NUVO Black Holes: Sinertia Collapse, Kenos Regions, and Geometric Condensation in Flat Space - Part 10 of the NUVO Theory Series

1. Introduction

Black holes in general relativity are defined as regions of extreme spacetime curvature bounded by an event horizon, beyond which escape is classically impossible [1]. At their core lies a singularity where the curvature of spacetime diverges and the theory breaks down. While this framework has led to profound predictions — including gravitational wave emission, Hawking radiation, and the no-hair theorem — it also gives rise to unresolved paradoxes concerning information loss, entropy, and quantum coherence.

NUVO theory offers a fundamentally different framework in which all gravitational phenomena arise not from curved spacetime, but from a conformal scalar field $\lambda (t,r,v)$ that modulates local measurements of space and time. This scalar is determined by a particle’s velocity and position relative to gravitational sources[2]:

$$\lambda (t,r,v)={\displaystyle \frac{1}{\sqrt{1-\frac{v^2}{c^2}}}}+{\displaystyle \frac{GM}{r{c}^2}}.$$

Within NUVO, inertial structure is separated into two distinct components:

• Pinertia (${\iota }_p$): Governs modulation due to velocity, representing how a particle couples to geometry through motion.
• Sinertia (${\iota }_s$): Governs modulation due to gravitational potential, representing how a particle extracts structural coherence from space.

This decomposition enables NUVO to interpret gravitational collapse not as a divergence of curvature, but as a phase transition in modulation capacity. As mass concentrates, sinertia can vanish — cutting off a particle’s ability to interact with or be modulated by surrounding space. When this occurs, pinertia also collapses, and particles transition into a null-modulation state where motion is pure kinetic and geometry becomes inert.

We define this modulation-collapse region as the kenos — a flux-null vacuum in which mass is present but space is no longer structurally interactive. In this model, a NUVO black hole forms not when escape velocity exceeds the speed of light, but when space itself can no longer support geometric propagation. The resulting black hole is not a singularity but a condensate of non-modulating mass-energy confined by scalar boundary conditions.

This paper introduces the geometry, field structure, and physical implications of NUVO black holes. We derive the condition for scalar collapse and show that it coincides numerically with the Schwarzschild radius. We explore the behavior of proper time, geodesics, and modulation capacity across this boundary and discuss implications for information, entropy, and field coherence. The result is a novel model of gravitational collapse consistent with all known observational tests but devoid of singularities or metric divergence.

2. Scalar Modulation and Inertial Structure

In NUVO theory, gravitational and relativistic effects are not consequences of curved spacetime but instead arise from the scalar field $\lambda (t,r,v)$, which modulates local geometry while preserving global flatness. The scalar field is defined as:

$$\lambda (t,r,v)={\displaystyle \frac{1}{\sqrt{1-\frac{v^2}{c^2}}}}+{\displaystyle \frac{GM}{r{c}^2}}.$$

(1)

This conformal factor applies uniformly to all components of the Minkowski metric via:

$$g_{\mu \nu }(t,r,v)={\lambda }^2(t,r,v){\eta }_{\mu \nu },$$

(2)

where ${\eta }_{\mu \nu }$ is the flat Minkowski metric.

To interpret $\lambda$ physically, we decompose it into two distinct components:

$$\begin{array}{cc}\hfill {\iota }_p\left(v\right)& ={\displaystyle \frac{1}{\sqrt{1-\frac{v^2}{c^2}}}},\hfill \end{array}$$

(3)

$$\begin{array}{cc}\hfill {\iota }_s\left(r\right)& ={\displaystyle \frac{GM}{r{c}^2}},\hfill \end{array}$$

(4)

such that:

$$\lambda ={\iota }_p+{\iota }_s.$$

(5)

We define:

• Pinertia (${\iota }_p$): The inertial modulation of a particle due to its velocity. It represents how a particle’s motion through space modifies its local measurement of time and distance.
• Sinertia (${\iota }_s$): The scalar modulation associated with gravitational potential. It represents the extent to which a particle draws from spatial structure in order to maintain its existence as a coherent, geometrically embedded object.

In this framework, a particle’s total geometric modulation is the sum of these two contributions. A high-velocity particle has strong pinertial effects. A particle deep in a gravitational well experiences enhanced sinertial modulation.

Both components are essential to sustaining geometric propagation: pinertia enables time-like evolution, while sinertia enables space-like coherence. When either is removed, the capacity for modulation fails — leading to either complete decoupling from space (photon-like behavior) or collapse into the kenos (null-modulation vacuum).

