Black Hole Mimickers Research Articles

Frozen stars: Black hole mimickers sourced by a string fluid

The frozen star is a nonsingular, ultracompact object that, to an external observer, looks exactly like a Schwarzschild black hole, but with a different interior geometry and matter composition. The frozen star needs to be sourced by an extremely anisotropic fluid, for which the sum of the radial pressure and energy density is either vanishing or perturbatively small. Here, we show that this matter can be identified with the string fluid resulting from the decay of an unstable D-brane or a brane-antibrane system at the end of open-string tachyon condensation. The string fluid corresponds to flux tubes emanating from the center and ending at the Schwarzschild radius of the star. The effective Lagrangian for this fluid can be recast into a Born-Infeld form. When the fluid Lagrangian is coupled to that of Einstein’s gravity, the static, spherically symmetric solutions of the equations of motion are shown to be the same as those describing the frozen star model. Frozen stars can therefore be viewed as a gravitationally backreacted BIons model or that of gravitationally confined flux tubes. The Born-Infeld Lagrangian provides a complete set of equations that describe the dynamics of the frozen star in a generic state, which is not necessarily static nor spherically symmetric. Our framework therefore should allow a fully dynamical and out-of-equilibrium description of the frozen star model which will be relevant to gravitational waves observations of mergers of astrophysical black holes. Published by the American Physical Society 2024

Energetics of Buchdahl stars and the magnetic Penrose process

Buchdahl star is the most compact object without an event horizon and is an excellent candidate for a black hole mimicker. Unlike black holes, rotating Buchdahl star can be over-extremal with respect to the black hole, sustaining a larger spin. We show that it can also develop an ergosphere above the threshold spin β>1/2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\beta > 1/\\sqrt{2}$$\\end{document}, which allows extraction of its rotational energy. Electromagnetic field around Buchdahl star is also expected to differ from that of black hole in both strength and topology. In this paper, we explore the energetics of Buchdahl star focusing on the magnetic Penrose process in the two magnetic field configurations, i.e., uniform and dipole. Below the threshold spin, Buchdahl star is expected to be quiet, while above the threshold it can be much more efficient than the black hole if a dipolar magnetic field is developed on its surface.

Revisiting Relativistic Electrically Charged Polytropic Spheres

AbstractThe problem of the structure and physical properties of electrically charged static spherically symmetric solutions of the Einstein‐Maxwell system of equations is revisited, where the matter model is a polytropic gas. A relativistic polytrope equation of state (EOS) is considered and the electric charge density is assumed to be proportional to the rest mass density. Families of solutions corresponding to various sets of parameters are constructed and analyzed their stability and compliance with the causality requirement, emphasizing the possibility of obtaining black hole mimickers. Concretely, this study wants to test how much electric charge a given object can hold and how compact it can be. It is concluded that there is a microscopic bound on the charge density to rest mass density ratio coincident with the macroscopic bound regarding the extremal Reissner‐Nordström (ERN) black hole. The macroscopic charge to mass ratio for the object can exceed the corresponding microscopic ratio if the object is non‐extremal. Crucially, the only way to construct a black hole mimicker is by taking a subtle limit in which an electrically counterpoised dust (ECD) solution is attained.

Nonlinear Treatment of a Black Hole Mimicker Ringdown.

We perform the first nonlinear and self-consistent study of the merger and ringdown of a black hole mimicking object with stable light rings. To that end, we numerically solve the full Einstein-Klein-Gordon equations governing the head-on collisions of a series of binary boson stars in the large-mass-ratio regime resulting in spinning horizonless remnants with stable light rings. We broadly confirm the appearance of features in the extracted gravitational waveforms expected based on perturbative methods: the signal from the prompt response of the remnants approaches that of a Kerr black hole in the large-compactness limit, and the subsequent emissions contain periodically appearing bursts akin to so-called gravitational wave echoes. However, these bursts occur at high frequencies and are sourced by perturbations of the remnant's internal degrees of freedom. Furthermore, the emitted waveforms also contain a large-amplitude and long-lived component comparable in frequency to black hole quasinormal modes. We further characterize the emissions, obtain basic scaling relations of relevant timescales, and compute the energy emitted in gravitational waves.

No-go theorem for static spherically symmetric configurations composed of two charged pressureless fluid species

We present a no-go theorem for spherically symmetric configurations of two charged fluid species in equilibrium. The fluid species are assumed to be dusts, that is, perfect fluids without pressure, and the equilibrium can be attained for a single dust from the balance of electrostatic repulsion and gravitational attraction. We show that this is impossible for two dust species unless both of them are indistinguishable in terms of their electric charge density to matter density ratio. The result is obtained in the main three theories of mechanics, that is, in Newtonian Mechanics, in Special Relativity and in General Relativity. In particular, as charged dust solutions have been used to study the possibility of black hole mimickers, this result shows that such mimickers can not be constructed unless the underlying charged particle has the correct charge to mass ratio.

