Gravitational collapse of dark energy field configurations and supermassive black hole formation

Dark energy is the dominant component of the total energy density of our Universe. The primary interaction of dark energy with the rest of the Universe is gravitational. It is therefore important to understand the gravitational dynamics of dark energy. Since dark energy is a low-energy phenomenon from the perspective of particle physics and field theory, a fundamental approach based on fields in curved space should be sufficient to understand the current dynamics of dark energy. Here, we take a field theory approach to dark energy. We discuss the evolution equations for a generic dark energy field in curved space-time and then discuss the gravitational collapse for dark energy field configurations. We describe the 3 + 1 BSSN formalism to study the gravitational collapse of fields for any general potential for the fields and apply this formalism to models of dark energy motivated by particle physics considerations. We solve the resulting equations for the time evolution of field configurations and the dynamics of space-time. Our results show that gravitational collapse of dark energy field configurations occurs and must be considered in any complete picture of our Universe. We also demonstrate the black hole formation as a result of the gravitational collapse of the dark energy field configurations. The black holes produced by the collapse of dark energy fields are in the supermassive black hole category with the masses of these black holes being comparable to the masses of black holes at the centers of galaxies.     

Gravitational wave formation from the collapse of dark energy field configurations

Dark energy is the dominant component of the energy density in the Universe. In a previous paper, we have shown that the collapse of dark energy fields leads to the formation of supermassive black holes with masses comparable to the masses of black holes at the centers of galaxies. Thus, it becomes a pressing issue to investigate the other physical consequences of the collapse of dark energy fields. Given that the primary interactions of dark energy fields with the rest of the Universe are gravitational, it is particularly interesting to investigate the gravitational wave signals emitted during the collapse of dark energy fields. This is the focus of the current work described in this paper. We describe and use the 3+1 BSSN formalism to follow the evolution of the dark energy fields coupled with gravity and to extract the gravitational wave signals. Finally, we describe the results of our numerical computations and the gravitational wave signals produced by the collapse of dark energy fields.     

Rebounce and black hole formation in a gravitational collapse model with vanishing radial pressure

We examine here spherical gravitational collapse of a matter model with vanishing radial pressure and non-zero tangential pressure. It is seen analytically that the collapsing cloud either forms a black hole or disperses depending on values of the initial parameters which are initial density, tangential pressure and velocity profile of the cloud. A threshold of black hole formation is observed near which a scaling relation is obtained for the mass of black hole, assuming initial profiles to be smooth. The similarities in the behaviour of this model at the onset of black hole formation with that of numerical critical behaviour in other collapse models are indicated.     

Exact solutions for spherical gravitational collapse around a black hole:the effect of tangential pressure

Spherical gravitational collapse towards a black hole with non-zero tangential pressure is studied.Exact solutions corresponding to different equations of state are given.We find that when taking the tangential pressure into account,the exact solutions have three qualitatively different outcomes.For positive tangential pressure,the shell around a black hole may eventually collapse onto the black hole,or expand to infinity,or have a static but unstable solution,depending on the combination of black hole mass,mass of the shell and the pressure parameter.For vanishing or negative pressure,the shell will collapse onto the black hole.For all eventually collapsing solutions,the shell will cross the event horizon,instead of accumulating outside theeventhorizon,even if clocked by a distant stationary observer.     

The existence of a black hole due to condensation of matter

When enough matter is condensed in a small region, gravitational effects will be strong enough to cause collapse and a black hole will be formed. We formulate and prove here such a statement in the language of general relativity. (This is Theorem 2 of this paper.)     

Gravitational collapse of phantom fluid in (2 + 1)-dimensions

In this paper, we solve Einsteins’ field equations for a circularly symmetric anisotropic fluid, with kinematic self-similarity of the first kind, in (2 + 1)-dimensional spacetimes. Considering the case where the radial pressure vanishes, we show that there exists a solution that represents the gravitational collapse of an anisotropic fluid, and the collapse will finally form a black hole, even if the fluid is constituted by phantom energy.     

Pulsation of black holes

The Hawking–Penrose singularity theorem states that a singularity forms inside a black hole in general relativity. To remove this singularity one must resort to a more fundamental theory. Using a corrected dynamical equation arising in loop quantum cosmology and braneworld models, we study the gravitational collapse of a perfect fluid sphere with a rather general equation of state. In the frame of an observer comoving with this fluid, the sphere pulsates between a maximum and a minimum size, avoiding the singularity. The exterior geometry is also constructed. There are usually an outer and an inner apparent horizon, resembling the Reissner–Nordström situation. For a distant observer the horizon crossing occurs in an infinite time and the pulsations of the black hole quantum “beating heart” are completely unobservable. However, it may be observable if the black hole is not spherical symmetric and radiates gravitational wave due to the quadrupole moment, if any.     

