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E. Gaztañaga, K. Sravan Kumar, Swaraj Pradhan | Physical review. D/Physical review. D. | (2025)
Primary Link DOI Openalex Full text (OA)

Key Takeaways

Sample Definition And Size

The study investigates a fully relativistic spherical collapse model of a uniform mass distribution M with initial comoving radius χ* and spatial curvature k ≡ 1/χ_k² ≤ 1/χ*², representing an overdensity or bounded perturbation within a larger background. No numerical sample size is applicable, as this is a theoretical model. ([arxiv.org](https://arxiv.org/abs/2505.23877?utm_source=openai))

Study Type

The work is a theoretical, analytical study within general relativity, presenting an exact analytical solution for gravitational collapse and bounce, extended to cosmological implications. ([arxiv.org](https://arxiv.org/abs/2505.23877?utm_source=openai))

Conflicts Of Interest

No conflicts of interest are declared in the available abstract or metadata. ([journals.aps.org](https://journals.aps.org/prd/abstract/10.1103/PhysRevD.111.103537?utm_source=openai))

Results Summary

The model shows that a transition from pressureless dust to a ground state with constant energy density ρ_G—motivated by the quantum exclusion principle—induces a gravitational bounce at radius R_B = (8πGρ_G/3)⁻¹/², leading to an exponential expansion phase where P(ρ) acts like an inflation potential. Extended cosmologically, it predicts a small but nonzero closed spatial curvature: −0.07 ± 0.02 ≤ Ω_k < 0, with χ_k ≥ χ* ≃ 15.9 Gpc to address the CMB low quadrupole anomaly. The bounce remains within the initial Schwarzschild radius r_S = 2GM, which effectively acts as a cosmological constant Λ inside r_S = √(3/Λ), while externally appearing as a Schwarzschild black hole. ([arxiv.org](https://arxiv.org/abs/2505.23877?utm_source=openai))

Abstract

We investigate the fully relativistic spherical collapse model of a uniform distribution of mass 𝑀 with initial comoving radius 𝜒* and spatial curvature 𝑘 ≡1/𝜒2𝑘 ≤1/𝜒2* representing an overdensity or bounded perturbation within a larger background. Our model incorporates a perfect fluid with an evolving equation of state, 𝑃 =𝑃⁡(𝜌), which asymptotically transitions from pressureless dust (𝑃 =0) to a ground state characterized by a uniform, time-independent energy density 𝜌G. This transition is motivated by the quantum exclusion principle, which prevents singular collapse, as observed in supernova core-collapse explosions. We analytically demonstrate that this transition induces a gravitational bounce at a radius 𝑅B =(8⁢𝜋⁢𝐺⁡𝜌G/3)−1/2. The bounce leads to an exponential expansion phase, where 𝑃⁡(𝜌) behaves effectively as an inflation potential. This model provides novel insights into black hole interiors and, when extended to a cosmological setting, predicts a small but nonzero closed spatial curvature: −0.07 ±0.02 ≤Ω𝑘 <0. This lower bound follows from the requirement of 𝜒𝑘 ≥𝜒* ≃15.9 Gpc to address the cosmic microwave background low quadrupole anomaly. The bounce remains confined within the initial gravitational radius 𝑟S =2⁢𝐺⁡𝑀, which effectively acts as a cosmological constant Λ inside 𝑟S =√3/Λ while still appearing as a Schwarzschild black hole from an external perspective. This framework unifies the origin of inflation and dark energy, with its key observational signature being the presence of small but nonzero spatial curvature, a testable prediction for upcoming cosmological surveys.

Referenced In

StarTalk

Season 17, Episode 3: Are We Living Inside a Black Hole?

Hey StarTalkians! Season 17, Episode 3’s collection of “Cosmic Queries” saw Neil and Chuck tackle a lot of questions about black holes, and this question in particular stood out:

Alcubierre Drives, Antimatter Multiverses & More! | Cosmic Queries #103

Neil’s answer is solid. But lurking underneath that question is something they didn’t address in the episode: why would we be living in a black hole at all? This post takes a brief look at one recent paper making this argument as an example, but there are others .

Black Hole Universe: The Bounce Model

The paper investigated what happens when a cloud of matter collapses in on itself in curved space, taking into account quantum mechanics.

Quantum mechanics matters because of the Pauli Exclusion Principle, which says that no two fermions in the same system can occupy the same quantum state. There are two key parts to this definition:

  • Fermions include electrons, as well as composite particles like protons and neutrons. Basically, it includes all the “regular” matter we’re most familiar with.

  • Quantum states are defined by some key values. For example, in an atom, electrons occupy discrete “energy levels,” denoted by an integer physicists label n. So n = 1 is the lowest energy level. Other quantum numbers relate to magnetic properties and “spin.”

It’s like there are set seats for the particles, and if someone else has seat n = 1, ℓ = 1, m = 0 and s = 1/2, then the next fermion has to sit somewhere else.

So when all of the quantum numbers fill up, this limits how much the matter can be squashed. Some particles have to move to a different “seat.” This creates a kind of pressure that pushes the matter back outwards.

This bounce is what the paper investigates. While from the “outside,” an observer would see a black hole form, on the inside there would be a big bang. This is illustrated in the attached image.

  • The good news: It would explain the initial inflation phase of the universe and dark energy.

  • The bad news: It requires a curved universe, but most evidence says ours is flat.

So do we live in a black hole? Maybe! But probably not.

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