Black Hole Formation Research Articles

Gravitational collapse to extremal black holes and the third law of black hole thermodynamics

We construct examples of black hole formation from regular, one-ended asymptotically flat Cauchy data for the Einstein–Maxwell-charged scalar field system in spherical symmetry which are exactly isometric to extremal Reissner–Nordström after a finite advanced time along the event horizon. Moreover, in each of these examples the apparent horizon of the black hole coincides with that of a Schwarzschild solution at earlier advanced times. In particular, our result can be viewed as a definitive disproof of the “third law of black hole thermodynamics.” The main step in the construction is a novel C^{k} characteristic gluing procedure, which interpolates between a light cone in Minkowski space and a Reissner–Nordström event horizon with specified charge to mass ratio \frac{e}{M} . Our setup is inspired by the recent work of Aretakis–Czimek–Rodnianski on perturbative characteristic gluing for the Einstein vacuum equations. However, our construction is fundamentally nonperturbative and is based on a finite collection of scalar field pulses which are modulated by the Borsuk–Ulam theorem.

Transients by Black Hole Formation from Red Supergiants: Impact of Dense Circumstellar Matter

Abstract Failed supernovae (SNe), which are likely the main channel for forming stellar-mass black holes, are predicted to accompany mass ejections much weaker than typical core-collapse SNe. We conduct a grid of one-dimensional radiation hydrodynamical simulations to explore the emission of failed SNe from red supergiant progenitors, leveraging recent understanding of the weak explosion and the dense circumstellar matter (CSM) surrounding these stars. We find from these simulations and semianalytical modeling that diffusion in the CSM prolongs the early emission powered by shock breakout/cooling. The early emission has peak luminosities of ~107–108 L ⊙ in optical and UV and durations of days to weeks. The presence of dense CSM aids in the detection of the early bright peak from these events via near-future wide-field surveys such as Rubin Observatory, ULTRASAT, and UVEX.

Primordial black holes from effective field theory of stochastic single field inflation at NNNLO

We present a study of the Effective Field Theory (EFT) generalization of stochastic inflation in a model-independent single-field framework and its impact on primordial black hole (PBH) formation. We show how the Langevin equations for the “soft” modes in quasi de Sitter background is described by the Infra-Red (IR) contributions of scalar perturbations, and the subsequent Fokker–Planck equation driving the probability distribution for the stochastic duration N, significantly modify in the present EFT picture. An explicit perturbative analysis of the distribution function by implementing the stochastic-δN formalism is performed up to the next-to-next-to-next-to-leading order (NNNLO) for both the classical-drift and quantum-diffusion dominated regimes. In the drift-dominated limit, we perturbatively analyse the local non-Gaussianity parameters (fNL,gNL,τNL) with the EFT-induced modifications. In the diffusion-dominated limit, we numerically compute the probability distribution featuring exponential tails at each order of perturbative treatment.

The physical nature of the event horizon in the Schwarzschild black hole solution

Abstract This study explores the relationship between the Schwarzschild metric and alternative metrics used to describe the gravitational field of a black hole in free space. While it is well-established that an infinite number of coordinate systems can be employed in general relativity, we demonstrate that the black hole solution is unique when expressed in a physically meaningful (proper) coordinate system. Notably, this coordinate system differs from the Schwarzschild metric due to the distinction between the true physical distance R and the Schwarzschild coordinate distance r. Consequently, the event horizon, commonly associated with the Schwarzschild solution, is shown to be a coordinate artefact of the chosen covariant metric tensor rather than a coordinate-invariant physical feature. As a result, no boundary prevents outgoing photons from escaping the black hole’s vicinity. This finding challenges the mainstream interpretation but remains fully consistent with general relativity. Moreover, it is supported by numerical modelling of light rays near a black hole. By reconsidering the existence of event horizons, this work offers potential resolutions to long-standing issues in black hole formation theories and the emission of electromagnetic and gravitational waves from black holes. Graphical abstract

Star Cluster Population of High Mass Black Hole Mergers in Gravitational Wave Data