Comparison of magnetized thick disks around black holes and boson stars

Boson stars are considered as promising candidates for black hole mimickers. Similar to other compact objects they can form accretion disks around them. The properties of these disks could possibly distinguish them from other compact objects like black holes in future observations. Retrograde thick disks around boson stars and the influence of strong magnetic fields on them were already studied and it was shown that they can harbor very distinct features compared to black hole disks. However, the case of prograde thick disks is mostly unexplored, since they may appear much more similar to black hole disks. In this work we will investigate similarities and differences regarding prograde thick disks around non-selfinteracting rotating boson stars and rotating black holes. We assume thereby a polytropic equation of state and a constant specific angular momentum distribution of the disks. We classify the various conceivable boson star and black hole solutions by a dimensionless spin parameter a and compare their corresponding disk solutions. The influence of toroidal magnetic fields on the disks is analyzed by selected disk properties, as the rest-mass density distribution and the Bernoulli parameter. Disk solutions are characterized by their degree of magnetization represented by the magnetization parameter βmc\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\beta _{mc}$$\\end{document}. We found that strong magnetic fields can strengthen the differences of disk solutions or oppositely even lead to a correlation in disk properties, depending on the spin parameter of the boson star and black hole solutions. We identify the vertical thickness of the boson star disks as the main differentiating factor, since for most solutions the vertical density distribution is far more outreaching for boson star disks compared to black hole disks.

From black hole mimickers to black holes

From black hole mimickers to black holes

A rotating modified JNW spacetime as a Kerr black hole mimicker

AbstractThe Event Horizon Telescope has recently observed the images and shadows of the compact objects M87* and Sgr A* at the centres of the galaxies Messier 87 and Milky Way. This has opened up a new window in observational astronomy to probe and test gravity and fundamental physics in the strong-field regime. In this paper, we construct a rotating version of a modified Janis-Newman-Winicour metric obtained through the Simpson-Visser regularisation procedure and constrain the metric parameters using the observed shadows of M87* and Sgr A*. Depending on parameter values, the spacetime metric represents either a naked singularity or a wormhole. We find that the naked singularity case is not consistent with observations, as it casts a shadow that is much smaller than the observed ones. On the other hand, the shadow formed by the wormhole branch, depending on the parameter values, is consistent with the observations. We put constraints on the wormhole throat radius by comparing the shadow with the observed ones of M87* and Sgr A*.

Black Holes as Frozen Stars: Regular Interior Geometry

AbstractThe authors have proposed a model geometry for the interior of a regular black hole (BH) mimicker, the frozen star, whose most startling feature is that each spherical shell in its interior is a surface of infinite redshift. The geometry is a solution of the Einstein equations which is sourced by an exotic matter with maximally negative radial pressure. The frozen star geometry is previously presented in singular coordinates for which and vanish in the bulk and connect smoothly to the Schwarzschild exterior. Additionally, the geometry is mildly singular in the center of the star. Here, the authors present regular coordinates for the entirety of the frozen star. Each zero in the metric is replaced with a small, dimensionless parameter ε; in both and thus maintaining maximally negative radial pressure. The authors also regularize the geometry, energy density and pressure in the center of the star in a smooth way. The frozen star solution presented here is a completely regular solution of Einstein's equations whose compactness is arbitrarily close to that of a Schwarzschild BH. It obeys the null energy condition, the universally agreed‐upon energy condition, and it is free of any known pathology. As far as it is known, this is the first solution that obeys all of these constraints and, in addition, as will be shown in a future publication, can mimic all of the thermodynamic properties of a standard BH. Our initial analysis uses Schwarzschild‐like coordinates and applies the Killing equations to show that an infalling, point‐like object will move very slowly, effectively sticking to the surface of the star and never coming out. If one nevertheless follows the trajectory of the object into the interior of the star, it moves along an almost‐radial trajectory until it comes within a small distance from the star's center. Once there, if the object has any amount of angular momentum at all, it will be reflected outwards by a potential barrier onto a different almost‐radial trajectory. Finally, using Kruskal‐like coordinates, the causal structure of the regularized frozen star and discuss its limit, for which the geometry degenerates and becomes effectively two dimensional is considered.

Observable Properties of Thin Accretion Disk in the γ Spacetime

We study matter accretion in a static, axially symmetric and vacuum geometry describing the exterior gravitational field of a black hole mimicker called the γ metric. We evaluate the thermal and optical properties of thin accretion disks, including the emission rate, luminosity and shadow, in the gamma spacetime. Also, we explore the radial accretion of polytropic matter fields onto the central source and evaluate the thermal and optical properties of the infalling gas, such as temperature and luminosity. The results are discussed in the context of evaluating the possibility that the true nature of astrophysical black hole candidates may not be a black hole but some exotic compact object possessing a non-vanishing mass quadrupole moment.

