Core Concepts

Non-singular black holes embedded in an expanding universe exhibit a distinct cosmological coupling, characterized by a time-dependent apparent horizon that grows with redshift and is always larger than the event horizon of an isolated black hole.

Abstract

This research paper investigates the cosmological implications of embedding non-singular black holes within an expanding universe. The authors challenge the traditional notion of a static event horizon for black holes in a cosmological context, proposing instead the presence of a dynamic apparent horizon.

**Bibliographic Information:** M. Cadoni, M. Pitzalis, and A. P. Sanna, "Apparent horizons in cosmologically-embedded black holes," arXiv:2410.10459v1 (2024).

**Research Objective:** To derive explicit solutions for cosmologically-embedded non-singular black holes and analyze the evolution of their apparent horizons in relation to cosmological redshift and mass coupling.

**Methodology:** The authors employ Einstein's field equations within the framework of General Relativity, considering anisotropic fluid sources to construct exact solutions for cosmologically-embedded black holes. They focus on a class of non-singular black hole models characterized by a de Sitter core and asymptotic Schwarzschild behavior, including the Hayward and Fan & Wang models.

**Key Findings:**

- The study demonstrates that these non-singular black holes, when embedded in a cosmological background, exhibit a time-dependent apparent horizon.
- The size of the apparent horizon exceeds that of the event horizon of an isolated black hole and increases monotonically with increasing redshift.
- The authors identify a threshold redshift beyond which the apparent horizon cannot form, suggesting distinct behavior for astrophysical and primordial black holes.

**Main Conclusions:**

- The existence of an apparent horizon in cosmologically-embedded black holes is a robust feature, potentially serving as a proxy for cosmological mass coupling.
- The study highlights the distinct dynamical roles of event and apparent horizons in a cosmological context, emphasizing the limitations of applying the concept of a static event horizon to black holes embedded in an expanding universe.

**Significance:** This research provides valuable insights into the interplay between black hole physics and cosmology, particularly in the context of non-singular black hole models. The findings have implications for understanding the evolution of black holes in an expanding universe and the potential observational signatures of cosmological coupling.

**Limitations and Future Research:** The study primarily focuses on a specific class of non-singular black hole models. Further research could explore the generality of these findings for other black hole solutions and investigate the potential observational consequences of the evolving apparent horizon.

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from source content

arxiv.org

Stats

The authors use a test mass of M = 10^6 M⊙, corresponding to a typical supermassive black hole.
They adopt a Hubble constant of H0 = 67.7 km · s−1 · Mpc−1.
Two cosmological scenarios are considered: a dust-dominated universe with Ω= Ω0 ≃0.3 and w = 0, and a cosmological-constant-dominated universe with Ω= ΩΛ0 ≃0.7 and w = −1.

Quotes

"The possibility of a dynamical coupling between local astrophysical objects, such as black holes, and the large-scale cosmological dynamics within the framework of General Relativity (GR) is an old issue."
"A recent study [58], approaching the issue from a different perspective, argues that the cosmological coupling of black holes is unavoidable."
"While the findings of Ref. [58] strongly support cosmological coupling for black holes, they also raise several new questions."