Stellar evolution theories predict a gap in the black hole birth mass spectrum as the result of pair instability processes in the cores of massive stars. This gap, however, is not seen in the binary black hole masses inferred from gravitational wave data. One explanation is that black holes form dynamically in dense star clusters where smaller black holes merge to form more massive black holes, populating the mass gap. We show that this model predicts a distribution of the effective and precessing spin parameters, χeff and χp, within the mass gap that is insensitive to assumptions about black hole natal spins and other astrophysical parameters. We analyze the distribution of χeff as a function of primary mass for the black hole binaries in the third gravitational wave transient catalog. We infer the presence of a high mass and isotropically spinning population of black holes that is consistent with hierarchical formation in dense star clusters and a pair-instability mass gap with a lower edge at 44−4+6M⊙. We compute a Bayes factor B>104 relative to models that do not allow for a high mass population with a distinct χeff distribution. Upcoming data will enable us to tightly constrain the hierarchical formation hypothesis and refine our understanding of binary black hole formation. Published by the American Physical Society 2025

Primordial black holes in SB SUSY Gauss-Bonnet inflation

Here, we explore the formation of primordial black holes (PBHs) within a scalar field inflationary model coupled to the Gauss-Bonnet (GB) term, incorporating the low-scale spontaneously broken supersymmetric (SB SUSY) potential.The coupling function amplifies the curvature perturbations, consequently leading to the formation of PBHs and detectable secondary gravitational waves (GWs).Through the adjustment of the model parameters, the inflaton can be decelerated during an ultra-slow-roll (USR) phase, thereby augmenting curvature perturbations. Beside the observational constraints, the swampland criteria are investigated.Our computations forecast the formation of PBHs with masses around 𝒪(10)M ⊙, aligning with the observational data of LIGO-Virgo, and PBHs with masses 𝒪(10-6)M ⊙ as potential explanation for the ultrashort-timescale microlensing events recorded in the OGLE data.Additionally, our proposed mechanism can generate PBHs with masses around 𝒪(10-13)M ⊙, constituting roughly 99% of the dark matter.The density parameters of the produced GWs (ΩGW 0) intersect with the sensitivity curves of GW detectors. Two cases of our model fall within the nano-Hz frequency regime. One of them satisfies the power-law scaling as ΩGW(f) ∼ f 5-γ, with the γ = 3.51, which is consistent with the data of NANOGrav 15-year.

Early formation of supermassive black holes from the collapse of strongly self-interacting dark matter

Evidence for high-redshift supermassive black holes challenges standard scenarios for how such objects form in the early universe. Here, we entertain the possibility that a fraction of the cosmological dark matter could be ultra-strongly self interacting. This would imply that gravothermal collapse occur at early times in the cores of dark matter halos, followed by accretion. We study under which conditions on the abundance and interaction strength and structure of such ultra self-interacting dark matter the black holes resulting from the end-point of gravothermal core collapse can seed the observed, early-forming supermassive black holes. We find, depending on the velocity dependence of the self-interaction cross section, a bimodal structure in the favored parameter space, where data points to either a small collapsing dark matter fraction with a large cross section, or a large fraction and a relatively small cross section. While self-interaction cross sections with different velocity dependence can explain observations, we find that the best, self-consistent results correspond to a Rutherford-like self-interaction, typical of long-range dark-sector forces with light mediators. We discuss complementary observational probes if this scenario is realized in nature, focusing especially on the expected intermediate mass black holes predicted to exist in smaller galaxies.

Primordial naked singularities

Primordial black hole formation has been discussed widely, when density perturbations in the early universe cause matter to collapse gravitationally, giving rise to these ultra-compact objects. We propose and point out that such a gravitational collapse would also give rise to primordial naked singularities, that would play an important role in the observable features of present universe. We consider two types of collapse scenarios that give rise to event-like and object-like visible singularities within a cosmological background. We briefly discuss implications of primordial naked singularities, including those for dark matter, vis-a-vis primordial black holes.