On thermodynamics of compact objects

With the recent progress in observations of astrophysical black holes, it has become more important to understand in detail the physics of strongly gravitating horizonless objects. If the objects identified in the observations are indeed horizonless and ultracompact, high curvature effects may become important, and their explorations may be intimately related to new physics beyond General Relativity (GR). In this paper, we revisit the concept of statistical thermodynamics in curved spacetime, focusing on self-gravitating compact systems without event horizons. In the literature, gravitational field equations are in general assumed a priori in the thermodynamic treatment, which may lead to difficulties for theories of modified gravity, given the more complicated structure of field equations. Here, we consider thermodynamic behavior of the matter source, instead of the physical mass, hence avoiding the explicit input of field equations in the derivation of thermodynamic laws. We show that the conventional first law of thermodynamics is retrieved once the thermodynamic volume, which is in general different from the geometric volume, is appropriately identified. For demonstrations of our approach, we consider familiar examples of self-gravitating gas in GR, where the connection to previous studies becomes clear. We also discuss 2-2-holes in quadratic gravity, a novel example of black hole mimickers that features super-Planckian curvatures in the interior. These objects exhibit universal high curvature effects in thermodynamics, which happen to be conveniently encoded in the thermodynamic volume. Interesting connections to black hole thermodynamics also emerge when the physical mass is treated as the total internal energy.

A connection between regular black holes and horizonless ultracompact stars

We illustrate that regular black holes and horizonless stars, typically considered as quite distinct families of black hole mimickers, are intimately intertwined. We show that any spherically symmetric regular black hole can be continuously deformed into a horizonless star under the mild conditions of non-negativity of gravitational energy (Misner-Sharp quasi-local mass), and an assumed linear relation between the latter and the Arnowitt-Deser-Misner (ADM) mass. We illustrate this general result by considering the family of geometries proposed by Hayward as the description of regular black holes, and we also describe the properties of the corresponding horizonless stars. The form of the associated effective stress-energy tensor shows that these horizonless stars can be identified as anisotropic gravastars with a soft surface and inner/outer light rings. We also construct dynamical geometries that could describe the evolution of regular black holes towards horizonless stars, and show that it is plausible that the effective stress-energy tensor in the first stages of evolution is generated by semiclassical effects, in agreement with independent works analyzing semiclassical backreaction.

Stellar equilibrium on a physical vacuum soil

We show that the repulsive effects associated to the zero-point energies of quantum fields are capable of supporting ultracompact stars that overcome the compactness limits present in general relativity for any object in hydrostatic equilibrium. These objects are exact self-consistent solutions in semiclassical gravity that incorporate the backreaction of the renormalized stress-energy tensor (RSET) of quantum fields in vacuum. We arrive at stars of striking qualitative agreement through two independent modelings of the RSET, evidencing the generality and robustness of this result. The main physical properties of these novel black hole mimickers are reviewed.

Testing black hole mimickers with the Event Horizon Telescope image of Sagittarius A*

ABSTRACT The Event Horizon Telescope (EHT) has recently observed the image and shadow of the supermassive compact object Sagittarius A* (Sgr A*). According to the EHT collaboration, the observed image is consistent with the expected appearance of a Kerr black hole. However, it is well-known that some non-Kerr objects may mimic many of the properties of the Kerr black hole, and hence, their shadows might be consistent with the observed shadow of Sgr A*. In this work, we consider two black hole mimickers and study their shadows. The first mimicker is a rotating generalization of the recently proposed static, spherically symmetric black-bounce space–time by Simpson and Visser where the central Schwarzschild singularity is replaced by a minimal surface. The second one is the γ-metric which is a static, axially-symmetric singular solution of the vacuum Einstein’s equations without an event horizon. We put constraint on the parameters of these black hole mimickers by comparing their shadows with the observed shadow of Sgr A*.

Dynamical Instability of Self-Gravitating Membranes.

We show that a generic relativistic membrane with in-plane pressure and surface density having the same sign is unstable with respect to a series of warping mode instabilities with high wave numbers. We also examine the criteria of instability for commonly studied exotic compact objects with membranes, such as gravastars, anti-de Sitter bubbles, and thin-shell wormholes. For example, a gravastar which satisfies the weak energy condition turns out to be dynamically unstable. A thin-layer black hole mimicker is stable only if it has positive pressure and negative surface density (such as a wormhole), or vice versa.