Key Insights Distilled From

by Mariano Cado... at **arxiv.org** 10-15-2024

Deeper Inquiries

The presence of an evolving apparent horizon (AH) in cosmologically-embedded black holes could significantly influence the dynamics of accretion disks and the emission of gravitational waves in several ways:
Accretion Disk Dynamics:
Modified Inner Edge: The evolving AH, being typically larger than the event horizon (EH), would push the inner edge of the accretion disk outwards. This is because the AH, being a null surface, dictates the innermost stable circular orbit (ISCO) for accreting matter.
Variable Accretion Rate: The changing size of the AH with redshift would lead to a time-dependent gravitational potential, affecting the accretion rate of matter onto the black hole. This could result in observable variations in luminosity and spectral features of the accretion disk.
Jet Formation: The interplay between the evolving AH and the black hole's spin could influence the mechanisms of jet formation and collimation, potentially leading to observable differences in jet morphology and power.
Gravitational Wave Emission:
Modified Ringdown Signal: The ringdown phase of a black hole merger, characterized by the emission of characteristic gravitational waves, would be modified by the presence of an evolving AH. This is because the AH influences the quasi-normal modes of the black hole, which determine the frequencies and damping times of the emitted gravitational waves.
Cosmological Evolution of Waveforms: The redshifting of gravitational waves as they travel through the expanding universe would be further affected by the evolving AH of the black hole. This could lead to subtle but potentially detectable changes in the observed waveforms, providing information about both the black hole and the cosmological expansion.
Observational Signatures:
Observing these effects could be challenging but potentially rewarding:
Time-domain astronomy could reveal variations in the luminosity and spectral properties of active galactic nuclei (AGN), potentially correlated with the redshift of the host galaxy.
Gravitational wave astronomy, with future detectors, might be able to discern the subtle modifications in ringdown signals and cosmological evolution of waveforms, offering a new probe of black hole physics and cosmology.

Yes, the absence of an apparent horizon (AH) for black holes forming at redshifts exceeding a certain threshold (zM) could have significant implications for the existence and detectability of primordial black holes (PBHs):
Existence: The absence of an AH suggests that black holes forming at zi > zM might not be able to maintain an event horizon (EH) in the early universe. This could imply that PBHs forming at very high redshifts might not exist as stable objects, potentially constraining models of PBH formation.
Detectability: Even if PBHs forming at zi > zM could exist, the lack of an AH during their early evolution would significantly impact their observational signatures. For instance, the absence of an AH would affect their accretion properties and the lensing of background radiation, potentially making them harder to detect through traditional methods.
Implications for PBH Scenarios:
Constraints on Formation Models: The existence of a redshift threshold zM for AH formation could impose constraints on models of PBH formation. If observations rule out the existence of black holes with specific masses forming at certain redshifts, corresponding PBH formation scenarios could be constrained or ruled out.
Alternative Search Strategies: The potential absence of an AH for early PBHs necessitates exploring alternative search strategies beyond traditional methods relying on accretion or lensing signatures. These could include searching for their potential impact on the cosmic microwave background (CMB) or their contribution to the dark matter content of the universe.

Yes, the concept of an apparent horizon (AH) can be extended to define a cosmological horizon for the observable universe when considering the universe as a dynamical system.
Here's how the analogy works:
Black Hole AH: In a black hole spacetime, the AH represents the boundary beyond which null geodesics are trapped and cannot escape to future null infinity. It's a local concept, dependent on the spacetime geometry at a given time.
Cosmological Horizon: In an expanding universe, like our own, a cosmological horizon can be defined as the boundary beyond which events are causally disconnected from us. This is because the expansion of space can "outpace" the speed of light, making it impossible for signals from beyond this boundary to ever reach us.
Extending the AH Concept:
Just as the AH in a black hole is defined by the convergence of outgoing null geodesics, a cosmological horizon can be defined by the convergence of past-directed null geodesics. This horizon represents the furthest distance from which light emitted in the past could have traveled to reach us today.
Dynamical Nature:
Both the AH of a black hole and the cosmological horizon are dynamical entities. The AH of a black hole can grow or shrink depending on the infalling matter and energy. Similarly, the cosmological horizon in an expanding universe also changes with time, generally growing as the universe expands.
Observational Implications:
The concept of a cosmological horizon has profound implications for our understanding of the universe:
Observable Universe: It defines the limit of our observable universe, beyond which we cannot receive any information.
Cosmic Microwave Background: The cosmic microwave background (CMB) originates from the surface of last scattering, which can be considered as a type of cosmological horizon at the time of recombination.
Future Evolution: The future evolution of the cosmological horizon depends on the nature of dark energy and the ultimate fate of the universe.
In conclusion, while the concept of an AH is typically applied to black holes, it can be extended to define a cosmological horizon for the observable universe. This horizon, like its black hole counterpart, is a dynamical entity that reflects the evolving nature of the universe as a whole.

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