On the Global Visibility of the Singularity in Quasi-Spherical Collapse

We analyze here the issue of local versus global visibility of a singularity that forms in gravitational collapse of a dust cloud, which has important implications for the weak and strong versions of the cosmic censorship hypothesis. We find conditions for when a singularity will be only locally naked, rather than being globally visible, thus preserving the weak censorship hypothesis. The conditions for the formation of a black hole or a naked singularity in the Szekeres quasi-spherical collapse models are worked out. The causal behaviour of the singularity curve is studied by examining the outgoing radial null geodesics, and the final outcome of collapse is related to the nature of the regular initial data specified on an initial hypersurface from which the collapse evolves. An interesting feature that emerges is that the singularity in Szekeres spacetimes can be directionally naked.     

Essay: The Quantum Gravitational Black Hole Is Neither Black Nor White

Understanding the end state of black hole evaporation, the microscopic origin of black hole entropy, the information loss paradox, and the nature of the singularity arising in gravitational collapse - these are outstanding challenges for any candidate quantum theory of gravity. Recently, a midisuperspace model of quantum gravitational collapse has been solved using a lattice regularization scheme. It is shown that the mass of an eternal black hole follows the Bekenstein spectrum, and a related argument provides a fairly accurate estimate of the entropy. The solution also describes a quantized mass-energy distribution around a central black hole, which in the WKB approximation, is precisely Hawking radiation. The leading quantum gravitational correction makes the spectrum non-thermal, thus providing a plausible resolution of the information loss problem.     

Phenomenological gravitational radiation from rotating stellar collapse to an intermediate mass Kerr black hole

Intermediate mass black holes may be formed through repeated coalescences of compact objects or through the direct collapse of a hypermassive star formed through runaway collisions of main sequence stars. The gravitational wave signature of these two formation scenarios will be different. Here we present an initial study of the waveform generated during the direct axisymmetric collapse of a hypermassive star in order to facilitate searches for this source. We approximate the collapse of the core as an axisymmetric Newtonian free-fall of a rotating relativistic degenerate iron core. The collapse waveform can be reasonably well modeled by an exponential growth.     

Gravitational collapse: The story so far

An outstanding problem in gravitation theory and relativistic astrophysics today is to understand the final outcome of an endless gravitational collapse. Such a continual collapse would take place when stars more massive than few times the mass of the sun collapse under their own gravity on exhausting their nuclear fuel. According to the general theory of relativity, this results either in a black hole, or a naked singularity — which can communicate with far away observers in the universe. While black holes are (almost) being detected and are increasingly used to model high energy astrophysical phenomena, naked singularities have turned into a topic of active discussion, aimed at understanding their structure and implications. Recent developments here are reviewed, indicating future directions.     

Radiating gravitational collapse with an initial inhomogeneous energy density distribution

A new model is proposed to a collapsing star consisting of an initial inhomogeneous energy density and anisotropic pressure fluid with shear, radial heat flow and outgoing radiation. In previous papers one of us has always assumed an initial star with homogeneous energy density. The aim of this work is to generalize the previous models by introducing an initial inhomogeneous energy density and compare it to the initial homogeneous energy density collapse model. We will show the differences between these models in the evolution of all physical quantities that characterizes the gravitational collapse. The behavior of the energy density, pressure, mass, luminosity and the effective adiabatic index is analyzed. The pressure of the star, at the beginning of the collapse, is isotropic but due to the presence of the shear the pressure becomes more and more anisotropic. The black hole is never formed because the apparent horizon formation condition is never satisfied, in contrast of the previous model where a black hole is formed. An observer at infinity sees a radial point source radiating exponentially until reaches the time of maximum luminosity and suddenly the star turns off. In contrast of the former model where the luminosity also increases exponentially, reaching a maximum and after it decreases until the formation of the black hole. The effective adiabatic index is always positive without any discontinuity in contrast of the former model where there is a discontinuity around the time of maximum luminosity. The collapse is about three thousand times slower than in the case where the energy density is initially homogeneous.     

An interpretation for the entropy of a black hole

We investigate the meaning of the entropy carried away by Hawking radiations from a black hole. We propose that the entropy for a black hole measures the uncertainty of the information about the black hole forming matter’s precollapsed configurations, self-collapsed configurations, and inter-collapsed configurations. We find that gravitational wave or gravitational radiation alone cannot carry all information about the processes of black hole coalescence and collapse, while the total information locked in the hole could be carried away completely by Hawking radiation as tunneling.     

