Cosmological Singularity Research Articles

Einstein field equations for Bose-Einstein condensates in cosmology

In this work we consider the Gross-Pitaevskii equation for Bose-Einstein condensates (BECs) in a general Riemannian metric. Given initial conditions dictated by an external potential, we consider the free expansion of the condensate when the external potential is turned off. Focusing on the forces associated with the geometry of the initial configuration, we show how these are related to the Ricci curvature tensor and the Ricci scalar and we find an Einstein field equation governing the steady flow. Some important correlations between the study of defects in BECs and the appearance of cosmological singularities will be addressed, in particular the emergence of an effective Lorentzian spacetime geometry, which is what is needed to obtain Hawking radiation effects.

Spike behavior in the approach to spacetime singularities

We perform numerical simulations of the approach to spacetime singularities. The simulations are done with sufficient resolution to resolve the small scale features (known as spikes) that form in this process. We find an analytical formula for the shape of the spikes and show that the spikes in the simulations are well described by this formula.

Quantum Spacetime and the Universe at the Big Bang, Vanishing Interactions and Fading Degrees of Freedom

As discussed in Bahns et al. (2015) fundamental physical principles suggests that, close to cosmological singularities, the effective Planck length diverges, hence a “quantum point” becomes infinitely extended. We argue that, as a consequence, at the origin of times spacetime might reduce effectively to a single point and interactions disappear. This conclusion is supported by converging evidences in two different approaches to interacting quantum fields on Quantum Spacetime: (1) as the Planck length diverges, the field operators evaluated at a “quantum point” converge to zero, and so do the lowest order expressions for interacting fields in the Yang Feldman approach; (2) in the same limit, we find convergence of the interacting vacuum to the free one at all perturbative orders. The latter result is obtained using the adaptation, performed in Doplicher et al. (2020), of the methods of perturbative Algebraic Quantum Field Theory to Quantum Spacetime, through a novel picture of the effective Lagrangian, which maintains the ultraviolet finiteness of the perturbation expansion and allows one to prove also the existence of the adiabatic limit. It remains an open question whether the S matrix itself converges to unity and whether the limit in which the effective Planck length diverges is a unique initial condition or an unreachable limit, and only different asymptotics matter.

Gravitational dynamics in the toy model of the Higgs-dark matter sector: the field theoretic perspective

The objective of the paper was to examine gravitational evolutions in the Higgs-dark matter sector toy model. The real part of the Higgs doublet was modelled by a neutral scalar. Two dark matter candidates introduced were the dark photon and a charged complex scalar. Non-minimal couplings of both scalars to gravity were included. The coupling channels between the ordinary and dark matter sectors were kinetic mixing between the electromagnetic and dark U(1) fields and the Higgs portal coupling among the scalars. The structures of emerging singular spacetimes were either of Schwarzschild or Reissner–Nordström types. The non-minimal scalar–gravity couplings led to an appearance of timelike portions of apparent horizons where they transform from spacelike to null. The features of dynamical black holes were described as functions of the model parameters. The black holes formed later and their radii and masses were smaller as the mass parameter of the complex scalar increased. The dependencies on the coupling of the Higgs field to gravity exhibited extrema, which were a maximum for the time of the black holes formation and minima in the cases of their radii and masses. A set of quantities associated with an observer moving with the evolving matter was proposed. The energy density, radial pressure and pressure anisotropy within dynamical spacetimes get bigger as the singularity is approached. The increase is more considerable in the Reissner–Nordström spacetimes. The apparent horizon local temperature changes monotonically in the minimally coupled case and non-monotonically when non-minimal scalar–gravity couplings are involved.

Specific entropy as a clock for the evolutionary quantization of the isotropic Universe

In this paper, we analyze the dynamics of an isotropic closed Universe in presence of a cosmological constant term and we compare its behavior in the standard Wheeler–DeWitt equation approach with the one when a Lagrangian fluid is considered in the spirit of the Kuchar–Brown paradigm. In particular, we compare the tunnelling of the Universe from the classically forbidden region to the allowed one, showing that considering a time evolution deeply influences the nature of the model. In fact, we show that in the presence of the Lagrangian fluid, the cosmological singularity is restored both in the classical and the quantum regime. However, in the quantum regime the singularity is probabilistically suppressed for some energy eigenvalues and in the case the latter is equal to zero one recovers the standard WDW case. Finally, we introduce a cut-off physics feature in the Minisuperspace by considering a Polymer quantum mechanical approach limiting our attention to the semi-classical dynamics mainly (the quantum treatment is inhibited by the non-local nature of the Hamiltonian operator). We show that the singularity is again removed, like in the fluid-free model, and a bouncing cosmology emerges so that the present model could mimic a cyclic cosmology.

Rainbow spacetime from a nonlocal gravitational uncertainty principle

The occurrence of spacetime singularities is one of the peculiar features of Einstein gravity, signalling limitation on probing short distances in spacetime. This alludes to the existence of a fundamental length scale in nature. On the contrary, the Heisenberg quantum uncertainty relation seems to allow for probing arbitrarily small length scales. To reconcile these two conflicting ideas in line with a well-known framework of quantum gravity, several modifications of Heisenberg algebra have been proposed. However, it has been extensively argued that such a minimum length would introduce nonlocality in theories of quantum gravity. In this letter, we analyze a previously proposed deformation of the Heisenberg algebra (i.e., ) for a particle confined in a box subjected to a gravitational field. For the problem in hand, such deformation seems to yield an energy-dependent behavior of spacetime in a way consistent with gravity's rainbow, hence demonstrating a connection between non-locality and gravity's rainbow.