We interpret this framework as an energy-based encoding of geometry. Rather than space being curved by mass-energy, space responds through the modulation field $\lambda$, which expresses geometry as a dimensionless, energy-normalized quantity. In this sense, the NUVO model unifies kinematic and gravitational phenomena through scalar modulation rather than metric deformation.

3. Defining Sinertia Collapse

In the NUVO framework, the modulation of geometry by the scalar field $\lambda$ depends on two distinct components: pinertia and sinertia. Whereas pinertia encodes a particle’s kinetic modulation due to its velocity, sinertia describes the particle’s ability to draw geometric coherence from the surrounding space.

Sinertia is defined as:

$${\iota }_s\left(r\right)={\displaystyle \frac{GM}{r{c}^2}}.$$

(6)

It is a purely position-dependent term that reflects how deeply embedded a particle is in a gravitational well. Unlike pinertia, which can be altered by motion, sinertia is governed solely by the geometric relationship between the particle and the mass distribution around it.

We define sinertia collapse as the condition under which ${\iota }_s\to 0$ and the modulation capacity of space vanishes. In this regime:

• The scalar field $\lambda$ no longer changes with position: $\nabla \lambda =0$.
• The space around the particle becomes inert — unable to support modulation.
• Propagation, structure, and forces cease to operate; geometry becomes static and decoupled.

This regime marks the onset of the kenos, a region where space exists but no longer modulates. Unlike a singularity, where physical quantities diverge, the kenos represents a scalar limit where all gradients vanish. It is a vacuum not of energy, but of geometric response.

The physical interpretation is as follows:

• Outside the kenos: sinertia is positive, $\lambda$ varies, and space can mediate structure.
• At the boundary: $\nabla \lambda =0$, the modulation field stalls.
• Inside the kenos: sinertia is zero, and pinertia becomes ineffective; the particle cannot sustain interaction with geometry.

In this picture, collapse occurs not through curvature, but through the exhaustion of geometry’s capacity to respond. Just as a photon has no pinertia and moves at c, a particle inside the kenos has no sinertia and collapses to a state of pure kinetic motion. Motion is still possible, but modulation is not — and thus, the particle becomes trapped in a flux-null phase of flat but inert geometry.

This defines a fundamentally different conception of a black hole. In NUVO, black holes are not singularities in spacetime curvature but boundaries in scalar modulation, separating the coherent, modulatable universe from the inert kenos phase.

4. NUVO Black Hole Boundary

The NUVO model replaces the concept of a general relativistic event horizon with a scalar modulation boundary — a radius at which the ability of space to propagate structure through $\lambda$ vanishes. This modulation limit is not defined by escape velocity, but by a condition on inertial structure: specifically, the point at which a falling particle reaches the speed of light and pinertia diverges.

In NUVO, the scalar field is given by:

$$\lambda (r,v)={\displaystyle \frac{1}{\sqrt{1-\frac{v^2}{c^2}}}}+{\displaystyle \frac{GM}{r{c}^2}}={\iota }_p+{\iota }_s.$$

(7)

We define the boundary of a NUVO black hole as the surface at which a test particle in free fall reaches $v=c$, causing $\gamma \to \infty$ and thus $\lambda \to \infty$. This is not a geometric singularity, but a breakdown in modulation capacity — a point at which scalar gradients cease and the field becomes non-responsive.

To find this critical radius, we apply Newtonian energy conservation for a particle falling from rest at infinity:

$${\displaystyle \frac{1}{2}}{v}^2={\displaystyle \frac{GM}{r}}.$$

(8)

Solving for the radius where $v=c$ gives:

$$c^2={\displaystyle \frac{2GM}{r_h}},$$

(9)

and thus:

$$\begin{array}{|c|}\hline r_h={\displaystyle \frac{2GM}{c^2}}\\ \hline\end{array}.$$

(10)

This is formally identical to the Schwarzschild radius in general relativity, but its interpretation is fundamentally different. In NUVO, $r_h$ marks the point beyond which the scalar field cannot modulate. Both sinertia and pinertia fail to support structure. No curvature occurs, and no physical quantity diverges — but the particle becomes embedded in a fluxless, modulation-null vacuum.

Beyond $r_h$, space continues to exist but cannot respond. The geometry is flat, but inert. Particles trapped within this region behave as if massless, confined to $v=c$, unable to interact with the external field. This defines the kenos: the modulation vacuum that replaces the GR black hole singularity.

This reinterpretation provides a consistent, singularity-free model of collapse. It preserves the gravitational radius as a meaningful boundary but removes the need for spacetime curvature and infinite compression. Instead, the collapse is one of modulation capacity — a scalar exhaustion, not a geometric divergence.