A shadows from the static black hole mimickers

In this work, we study shadows from the naked singularity spacetime. The most analytical solutions of black hole shadows only investigated the case that the geodesic equations for photons can separate variables. We review the spherical null naked singularity metric and this spherically symmetric naked singularity spacetime metric is the solution of Einstein equations with an anisotropic fluid source which has no photon sphere. We also review a static, axially-symmetric singular solution of the vacuum Einstein’s equations without an event horizon which is can be used to describe the exterior gravitational field of a mass distribution with quadrupole moment. Moreover, the corresponding spacetime is characterized by the presence of naked singularities. It is theoretically known that not only a black hole can cast shadow, but other compact objects such as naked singularities, gravastar or boson stars can also cast shadows. We present the analytical calculation of shadows for both naked singularities spacetime and compare with the shadow of Schwarzschild static black hole, we show that this can serve as a black hole mimicker. Keywords: compact object, naked singularity, shadow.

Rotational Energy Extraction from the Kerr Black Hole’s Mimickers

In this paper, the Penrose process is used to extract rotational energy from regular black holes. Initially, we consider the rotating Simpson–Visser regular spacetime, which describes the class of geometries of Kerr black hole mimickers. The Penrose process is then studied through conformally transformed rotating singular and regular black hole solutions. Both the Simpson–Visser and conformally transformed geometries depend on mass, spin, and an additional regularisation parameter l. In both cases, we investigate how the spin and regularisation parameter l affect the configuration of an ergoregion and event horizons. Surprisingly, we find that the energy extraction efficiency from the event horizon surface is not dependent on the regularisation parameter l in the Simpson–Visser regular spacetimes, and hence, it does not vary from that of the Kerr black hole. Meanwhile, in conformally transformed singular and regular black holes, we obtain that the efficiency rate of extracted energies is extremely high compared to that of the Kerr black hole. This distinct signature of conformally transformed singular and regular black holes is useful to distinguish them from Kerr black holes in observation.

Hunting extra dimensions in the shadow of Sgr A*

We show that the observed angular diameter of the shadow of the ultra compact object Sgr A*, favours the existence of an extra spatial dimension. This holds irrespective of the nature of the ultra compact object, i.e., whether it is a wormhole or, a black hole mimicker, but with the common feature that both of them have an extra dimensional origin. This result holds true for the mass and the distance measurements of Sgr A* using both Keck and the Gravity collaborations and whether we use the observed image or, the observed shadow diameter. In particular, the central value of the observed shadow or, the observed image diameter predicts non-zero hairs inherited from the extra dimensions.

Constraining the deformation of a rotating black hole mimicker from its shadow

We consider a black hole mimicker given by an exact solution of the stationary and axially-symmetric field equations in vacuum known as the $\ensuremath{\delta}$-Kerr metric. We study its optical properties based on a ray-tracing code for photon motion and characterize the apparent shape of the shadow of the compact object and compare it with the Kerr black hole. For the purpose of obtaining qualitative estimates related to the observed shadow of the supermassive compact object in the galaxy M87 we focus on values of the object's spin $a$ and inclination angle of observation ${\ensuremath{\theta}}_{0}$ close to the measured values. We then apply the model to the shadow of the $\ensuremath{\delta}$-Kerr metric to obtain constraints on the allowed values of the deformation parameter. We show that based uniquely on one set of observations of the shadow's boundary it is not possible to exclude the $\ensuremath{\delta}$-Kerr solution as a viable source for the geometry in the exterior of the compact object.

Damour–Solodukhin Wormhole as a Black Hole Mimicker: The Role of Observers’ Location

It has been recently argued that in semi-classical gravity, a minimal 2-sphere is not a horizon but a tiny throat of a wormhole, such as the Damour–Solodukhin wormhole (DSWH), with a free parameter λ≠0 separating it from a Schwarxzschild black hole (BH) (λ=0). As shown by DS, their horizonless WH can mimic many properties of a black hole (BH). Assuming that observing a BH mimicker is equivalent to observing a BH itself, we ask the question as to which identity of the object, a WH or a BH, an observer is likely to observe in a single experiment. To answer this, we introduce Tangherlini’s new concept of indeterminacy in the gravitational field by portraying the field as a refractive medium. We then postulate that the identity of the observed object will depend on the probabilistic outcome of photon motion probing the object. The probabilities will be described by Fresnel reflection (R) and transmission (T) coefficients derived by Tangherlini on the basis of a non-quantum statistical indeterminacy of photon motion in ordinary optical media. By adapting this approach to a gravitational “effective optical medium,” we obtain two intriguing results: (i) The Fresnel coefficients at the DSWH throat are independent of mass M but dependent solely on the parameter λ≠0. (ii) Depending on the location of the observer, what is a DSWH to one observer may appear as a BH to another observer for the same value of λ≠0.