Primordial black hole formation in a dust bouncing model

Linear scalar cosmological perturbations have increasing spectra in the contracting phase of bouncing models. We study the conditions for which these perturbations may collapse into primordial black holes and the hypothesis that these objects constitute a fraction of dark matter. We compute the critical density contrast that describes the collapse of matter perturbations in the flat-dust bounce model with a parametric solution, obtained from the Lemaitre-Tolman-Bondi metric that represents the spherical collapse. We discuss the inability of the Newtonian gauge to describe perturbations in contracting models as the perturbative hypothesis does not hold in such cases. We carry the calculations for a different Gauge choice and compute the perturbations' power spectra numerically. Finally, assuming a Gaussian distribution, we compute the primordial black hole abundance with the Press-Schechter formalism and compare it with observational constraints. From our analysis, we conclude that the primordial black hole formation in a dust-dominated contracting phase does not lead to a significant mass fraction of primordial black holes in dark matter today.

Ultra slow-roll with a black hole

We investigate ultra slow-roll inflation with a seed black hole in a de Sitter background. By numerically tracking transitions from slow-roll to ultra slow-roll inflation, we find that quasi-normal mode solutions of the scalar field are excited following the decay of the slow-roll attractor, depending on the mass of the black hole. For small black holes, the picture is similar to standard inflation with the usual damping of the scalar field; with a large black hole, we find that the ringing modes dominate. It is believed that the transition to ultra slow-roll in the pure inflationary case enhances the peak of the primordial power spectrum, thereby increasing the likelihood of primordial black hole formation. We comment on how the novel ringing behaviour due to the seed black hole might impact on cosmological perturbations.

Threshold Mass of the General-relativistic Instability for Supermassive Star Cores

Abstract The dependence of the final fate of supermassive star (SMS) cores on their mass and angular momentum is studied with simple modeling. SMS cores in the hydrogen-burning phase encounter the general-relativistic instability during stellar evolution if the mass is larger than ∼3 × 104 M ⊙. Spherical SMS cores in the helium-burning phase encounter the general-relativistic instability prior to the onset of the electron–positron pair instability if the mass is larger than ∼1 × 104 M ⊙. For rapidly rotating SMS cores, these values for the threshold mass are enhanced by up to a factor of ∼5, and thus, for SMSs with mass smaller than ∼104 M ⊙, the collapse is triggered by the pair instability, irrespective of the rotation. After the onset of the general-relativistic instability, SMS cores in the hydrogen-burning phase with reasonable metallicity are likely to collapse to a black hole irrespective of the degree of rotation, whereas SMS cores in the helium-burning phase could explode via nuclear burning with no black hole formation, as previous works demonstrate.

Transient electromagnetic sources can detect solitary black holes in Milky Way galaxy

Abstract The Milky Way galaxy is estimated to host up to a billion stellar-mass solitary black holes (BHs). The number and distribution of BH masses can provide crucial information about the processes involved in BH formation, the existence of primordial BHs, and the interpretation of gravitational wave (GW) signals detected in LIGO-VIRGO-KAGRA. Sahu et al. recently confirmed one solitary stellar-mass BH in our galaxy using astrometric microlensing. This work proposes a novel mechanism to identify such BH by analyzing the frequency and damping of the quasi-normal modes of GW generated from the interaction of the BH and EM wave originating from a transient electromagnetic (TEM) source. The incoming EM waves distort the curvature of a BH, releasing GWs as it returns to a steady state. Using the covariant semi-tetrad formalism, we quantify the generated GWs via the Regge-Wheeler tensor and relate the GW amplitude to the energy of the TEM. We demonstrate that isolated BHs at a distance of 50 pc from Earth can be detected by LIGO A+ and 100 pc by Cosmic Explorer/Einstein Telescope. Additionally, we discuss the observational implications for orphan afterglows associated with GRBs, highlighting the potential for further discoveries.

A blazar in the epoch of reionization

AbstractRelativistic jets are thought to play a crucial role in the formation and evolution of massive galaxies and supermassive black holes. Blazars, which are quasars with jets aligned along our line of sight, provide insights into the jetted population and have been observed up to redshifts of z = 6.1. Here, we report the discovery and multi-wavelength characterization of the blazar VLASS J041009.05−013919.88 at z = 7 (age of the Universe ~750 Myr), which is powered by a ~7 × 108 M⊙ black hole. The presence of this high-redshift blazar implies a large population of similar but unaligned jetted sources in the early Universe. Our findings suggest two possible scenarios. In one, the jet in J0410−0139 is intrinsically low power but appears highly luminous due to relativistic beaming, suggesting that most ultraviolet-bright quasars at this redshift host jets. Alternatively, if J0410−0139 represents an intrinsically powerful radio source, there should be hundreds to thousands of radio-quiet quasars at z ≈ 7 with properties like those of J0410−0139, a prediction in tension with observed quasar densities based on their ultraviolet luminosity function. These results support the hypothesis that the rapid growth of black holes in the early Universe may be driven by jet-enhanced or obscured super-Eddington accretion, potentially playing a key role in forming massive black holes during the epoch of reionization.

