravitational structure, not recessional motion. 5.3 Implications for Cosmology The above ndings motivate a reassessment of foundational assumptions in modern cosmology. If large redshifts can arise from compact PG objects, then the interpretation of redshift as a measure of universal expansion may not be necessary. This possibility has consequences for: • the inferred ages and sizes of highz galaxies, • standard-candle and standard-ruler methods, • early-universe structure formation, • the interpretation of JWST high-redshift observations, • the origin and meaning of the CMB redshift. 5.4 Reassessing Redshift in Light of PG Theory In standard GR cosmology, compact objects cannot produce redshifts comparable to the largest cosmological values, except near horizons where light cannot escape. This is a consequence of the GR massradius relation. PG modies this relation in two critical ways: 1. The PG radius R0 grows with total mass more rapidly than the GR Schwarzschild radius, allowing massive bodies with substantial radii to produce extreme redshifts. Whilst we mathematically equated x=RS r=R0 r for a graphical comparison, the Schwarzschild radius and the PG radius R0 correspond to two dierent physical systems and to dierent interpretations on account of a possible misconception of the meaning of mass. 2. The TAL becomes progressively thinner with increasing mass, with the absorptivity approaching its limiting value AR→1 . In this limit, the preceding PG analysis applies directly. For AR<1 we remain in the realm of stars, white dwarfs, and neutron stars, where a full PG-based luminosity theory must still be developed. This task is left for future work, ideally involving specialists in stellar structure and radiative processes. Thus, PG predicts many more massive and compact objects in the universe than GR would allow, each capable of producing strong gravitational redshifts. 5.5 A Malmquist Bias of a New Kind Classical Malmquist bias states that at large distances only the most luminous sources remain detectable. PG adds a new dimension to this selection eect: the most massive and compact sources also produce the largest gravitational redshifts. Consequently, as observational distance increases: • the detectable population shifts toward higher-mass compact objects, • their PG gravitational redshifts systematically increase, 8 • a redshiftdistance relation emerges that closely mimics Hubble's law. In this picture, the apparent expansion slope arises not from cosmic expansion, but from the massradiusredshift coupling inherent in PG. In any case, details of the various relations require further PG development to be fully implemented. Crucially, no recessional velocity or metric expansion of space is required. 5.6 Compatibility with JWST Observations JWST has revealed galaxies at z > 10 with inferred stellar masses &1010M , widely regarded as inconsistent with Λ CDM. In the PG framework: • Such redshifts may originate from the gravitational environment of the emitting regions, not from their cosmological distance. • PG compact objects possess large physical radii R0 , avoiding the extreme connement predicted by GR also avoiding a singularity, and permitting substantial luminosity. • Apparent discrepancies in mass functions, galaxy sizes, and early structure formation are resolved naturally. Thus, PG oers a coherent interpretation of JWST's impossible early galaxies without invoking exotic initial conditions, or inationary modications. 5.7 Toward a PG-Based Cosmology Collectively, these considerations suggest a viable PG-based cosmological framework with the following core components: 1. Redshift is primarily gravitational, not kinematic, particularly at large distances. Blueshifts and redshifts at well-established local distances remain interpreted conventionally (Doppler shifts, etc.), though PG may introduce corrections. 2. Distance scales follow from PG radiusux relations rather than GR luminosity or expansion-based distances. Angular-diameter distances should be reappraised in light of PG requirements. 3. Structure formation need not begin within a compressed early universe; it reects the mass distribution and PG physics of compact systems. 4. The CMB is reinterpreted as PG-shifted radiation from massive compact objects rather than a relic of recombination. 