5. Interior Dynamics and Condensate Behavior

Within the NUVO black hole boundary — the kenos — space no longer supports scalar modulation. The scalar field $\lambda$ becomes uniform and inert:

$$\nabla \lambda =0,\lambda \to \infty .$$

(11)

This does not imply a divergence of curvature or the breakdown of physical laws, but rather the cessation of interaction. The particle cannot couple to surrounding geometry, because both pinertia and sinertia have failed.

We interpret this state as a form of condensate: a configuration in which mass exists, but can no longer structure space. The particle moves with $v=c$, not because it is massless, but because no spatial feedback is available to slow or modulate its motion. This mirrors the behavior of photons, which also lack pinertia and move at the speed of light. However, while photons remain coupled to space via sinertia (they follow null geodesics), particles in the kenos are fully decoupled — embedded in a modulation-dead region.

The interior of a NUVO black hole is thus not a singularity, but a scalar condensate. All particles are confined to a null-modulation state:

$${\iota }_p=\gamma \to \infty ,{\iota }_s\to 0,\lambda =\mathrm{constant},\nabla \lambda =0.$$

(12)

In this regime:

• There are no forces — force requires a gradient in modulation.
• There is no structure — sinertia is zero, and space has no coherence.
• There is no information flow — propagation requires a varying field.
• All motion is kinetic — constrained to $v=c$, without resistance or reference.

This behavior resembles a Bose–Einstein condensate in its most abstract form [3]. Just as bosons collapse into a single coherent quantum state at low temperature, mass collapses into a fluxless, coherent geometric null-state in the kenos. The difference is that, in NUVO, this condensation occurs not in a quantum field, but in a modulation field. Geometry does not collapse — it simply ceases to respond.

This presents a new conception of gravitational interiors. No singularity forms. No infinite energy densities are required. The NUVO black hole is a final state in the scalar modulation structure of space — an inert geometry filled with kinetically confined but spatially non-coupling matter. This replaces the singularity with a field-theoretic condensate — mathematically finite, physically consistent, and observationally plausible.

6. Comparison to GR Black Holes

The NUVO black hole framework reproduces the empirical boundary condition of general relativity — the Schwarzschild radius — but does so using a fundamentally different mechanism [4]. In GR, black holes form through the curvature of spacetime driven by Einstein’s field equations. The event horizon marks a lightlike boundary beyond which causal contact is lost, and the interior contains a curvature singularity where spacetime and classical physics break down.

By contrast, NUVO black holes arise from the scalar modulation field $\lambda (t,r,v)$, which governs how geometry responds to mass and motion. Collapse occurs not when curvature diverges, but when modulation vanishes. The event horizon is defined not by escape velocity, but by the boundary at which sinertia collapses and pinertia becomes unbounded. There is no divergence in geometry — only a transition into a region where geometry cannot modulate.

The following table summarizes the key differences:

Table 1. Comparison of general relativistic and NUVO black holes.

Feature	GR Black Hole	NUVO Black Hole
Horizon definition	$r=2GM/c^2$ (escape velocity = c)	$r=2GM/c^2$ (modulation collapse)
Interior state	Curved spacetime, singularity at center	Flat, non-modulating scalar condensate
Field breakdown	Divergence in curvature tensors	Inactivation of $\nabla \lambda$
Causal isolation	Light cones tilt inward	Scalar gradients vanish
Matter state	Infinite compression, pointlike core	Null modulation, kinetic condensate
Information loss	Paradoxical	Prevented by boundary modulation
Time behavior	Freezes at horizon (from outside)	Pinertia diverges at horizon
Geometry behavior	Curved, singular	Flat, inert

Table 1. Comparison of general relativistic and NUVO black holes.

Feature	GR Black Hole	NUVO Black Hole
Horizon definition	$r=2GM/c^2$ (escape velocity = c)	$r=2GM/c^2$ (modulation collapse)
Interior state	Curved spacetime, singularity at center	Flat, non-modulating scalar condensate
Field breakdown	Divergence in curvature tensors	Inactivation of $\nabla \lambda$
Causal isolation	Light cones tilt inward	Scalar gradients vanish
Matter state	Infinite compression, pointlike core	Null modulation, kinetic condensate
Information loss	Paradoxical	Prevented by boundary modulation
Time behavior	Freezes at horizon (from outside)	Pinertia diverges at horizon
Geometry behavior	Curved, singular	Flat, inert

This reinterpreted framework avoids many of the unresolved issues in GR. There is no need for singularities, divergent tensors, or quantum gravity corrections to handle collapse. Instead, NUVO predicts a physically consistent, flat-space endpoint to gravitational collapse — a kenos bounded by scalar inactivation, not geometric pathology.

