Gravitational Condensation Research Articles

Axion star condensation around primordial black holes and microlensing limits

We present novel findings concerning the parameter space of axion stars, extended object forming in dense dark matter environments through gravitational condensation. We emphasize their formation within the dense minihalos that potentially surround primordial black holes and in axion miniclusters. Our study investigates the relation between the radius and mass of an axion star in these dense surroundings, revealing distinct morphological characteristics compared to isolated scenarios. We explore the implications of these results when applied to the bound state between a primordial black hole and an axion star and the gravitational microlensing from extended objects, leading to insights on the observational constraints from such “halo” axion stars. We provide a constraint on the fraction of the galactic population of axion stars from their contribution to the microlensing events from the EROS-2 survey, using the numerical resolution of the Schrödinger-Poisson equation.

Nested solutions of gravitational condensate stars

Black holes are normally and naturally associated to the end-point of gravitational collapse. Yet, alternatives have been proposed and a particularly interesting one is that of gravitational condensate stars, or gravastars. We here revisit the gravastar model and increase the degree of speculation by considering new solutions that are inspired by the original model of gravastars with anisotropic pressure, but also offer surprising new features. In particular, we show that it is possible to nest two gravastars into each other and obtain a new solution of the Einstein equations. Since each gravastar essentially behaves as a distinct self-gravitating equilibrium, a large and rich space of parameters exists for the construction of nested gravastars. In addition, we show that these nested-gravastar solutions can be extended to an arbitrarily large number of shells, with a prescription specified in terms of simple recursive relations. Although these ultra-compact objects are admittedly very exotic, some of the solutions found, provide an interesting alternative to a black hole by having a singularity-free origin, a full matter interior, a time-like matter surface, and a compactness C→(1/2)− .

Can gravitational vacuum condensate stars be a dark energy source?

Gravitational vacuum condensate stars, also known as gravastars, have been proposed as an alternative to black holes. Their interior contains a perfect fluid with an equation of state akin to that of a cosmological constant. For this reason, they have recently been considered as a possible astrophysical source of dark energy. In this work we argue that gravitational vacuum condensate stars cannot be the source of dark energy and highlight that a direct coupling of their mass to the dynamics of the Universe would lead to an additional velocity dependent acceleration, damping their motion with respect to the cosmological frame. We briefly discuss the potential impact of this additional acceleration in the context of a recent proposal that the observed mass growth of compact objects at the core of elliptical galaxies might result from such a cosmological coupling.

From quantum foam to graviton condensation: The Zel'dovich route

Based on a previous ansatz by Zel'dovich for the gravitational energy of virtual particle-antiparticle pairs, supplemented with the holographic principle, we estimate the vacuum energy in a fairly reasonable agreement with the experimental values of the cosmological constant. We further highlight a connection between Wheeler's quantum foam and graviton condensation, as contemplated in the quantum N-portrait paradigm, and show that such connection also leads to a satisfactory prediction of the value of the cosmological constant. The above results suggest that the “unnaturally” small value of the cosmological constant may find a quite “natural” explanation once the nonlocal perspective of the large N-portrait gravitational condensation is endorsed.

Thin-shell gravastar model in f(Q, T) gravity* *SP & PKS acknowledges the National Board for Higher Mathematics (NBHM) under the Department of Atomic Energy (DAE), Govt. of India for financial support to carry out the Research project No.: 02011/3/2022 NBHM(R.P.)/R & D II/2152 Dt.14.02.2022. PKS thanks Transilvania University of Brasov for Transilvania Fellowship for Visiting Professors

In the last few decades, gravastars have been proposed as an alternative to black holes. The stability of a gravastar has been examined in many modified theories of gravity along with Einstein's GR. The gravity, a successfully modified theory of gravity for describing the current accelerated expansion of the universe, has been used in this study to examine gravastar in different aspects. According to Mazur and Mottola [Proc. Natl. Acad. Sci. 101, 9545 (2004); Gravitational condensate stars: An alternative to black holes, I12-011, (2002)], a gravastar has three regions with three different equations of state. In this study, we examined the interior of a gravastar by considering EoS to describe the dark sector for the interior region. The next region is a thin shell of ultrarelativistic stiff fluid, in which we investigated several physical properties, including proper length, energy, entropy, and surface energy density. Additionally, we examined the surface redshift and speed of sound to check the potential stability of our proposed thin-shell gravastar model. Furthermore, we used the entropy maximization technique to verify the stability of the gravastar model. A gravastar's outer region is a complete vacuum described by exterior Schwarzschild geometry. Finally, we presented a stable gravastar model, which is singularity-free and devoid of any incompleteness in classical black hole theory.