Instability of black hole formation under small pressure perturbations

We investigate here the spectrum of gravitational collapse endstates when arbitrarily small perfect fluid pressures are introduced in the classic black hole formation scenario as described by Oppenheimer, Snyder and Datt (OSD) (Oppenheimer and Snyder in Phys Rev 56:455, 1939; Datt in Zs f Phys 108:314, 1938). This extends a previous result on tangential pressures (Joshi and Malafarina Phys Rev D 83:024009, 2011) to the physically more realistic scenario of perfect fluid collapse. The existence of classes of pressure perturbations is shown explicitly, which has the property that injecting any smallest pressure changes the final fate of the dynamical collapse from a black hole to a naked singularity. It is therefore seen that any smallest neighborhood of the OSD model, in the space of initial data, contains collapse evolutions that go to a naked singularity outcome. This gives an intriguing insight on the nature of naked singularity formation in gravitational collapse.     

Neutrino signals from the formation of a black hole: A probe of the equation of state of dense matter

The gravitational collapse of a nonrotating, black-hole-forming massive star is studied by nu-radiation-hydrodynamical simulations for two different sets of realistic equation of state of dense matter. We show that the event will produce as many neutrinos as the ordinary supernova, but with distinctive characteristics in luminosities and spectra that will be an unmistakable indication of black hole formation. More importantly, the neutrino signals are quite sensitive to the difference of equation of state and can be used as a useful probe into the properties of dense matter. The event will be unique in that they will be shining only by neutrinos (and, possibly, gravitational waves) but not by photons, and hence they should be an important target of neutrino astronomy.     

Gravitational collapse and naked singularities

Gravitational collapse is one of the most striking phenomena in gravitational physics. The cosmic censorship conjecture has provided strong motivation for research in this field. In the absence of a general proof for censorship, many examples have been proposed, in which naked singularity is the outcome of gravitational collapse. Recent developments have revealed that there are examples of naked singularity formation in the collapse of physically reasonable matter fields, although the stability of these examples is still uncertain. We propose the concept of ‘effective naked singularities’, which will be quite helpful because general relativity has limitation in its application at the high-energy end. The appearance of naked singularities is not detestable but can open a window for the new physics of strongly curved space-times.     

Spherically symmetric free fall collapse

The general dynamical equations for spherical gravitational collapse are derived by introducing the eigenvalue of the conformal Weyl tensor in the 2-2 component of the Einstein tensor and assuming the material content of the models to be a perfect fluid. Since this eigenvalue is coupled always with the material energy density, it has been interpreted as theenergy density of the free gravitational field whose presence is related with anisotropy and inhomogeneity. As a particular case, the collapse of a spherically symmetric dust (zero pressure) with vanishing radial acceleration (free fall collapse) is discussed. It is shown that the model is inhomogeneous with non-vanishing shear of the congruence of world lines of the dust particles. The model contains gravitational radiation by Szekere’s criterion since both shear invariant and the spatial gradient of density are non-vanishing. This is in contrast to the Oppenheimer-Synder model for which both the above mentioned characteristics are absent. A particular solution which is anisotropic and inhomogeneous has been given to prove the emission of gravitational radiation by the freely falling dust and in this case the energy density of the free gravitational field contains a typeN term superposed on the coulombian field.     

Formation of a black string in a higher dimensional vacuum gravitational collapse

We present a solution to the vacuum Einstein equations which represents a collapse of a gravitational wave in 5 dimensions. Depending on the “focal length” of the wave the collapse results, either in a black string covered by a horizon, or in a naked singularity which can be removed.     

Non-Spherical Gravitational Collapse of Strange Quark Matter

We study the non-spherical gravitational collapse of the strange quark null fluid. The interesting feature which emerges is that the non-spherical collapse of charged strange quark matter leads to a naked singularity whereas the gravitational collapse of neutral quark matter proceeds to form a black hole. We extend the earlier work of Harko and Cheng [Phys. Lett. A 266 （2000） 249] to the non-spherical case.     

Possibility of QCD critical point sweep during black hole formation

We discuss the possibility to probe the QCD critical point during the dynamical black hole formation from a gravitational collapse of a massive star, where the temperature and the baryon chemical potential become as high as T∼90 MeV and μB∼1300 MeV. Comparison with the phase boundary in chiral effective models suggests that quark matter is likely to be formed before the horizon is formed. Furthermore, the QCD critical point may be probed during the black hole formation. The critical point is found to move in the lower temperature direction in asymmetric nuclear matter, and in some of the chiral models it is found to be in the reachable region during the black hole formation processes.