Because the Schwarzschild radius emerges naturally from energy conservation in this model, the observational predictions of GR — such as orbital precession, gravitational lensing, and gravitational wave ringdown — remain matched. However, NUVO differs sharply in its description of what lies inside: not infinite curvature, but inert modulation.

This opens new conceptual avenues for understanding entropy, information preservation, and field structure in the strongest gravitational regimes.

7. Conceptual Implications

The reinterpretation of black holes as scalar modulation collapse boundaries rather than spacetime singularities opens new possibilities for addressing longstanding puzzles in gravitational physics and quantum information theory.

7.1 Information and Modulation Gradients

In GR, the fate of information falling into a black hole remains an unresolved paradox. Because the interior geometry includes a singularity and classical causal structures, it is unclear how — or whether — information is preserved. In NUVO, the situation is fundamentally different. Because the interior of a NUVO black hole is a fluxless, non-modulating region, information is not destroyed — it is simply trapped at a modulation boundary.

Escape becomes impossible not due to infinite curvature, but due to the vanishing of scalar gradients. Information is localized at the surface where $\nabla \lambda \to 0$. If modulation ever resumes (for example, through external influence or decay of the boundary), information may become accessible again. This provides a pathway to resolving the information paradox without resorting to holography or exotic field theories.

7.2 Entropy and the Modulation Surface

In general relativity, black hole entropy is proportional to horizon area. In NUVO, this proportionality emerges from a different mechanism. Because $\lambda$ controls geometric modulation, the outer boundary of a black hole — where $\nabla \lambda$ becomes steep but finite — contains the entire field gradient. All modulation occurs at or near this boundary, while the interior is inert.

We therefore propose that entropy in NUVO black holes corresponds to the scalar modulation content of the boundary layer. This could be proportional to:

$$S\propto {\int }_{\partial V}{|\nabla \lambda |}^{2}dA,$$

(13)

where $\partial V$ is the surface of the kenos. This aligns conceptually with the area-scaling of entropy, while replacing metric curvature with scalar field variation as the carrier of structure.

7.3 Modulation-Based Holography

In GR-based holography, all information inside a black hole is encoded on its horizon surface. NUVO provides a natural scalar-field analog. Because the modulation gradient $\nabla \lambda$ vanishes in the interior, all observable geometry, force, and interaction must occur in the narrow shell where $\lambda$ still varies.

This naturally gives rise to a form of holography in which the modulation boundary encodes the full dynamical state of the system. Unlike GR, this does not require curved spacetime or dual field theories — the behavior emerges directly from the scalar structure.

7.4 Quantum Field Compatibility

Because the NUVO model avoids infinite curvature and retains flat spacetime, it may be inherently more compatible with quantum field theory [5]. The background geometry remains Minkowski everywhere; only the scalar modulation varies. This allows the use of standard quantization techniques and suggests a path toward integrating gravitational collapse with quantum behavior without requiring quantum gravity or renormalization of singularities.

NUVO black holes may therefore serve as a bridge between flat-space quantum physics and gravitation — providing a coherent geometric substrate on which both can operate.

8. Conclusion

NUVO theory reinterprets gravitational collapse not as a geometric singularity, but as a breakdown in the scalar modulation capacity of space. In this framework, black holes form when sinertia — the component of inertial structure derived from gravitational potential — vanishes, and pinertia — the velocity-dependent component — diverges. This condition defines a critical boundary, identical in form to the Schwarzschild radius, but physically reimagined as a modulation horizon rather than a spacetime trap.

Within this boundary, the scalar field $\lambda$ becomes constant and structureless. Gradients vanish, and space ceases to modulate. The resulting region — the kenos — is a flux-null vacuum, where matter persists but cannot interact with or be influenced by external geometry. Particles inside the kenos move at the speed of light, not because they are massless, but because the geometry has lost the capacity to slow them.

This model preserves all empirical predictions of general relativity at the horizon scale while avoiding singularities, divergences, and the breakdown of classical geometry. It offers a new picture of black holes as modulation-bound condensates, consistent with flat-space dynamics and compatible with quantum field theory.

By separating inertial structure into pinertia and sinertia, NUVO opens a new geometric framework for understanding motion, structure, and collapse. It resolves the endpoint of gravitational compression without invoking curvature or exotic matter, instead relying on the scalar exhaustion of geometry’s capacity to respond.

This new interpretation repositions black holes not as holes in space, but as boundaries in field structure — and with it, NUVO establishes a gravitational theory that preserves coherence, avoids divergence, and reframes the most extreme objects in the universe in terms of scalar modulation.