Gravitational Condensate Stars: An Alternative to Black Holes

A new final endpoint of complete gravitational collapse is proposed. By extending the concept of Bose–Einstein condensation to gravitational systems, a static, spherically symmetric solution to Einstein’s equations is obtained, characterized by an interior de Sitter region of p=−ρ gravitational vacuum condensate and an exterior Schwarzschild geometry of arbitrary total mass M. These are separated by a phase boundary with a small but finite thickness ℓ, replacing both the Schwarzschild and de Sitter classical horizons. The resulting collapsed cold, compact object has no singularities, no event horizons, and a globally defined Killing time. Its entropy is maximized under small fluctuations and is given by the standard hydrodynamic entropy of the thin shell, which is of order kBℓMc/ℏ, instead of the Bekenstein–Hawking entropy, SBH=4πkBGM2/ℏc. Unlike BHs, a collapsed star of this kind is consistent with quantum theory, thermodynamically stable, and suffers from no information paradox.

Probability of Obtaining the Planck Constant, in a Universe Modeled as a Giant Black Hole by Bose Einstein Condensates of Gravitons Using Hawking Argument and Scaling

We use the methodology of A. D. Linde to model the probability of obtaining a cosmological constant which is in turn affected by scaling arguments for a Bose Einstein gravitational condensate as given by Chavanis, in 2015. The net result, is that the scaling argument so provided allows for a gravitational constant commensurate with the size of the Universe, using arguments which appear to be simple but which give, if one has the conditions for modeling the Universe as a “black hole” virtually 100 % chance for the cosmological constant arising.

The effective theory of gravity and dynamical vacuum energy

Gravity and general relativity are considered as an Effective Field Theory (EFT) at low energies and macroscopic distances. The effective action of the conformal anomaly of light or massless quantum fields has significant effects on macroscopic scales, due to associated light cone singularities that are not captured by an expansion in local curvature invariants. A compact local form for the Wess-Zumino effective action of the conformal anomaly and stress tensor is given, requiring the introduction of a new light scalar field, which it is argued should be included in the low energy effective action for gravity. This scalar conformalon couples to the conformal part of the spacetime metric and allows the effective value of the vacuum energy, described as a condensate of an exact 4-form abelian gauge field strength F = dA, to change in space and time. This is achieved by the identification of the torsion dependent part of the Chern-Simons 3-form of the Euler class with the gauge potential A, which enters the effective action of the conformal anomaly as a J · A interaction analogous to electromagnetism. The conserved 3-current J describes the worldtube of 2-surfaces that separate regions of differing vacuum energy. The resulting EFT thus replaces the fixed constant Λ of classical gravity, and its apparently unnaturally large sensitivity to UV physics, with a dynamical condensate whose ground state value in empty flat space is Λeff = 0 identically. By allowing Λeff to vary rapidly near the 2-surface of a black hole horizon, the proposed EFT of dynamical vacuum energy provides an effective Lagrangian framework for gravitational condensate stars, as the final state of complete gravitational collapse consistent with quantum theory. The possible consequences of dynamical vacuum dark energy for cosmology, the cosmic coincidence problem, and the role of conformal invariance for other fine tuning issues in the Standard Model are discussed.

The generalized nonlinear Schrödinger-like equation of cosmogonical body forming: Justification and determination of its particular solutions

This work justifies the generalized Schrödinger-like equation with logarithmic nonlinearity in the statistical theory of cosmogonical body formation. Within the framework of this theory, the models and evolution equations of the statistical mechanics have been proposed, while well-known problems of gravitational condensation of infinite distributed cosmic substances have been solved on the basis of the proposed statistical model of spheroidal bodies. Equation relative to the complete time-derivative of the common (hydrodynamic plus anti-diffusion) velocity is obtained. Taking into account equations obtained the generalized nonlinear time-dependent Schrödinger-like equation of cosmogonical body formation is derived. This paper investigates different particular forms of the generalized nonlinear time-dependent Schrödinger-like equation corresponding to the respective dynamical states of a forming spheroidal body. The cubic nonlinear time-dependent Schrödinger equation describing cosmogonical body formation in the state of nonlinear wave disturbances is derived. The soliton solution of the one-dimensional cubic nonlinear Schrödinger equation is obtained her e. This paper considers the determination of nonlinear wave solutions from the point of view of the inverse scattering problem method as well as the modified (G/G′)-expansion method.