Gravitational waves and primordial black holes from axion domain walls in level crossing

Abstract In this paper, we investigate the nano-Hertz gravitational waves (GWs) emission and the massive primordial black holes (PBHs) formation from the light QCD axion scenario.
We consider the axion domain walls formation from the level crossing induced by the mass mixing between the light $Z_{\mathcal N}$ QCD axion and axion-like particle.
A general mixing case is considered that the heavy and light mass eigenvalues do not necessarily have to coincide with the axion masses.
In order to form the domain walls, the axions should start to oscillate slightly before the level crossing.
The domain walls must annihilate before dominating the Universe to avoid the cosmological catastrophe.
Then we focus our attention on the GWs emission from the domain walls annihilation and the PBHs formation from the domain walls collapse.
We show the predicted GWs spectra with the peak frequency $\sim 0.2\, \rm nHz$ and the peak amplitude $\sim 5\times 10^{-9}$, which can be tested by the future pulsar timing array projects.
In addition, during the domain walls annihilation, the closed walls could shrink to the Schwarzschild radius and collapse into the PBHs.
We find that the PBHs in the mass range of $\mathcal{O}(10^5-10^8) M_\odot$ could potentially form in this scenario and account for a small fraction $\sim 10^{-5}$ of the cold dark matter.Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Article funded by SCOAP3 and published under licence by Chinese Physical Society and the Institute of High Energy Physics of the Chinese Academy of Science and the Institute of Modern Physics of the Chinese Academy of Sciences and IOP Publishing Ltd.

Two-Loop Corrections in Power Spectrum in Models of Inflation with Primordial Black Hole Formation

Two-Loop Corrections in Power Spectrum in Models of Inflation with Primordial Black Hole Formation

Building a Semi-analytic Black Hole Seeding Model using IllustrisTNG Host Galaxies

ABSTRACT A major open question in astrophysics is the mechanisms by which massive black holes (BHs) form in the early Universe, which pose constraints on seeding models. We study BH formation and evolution in a flexible model combining the cosmological IllustrisTNG (TNG) simulations with semi-analytic modelling in post-processing. We identify our TNG model hosts based on various criteria including a minimum gas mass of $10^7$–$10^9$${\rm M}_{\odot }$, total host mass of $10^{8.5}$–$10^{10.5}$${\rm M}_{\odot }$, and a maximum gas metallicity of 0.01–0.1 $\mathrm{Z}_{\odot }$. Each potential host is assigned a BH seed with a probability of 0.01–1. The populations follow the TNG galaxy merger tree. This approach improves upon the predictive power of the simple TNG BH seeding prescription, narrowing down plausible seeding parameter spaces, and it is readily adaptable to other cosmological simulations. Several model realizations predict $z\lesssim 4$ BH mass densities that are consistent with empirical data as well as the TNG BHs. However, high-redshift BH number densities can differ by factors of $\sim$ 10 to $\gtrsim$ 100 between seeding parameters. In most model realizations, $\lesssim 10^5$${\rm M}_{\odot }$ BHs substantially outnumber heavier BHs at high redshifts. Mergers between such BHs are prime targets for gravitational-wave detection with Laser Interferometer Space Antenna. The $z=0$ BH mass densities in most realizations of the model agree well with observations, but our strictest seeding criteria fail at high redshift. Our findings strongly motivate the need for better empirical constraints on high-z BHs, and they underscore the significance of recent active galactic nucleus discoveries with JWST.