5. Hence, we may plausibly live in an overall static universe, whose observed extent is in a steady-state condition over preceding innite times. These ideas set the stage for the deeper theoretical developments presented in the next section, where the underlying physics of mass, gravity, cosmology, eld theory and more are examined in the broader PG framework. Because this work is extensive (Danilatos, 2025b) and still evolving, we compile in the next Section only the minimum background needed to support the cosmological interpretation outlined above 6 Emergence of New Physics: A Novel Theoretical Framework for Mass, Gravity, and Cosmology In this section we outline the foundational principles of Push Gravity (PG), a developing theoretical framework that reinterprets mass, gravity, and energy exchange from rst principles. The material presented here is a brief and self-contained synthesis of the key concepts required to support the cosmological reinterpretations proposed in the preceding sections. Full derivations, numerical analyses, and supplementary theory will be provided in a dedicated monograph in working progress at present . PG originated as an extension of earlier push-gravity ideas attributed to Fatio and Le Sage (de Duillier, 1929), but has evolved through more than twenty-seven research versions into a broader physical framework that connects gravitational dynamics, eective mass, luminosity, eld theory, particle physics and cosmology. The hypothesis that large gravitational redshifts are systematically underestimated in conventional theory emerges naturally from this framework. 9 Several common objections to static-universe or non-expansion models are often raised. The key point is that none of these objections directly invalidate PG, because PG introduces a distinct physical mechanismgravitational redshift produced by extended TAL structuresthat can reproduce many observational signatures normally attributed to expansion. Supernova time dilation. PG does not dispute the observed time dilation of Type Ia supernova light curves. Rather, PG asserts that the highz component of cosmological redshift may be gravitational, with standard Doppler contributions still operating at ordinary distances. The separation of these components requires systematic reassessment with PG luminosity and massradius relations. Uniform redshift across spectral lines. Critiques that gravitational redshift would produce inconsistent line shifts assume GR-like compactness relations. In PG, light originating from the TAL of a maximally compact object emerges from a nearly uniform gravitational potential, ensuring consistent shifts across all spectral linesmatching observations of distant galaxies. CMB isotropy and spectrum. CMB properties do not exclude PG. Under PG, radiation from a vast population of extremely compact, extremely distant TAL-dominated objects can produce a uniform, thermalized background without invoking a hot Big Bang. This alternative interpretation requires the full PG framework (mass activation, TAL structure, push-particle media) and is developed in the main work. Elemental abundances and large-scale structure. PG modies the underlying massradiusdensity relations of astrophysical systems. As a result, both primordial nucleosynthesis constraints and structure formation scenarios require re-evaluation. These issues do not undermine PG; rather, they represent directions for future detailed work once the expanded QPFT formalism is fully developed. The present exposition focuses on the gravitational eld, characterized by the pair (g0, G) with values (1.33×109,6.67×10−11) , in SI units. In the broader theory developed in the main work, each physical force eld is mediated by its own class of push particles, described by analogous pairs: • Electric eld: (g02 = 5.56 ×1051, G2= 8.25 ×1025) • Nuclear eld: (g04 = 5.56 ×1051, G4= 8.25 ×1027) • Planck (new) eld: (g05 = 5.56 ×1051, G5= 2.79 ×1032) The TAL of a maximally compact body acts as a layered atmosphere containing the push particles for all force elds, each contributing to a corresponding eective mass distribution. This layered structure cannot be fully elaborated here; its derivation belongs to the ongoing development of Quantum Push Field Theory (QPFT). For a complete understanding of the cosmological implications, the reader must consult the main PG monograph (Danilatos, 2025b), where these mechanisms, eld hierarchies, and governing equations are developed in detail. A broader qualitative discussion of cosmology from the PG perspective, including early formulations of the static-universe argument, can be found in the earlier preprint Is the Big Bang an Artifact? (Danilatos, 2024). 7.6 A Path Forward The conclusions of this work can be summarized as follows: 1. PG provides a quantitative mechanism for generating very large gravitational redshifts from compact objects with radii far larger than GR permits. 2. A natural selection bias emerges: at greater distances only the most massive PG objects remain visible, producing an apparent Hubble law without expansion. 3. The Big Bang, cosmic expansion, and associated cosmological constructs may therefore be artifacts of misinterpreting gravitational redshift. 4. JWST observationswhich strongly contradict Λ CDM early-galaxy formation timelinesare consistent with PG expectations. 16 5. 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