Slowly rotating gravastars

We solve Einstein's equations for slowly rotating gravitational condensate stars (gravastars) up to second order in the rotation by expanding about the spherically symmetric gravastar with de Sitter interior and Schwarzschild exterior matched at their common horizon. Requiring that the perturbations are finite on the null surface reduces the exterior geometry to that of a Kerr black hole, implying that a slowly rotating gravastar cannot be distinguished from a Kerr black hole by any measurement or observation restricted to the macroscopic spacetime exterior to the horizon. We determine the interior solution, the surface stress tensor, and the Komar mass and angular momentum localized on the slowly rotating horizon surface. With the interior equation of state fixed at $p=\ensuremath{-}\ensuremath{\rho}$, finite junction conditions on the null horizon surface necessarily lead to an interior solution with a singular core, where the perturbative expansion breaks down. Comparison to other models and implications for more rapidly rotating gravastars are briefly discussed.

On the Analytical Models of Protoplanetary Formation in Extrasolar Systems

In this work, we consider a statistical theory for a cosmogonical body formation (so-called spheroidal body) to develop the analytical models of protoplanetary formation in extrasolar systems. Within the framework of this theory, the models and evolution equations of the statistical mechanics have been proposed, while the well-known problem of gravitational condensation of infinite distributed cosmic substances has been solved. This paper derives the general equation of distribution of the specific angular momentum of forming protoplanets since the specific angular momentums (for particles or planetesimals) are averaged during a conglomeration process (under a planetary embryo formation). As a result, a new law for planetary distances (which generalizes Schmidt’s law) is derived theoretically. This paper develops also an alternative thermal emission of particles model of the formation of protoplanets in extrasolar systems. Within the framework of this model, the equation for the thermal distribution function of the specific angular momentums of particles moving in elliptical orbits in the gravitational field is derived. According to this thermal escape model, only 0.8% of the total number of particles in the solar system composing the protoplanetary cloud has angular momentum 15.6 times higher than the angular momentum of the remaining 99% of particles. This conclusion agrees completely with the known fact of a nonuniform distribution of the angular momentums in our solar system noted by ter Haar. As pointed out here, the exponential laws of planetary distances occur in some extrasolar systems.

Can QCD axion stars explain Subaru HSC microlensing?

A non-negligible fraction of the QCD axion dark matter may form gravitationally bound Bose Einstein condensates, which are commonly known as axion stars or axion clumps. Such astrophysical objects have been recently proposed as the cause for the single candidate event reported by Subaru Hyper Suprime-Cam (HSC) microlensing search in the Andromeda galaxy. Depending on the breaking scale of the Peccei-Quinn symmetry and the details of the dark matter scenario, QCD axion clumps may form via gravitational condensation during radiation domination, in the dense core of axion miniclusters, or within axion minihalos around primordial black holes. We analyze all these scenarios and conclude that the microlensing candidate detected by the Subaru HSC survey is likely not caused by QCD axion stars.

New insights into the formation and growth of boson stars in dark matter halos

This work studies the formation and growth of boson stars and their surrounding miniclusters by gravitational condensation using non-linear dynamical numerical methods. Fully dynamical attractive and repulsive self-interactions are also considered for the first time. In the case of pure gravity, we numerically prove that the growth of boson stars inside halos slows down and saturates as has been previously conjectured, and detail its conditions. Self-interactions are included using the Gross-Pitaevskii-Poisson equations. We find that in the case of strong attractive self-interactions the boson stars can become unstable and collapse, in agreement with previous stationary computations. At even stronger coupling, the condensate fragments. Repulsive self-interactions, as expected, promote boson star formation, and lead to solutions with larger radii.

Influence of ionization and ion loss on radiative and gravitational instabilities of inhomogeneous plasma with dust polarization force

In the present work, the radiative condensation and gravitational instabilities of inhomogeneous self-gravitating partially ionized dusty plasma have been studied with dust polarization force, ionization and recombination. The basic equations are constructed using four fluid model. The full dynamics of charged dust grains, ions and neutral species are employed considering the electrons as inertialess which have finite thermal conductivity and radiative cooling. The general dispersion relation is derived and discussed for different dusty plasma situations. It is found that the instability conditions are greatly affected due to the polarization force and recombination. Specifically, it is pointed out that the polarization force enhances the growth rate of both the radiative and gravitational instability while the recombination frequency decreases it. Both the parameters have influencing role in short wavelength regime. The e-folding times are calculated for maximum growth rates of gravitational and radiative condensation instabilities. The present work is applicable for study of interstellar molecular clouds and therefore the corresponding free fall time of molecular clouds is also presented.