Reanalysis of the MACHO Constraints on PBH in the Light of Gaia DR3 Data

The recent astrometric data of hundreds of millions of stars from Gaia DR3 has allowed for a precise determination of the Milky Way rotation curve up to 28 kpc. The data suggest a rapid decline in the density of dark matter beyond 19 kpc. We fit the whole rotation curve with four components (gas, disk, bulge, and halo), and compute the microlensing optical depth to the Large Magellanic Cloud. With this model of the galaxy we reanalyse the microlensing events of the MACHO and EROS-2 Collaborations. Using the published MACHO efficiency function for the duration of their survey, together with the rate of expected events according to the new density profile, we find that the Dark Matter halo could be composed of up to 20% of massive compact halo objects for any mass between 0.001 to 1M⊙. For the EROS-2 survey, using a modified efficiency curve for consistency with the MACHO analysis, we also find compatibility with a MACHO halo, but with a tighter constraint around 0.005M⊙ where the halo fraction cannot be larger than ∼10%. This result assumes that all the lenses have the same mass. If these were distributed in an extended mass function like that of the Thermal History Model, the constraints are weakened, allowing 100% of all DM in the form of Primordial Black Holes.

Addendum: Variable brane tension and dark energy

Original article: EPL, 145 (2024) 39001.

Length-preserving biconnection gravity and its cosmological implications

We consider a length preserving biconnection gravitational theory, inspired by information geometry, which extends general relativity, by using the mutual curvature as the fundamental object describing gravity. The two connections used to build up the theory are the Schrödinger connection, and its dual. In our geometric approach it can be seen that the dual of a non-metric Schrödinger connection possesses torsion, even if the Schrödinger connection itself does not, and consequently the pair (M,g,∇*) is a quasi-statistical manifold. The field equations are postulated to have the form of the standard Einstein equations, but with the Ricci tensor- and scalar replaced with the mutual curvature tensor, and the mutual curvature scalar, resulting in additional torsion-dependent terms. The covariant divergence of the matter energy-momentum does not vanish in this theory. We derive the equation of motion for massive particles, which shows the presence of an extra force, depending on the torsion vector. The Newtonian limit of the equations of motion is also considered. We explore the cosmological implications by deriving the generalized Friedmann equations for the Friedmann-Lemaitre-Robertson-Walker (FLRW geometry). They contain additional terms that can be interpreted as describing an effective, geometric type dark energy. We examine two cosmological models: one with conserved matter, and one where dark energy and pressure are related by a linear equation of state. The predictions of both models are compared with a set of observational values of the Hubble function, and with the standard ΛCDM model. Length-preserving biconnection gravity models fit well the observational data, and also align with ΛCDM at low redshifts (z < 3). The obtained results suggest that a modified biconnection geometry could explain the late-time acceleration through an effective geometric dark energy, as well as the formation of the supermassive black holes, as they predict a different age of our Universe as compared to standard cosmology.

Kicking Time Back in Black Hole Mergers: Ancestral Masses, Spins, Birth Recoils, and Hierarchical-formation Viability of GW190521

A pair-instability supernova (PISN) prevents black hole (BH) formation from stellar collapse within the approximate mass range M ∈ [65, 130] M ⊙. However, such BHs may form hierarchically through merging ancestral BHs, whose properties determine those of the “child” one: mass, spin, and recoil velocity. Crucially, the child will leave its host environment if its birth recoil exceeds the corresponding escape velocity, preventing further mergers. We exploit relations between the final recoil and spin of quasi-circular BH mergers to obtain posterior probability distributions for the hypothetical ancestral masses, spins, and birth recoils of the component BHs of GW190521. To this, we present a Bayesian framework applicable to existing estimates for the components of BH merger observations. We consider both the quasi-circular (generically spinning) analysis performed by the LIGO–Virgo–KAGRA collaboration and the eccentric (aligned-spin) one performed by Romero-Shaw et al. We evaluate the probability p 2g that the GW190521 components inferred by these analyses formed from the merger of stellar-origin BHs and were retained by their environment. For the primary component, which populates the PISN gap, such scenario is strongly suppressed if GW190521 happened in a globular cluster with p 2g ∼ 10−3 unless it was quasi circular and its ancestors had aligned spins, uncharacteristic of hierarchical formation channels, or small spins, which yields p 2g ≃ 10−2. If GW190521 was eccentric, we obtain p 2g ≃ 0.1 for any host other than an active galactic nucleus, and zero for a globular cluster. If GW190521 was quasi circular, a nuclear star cluster origin is possible with p 2g ∈ (∼0.4, ∼0.8).