String-Inspired Running Vacuum—The “Vacuumon”—And the Swampland Criteria

We elaborate further on the compatibility of the “vacuumon potential” that characterises the inflationary phase of the running vacuum model (RVM) with the swampland criteria. The work is motivated by the fact that, as demonstrated recently by the authors, the RVM framework can be derived as an effective gravitational field theory stemming from underlying microscopic (critical) string theory models with gravitational anomalies, involving condensation of primordial gravitational waves. Although believed to be a classical scalar field description, not representing a fully fledged quantum field, we show here that the vacuumon potential satisfies certain swampland criteria for the relevant regime of parameters and field range. We link the criteria to the Gibbons–Hawking entropy that has been argued to characterise the RVM during the de Sitter phase. These results imply that the vacuumon may, after all, admit under certain conditions, a rôle as a quantum field during the inflationary (almost de Sitter) phase of the running vacuum. The conventional slow-roll interpretation of this field, however, fails just because it satisfies the swampland criteria. The RVM effective theory derived from the low-energy effective action of string theory does, however, successfully describe inflation thanks to the ∼H4 terms induced by the gravitational anomalous condensates. In addition, the stringy version of the RVM involves the Kalb–Ramond (KR) axion field, which, in contrast to the vacuumon, does perfectly satisfy the slow-roll condition. We conclude that the vacuumon description is not fully equivalent to the stringy formulation of the RVM. Our study provides a particularly interesting example of a successful phenomenological theory beyond the ΛCDM, such as the RVM, in which the fulfilment of the swampland criteria by the associated scalar field potential, along with its compatibility with (an appropriate form of) the weak gravity conjecture, prove to be insufficient conditions for warranting consistency of the scalar vacuum field representation as a faithful ultraviolet complete representation of the RVM at the quantum gravity level.

Axion star nucleation in dark minihalos around primordial black holes

We consider a general class of axion models, including the QCD and string axion, in which the PQ symmetry is broken before or during inflation. Assuming the axion is the dominant component of the dark matter, we discuss axion star formation in virialized dark minihalos around primordial black holes through gravitational Bose-Einstein condensation. We determine the conditions for minihalos to kinetically produce axion stars before galaxy formation. Today, we expect up to $\sim 10^{17}$ ($\sim 10^9$) axion stars in a radius of 100 parsecs around the Sun for the case of the QCD (string) axion.

Gravitational Fluctuations as an Alternative to Inflation III. Numerical Results

Power spectra play an important role in the theory of inflation, and their ability to reproduce current observational data to high accuracy is often considered a triumph of inflation, largely because of a lack of credible alternatives. In previous work we introduced an alternative picture for the cosmological power spectra based on the nonperturbative features of the quantum version of Einstein’s gravity, instead of currently popular inflation models based on scalar fields. The key ingredients in this new picture are the appearance of a nontrivial gravitational vacuum condensate (directly related to the observed cosmological constant), and a calculable renormalization group running of Newton’s G on cosmological scales. More importantly, one notes the absence of any fundamental scalar fields in this approach. Results obtained previously were largely based on a semi-analytical treatment, and thus, while generally transparent in their implementation, often suffered from the limitations of various approximations and simplifying assumptions. In this work, we extend and refine our previous calculations by laying out an updated and extended analysis, which now utilizes a set of suitably modified state-of-the-art numerical programs (ISiTGR, MGCAMB and MGCLASS) developed for observational cosmology. As a result, we are able to remove some of the approximations employed in our previous studies, leading to a number of novel and detailed physical predictions. These should help in potentially distinguishing the vacuum condensate picture of quantum gravity from that of other models such as scalar field inflation. Here, besides the matter power spectrum P m ( k ) , we work out, in detail, predictions for what are referred to as the TT, TE, EE, BB angular spectra, as well as their closely related lensing spectra. However, the current limited precision of observational data today (especially on large angular scales) does not allow us yet to clearly prove or disprove either set of ideas. Nevertheless, by exploring in more details the relationship between gravity and cosmological matter and radiation both analytically and numerically, together with an expected future influx of increasingly accurate observational data, one can hope that the new quantum gravitational picture can be subjected to further stringent tests in the near future.

Radiative and gravitating modes in the partially ionized magnetized dusty plasma

In the present study, fluid theory is used to investigate the gravitational and radiative condensation instabilities of a partially ionized magnetized dusty plasma system. The effects of ion and electron capture by dust grains, the charge variation of dust grains, and the radiative effects of electron species are also taken into account. The dynamics of all four species are considered to derive modified densities that further lead to a general dispersion relation. The general dispersion relation describes the propagation of low frequency electrostatic dust acoustic waves in magnetized self-gravitating partially ionized dusty plasma with ionization-recombination, dust charge variations, and radiative effects. Gravitational modes of propagation and radiative modes of propagation are illustrated separately for both parallel and perpendicular cases. Conditions for instabilities are also derived to explain the gravitational collapse and radiative condensation of the system. The numerical results are presented to signify the role of dust neutral collision frequency, dust charge fluctuation, magnetic field, and recombination ionization effects on both the radiative condensation and gravitational instabilities. The relevance of the present study to interstellar molecular clouds is also discussed and the effect of considered parameters on the critical wavelength, critical wave number, luminosity, etc., has been investigated.

Lorentz violation with an invariant minimum speed as foundation of the Gravitational Bose Einstein Condensate of a Dark Energy Star

We aim to search for the connection between the spacetime with an invariant minimum speed so-called Symmetrical Special Relativity (SSR) with Lorentz violation and the Gravitational Bose Einstein Condensate (GBEC) as the central core of a star of gravitational vacuum (gravastar), where one normally introduces a cosmological constant for representing an anti-gravity. This usual model of gravastar with an equation of state (EOS) for vacuum energy inside the core will be generalized for many modes of vacuum (dark energy star) in order to circumvent the embarrassment generated by the horizon singularity as the final stage of a gravitational collapse. In the place of the problem of a singularity of an event horizon, we introduce a phase transition between gravity and anti-gravity before reaching the Schwarzschild (divergent) radius $R_S$ for a given coexistence radius $R_{coexistence}$ slightly larger than $R_S$ and slightly smaller than the core radius $R_{core}$ of GBEC, where the metric of the repulsive sector (core of GBEC) would diverge for $r=R_{core}$, so that for such a given radius of phase coexistence $R_S<R_{coexistence} <R_{core}$, both divergences at $R_S$ of Schwarzschild metric and at $R_{core}$ of the repulsive core are eliminated, thus preventing the formation of the event horizon. So the causal structure of SSR helps us to elucidate such puzzle of singularity of event horizon by also providing a quantum interpretation for GBEC and thus by explaining the origin of a strong anisotropy due to the minimum speed that leads to the phase transition gravity/anti-gravity during the collapse of the star. Furthermore, due to the absence of an event horizon of black hole (BH) where any signal cannot propagate, the new collapsed structure presents a signal propagation in its region of coexistence of phases where the coexistence metric does not diverge.

Vacuum Condensate Picture of Quantum Gravity

In quantum gravity perturbation theory in Newton’s constant G is known to be badly divergent, and as a result not very useful. Nevertheless, some of the most interesting phenomena in physics are often associated with non-analytic behavior in the coupling constant and the existence of nontrivial quantum condensates. It is therefore possible that pathologies encountered in the case of gravity are more likely the result of inadequate analytical treatment, and not necessarily a reflection of some intrinsic insurmountable problem. The nonperturbative treatment of quantum gravity via the Regge–Wheeler lattice path integral formulation reveals the existence of a new phase involving a nontrivial gravitational vacuum condensate, and a new set of scaling exponents characterizing both the running of G and the long-distance behavior of invariant correlation functions. The appearance of such a gravitational condensate is viewed as analogous to the (equally nonperturbative) gluon and chiral condensates known to describe the physical vacuum of QCD. The resulting quantum theory of gravity is highly constrained, and its physical predictions are found to depend only on one adjustable parameter, a genuinely nonperturbative scale ξ in many ways analogous to the scaling violation parameter Λ M ¯ S of QCD. Recent results point to significant deviations from classical gravity on distance scales approaching the effective infrared cutoff set by the observed cosmological constant. Such subtle quantum effects are expected to be initially small on current cosmological scales, but could become detectable in future high precision satellite experiments.