Strong gravitational lensing by a strongly naked null singularity

We study strong gravitational lensing in a static, spherically symmetric, naked singularity spacetime, without a photon sphere. The nature of the singularity is found to be lightlike. We discuss the characteristic lensing features of this naked singularity in the strong deflection limit. In spite of the absence of a photon sphere in this spacetime, the bending angle of light diverges, as it approaches the singularity. However, unlike black holes, it is found that the nature of this divergence is nonlogarithmic, and we derive an analytic formula for the same. Moreover, the relativistic rings produced due to strong lensing by the singularity are found to be well separated from each other, making them easy to resolve and possibly detect. These features are expected to be important in the study of strong lensing by ultracompact objects, especially ones without event horizons.

Imprints of the Janis-Newman-Winicour spacetime on observations related to shadow and accretion

The final fate of gravitational collapse of massive stars has been a subject of interest for a long time since such a collapse may lead to black holes and naked singularities alike. Since, the formation of naked singularities is forbidden by the cosmic censorship conjecture, exploring their observational differences from black holes may be a possible avenue to search for these exotic objects. The simplest possible naked singularity spacetime emerges from the Einstein massless scalar field theory with the advantage that it smoothly translates to the Schwarzschild solution by the variation of the scalar charge. This background, known as the Janis-Newman-Winicour spacetime is the subject of interest in this work. %A further advantage of working with this spacetime is that it smoothly translates to the Schwarzschild solution by the variation of the scalar charge. We explore electromagnetic observations around this metric which involves investigating the characteristics of black hole accretion and shadow. We compute the shadow radius in this spacetime and compare it with the image of M87*, recently released by the Event Horizon Telescope Collaboration. Similarly, we derive the expression for the luminosity from the accretion disk and compare it with the observed optical luminosity of eleven Palomar Green quasars. Our analysis indicates that the shadow of M87* and the quasar optical data consistently favor the Schwarzschild background over the Janis-Newman-Winicour spacetime. The implications of this result are discussed.

The Mande Creation Myth,by Germaine Dieterlen, as a Historical Source for the Mali Empire

AbstractThis article proposes a new reading for Germaine Dieterlen’s classic text “The Mande Creation Myth,” and presents it as evidence for Kangaba’s prominent military role as ruler of the Niger and defender of the gold mines that for centuries provided the wealth of the Mali Empire. It is demonstrated that, although Dieterlen was in search of a unified cosmology, her informants in Kangaba provided answers that voiced Kangaba’s military concerns and claims as political heir of the medieval Mali Empire and ruler of the River Niger. The starting point of the analysis are new insights on how creation is envisioned in the West African savannah, with an emphasis on termite mounds, earth, and blacksmiths. These insights are compared to the fieldwork data that Dieterlen collected in 1953-55, which she used in 1955 for a publication on the Kamabolon ceremony in Kangaba and, under strikingly different personal circumstances, in 1957 in the article “The Mande Creation Myth.” The article explains why Dieterlen herself nor other researchers have never been able to reproduce neither her 1953-55 findings nor her 1957 findings by pointing to Kangaba’s raised prestige as a major historical site for a new Republic of Mali, which had acquired independence in 1960. Kangaba’s new position replaced the earlier focus on military rule on the Niger and defense of gold mines (in what had become the Republic of Guinée in 1958). This argument is substantiated by a recently discovered contemporary report of the 1961 Kamabolon ceremony, written by a leading contemporary intellectual, Mambi Sidibé.

Global visibility of a strong curvature singularity in nonmarginally bound dust collapse

We investigate here the local versus global visibility of a space-time singularity formed due to the gravitational collapse of a spherically symmetric dust cloud having a non-zero velocity function. The conditions are investigated that ensure the global visibility of the singularity, in the sense that the outgoing null geodesics leave the boundary of the matter cloud in the future, whereas, in the past, these terminate at the singularity. Explicit examples of this effect are constructed. We require that this must be a strong curvature singularity in the sense of Tipler, to ensure the physical significance of the scenario considered. This may act as a counterexample to the weak cosmic censorship hypothesis.

“Time”-Covariant Schrödinger Equation and the Canonical Quantization of the Reissner–Nordström Black Hole

A “time”-covariant Schrödinger equation is defined for the minisuperspace model of the Reissner–Nordström (RN) black hole, as a “hybrid” between the “intrinsic time” Schrödinger and Wheeler–DeWitt (WDW) equations. To do so, a reduced, regular, and “time(r)”-dependent Hamiltonian density was constructed, without “breaking” the re-parametrization covariance r→f(r˜). As a result, the evolution of states with respect to the parameter r and the probabilistic interpretation of the resulting quantum description is possible, while quantum schemes for different gauge choices are equivalent by construction. The solutions are found for Dirac’s delta and Gaussian initial states. A geometrical interpretation of the wavefunctions is presented via Bohm analysis. Alongside this, a criterion is presented to adjudicate which, between two singular spacetimes, is “more” or “less” singular. Two ways to adjudicate the existence of singularities are compared (vanishing of the probability density at the classical singularity and semi-classical spacetime singularity). Finally, an equivalence of the reduced equations with those of a 3D electromagnetic pp-wave spacetime is revealed.

Multifractality in the general cosmological solution of Einstein’s equations

We demonstrate the scale invariance of the vacuum Bianchi type IX equations and use this to argue for the possibility of multifractal turbulence as a realisation of the suggestion by Belinski that there will be a fragmentation of local regions of inhomogeneous Mixmaster chaos on approach to an initial inhomogeneous cosmological singularity. Differences between the gravitational and hydrodynamical situations are outlined. Various potential obstacles to this picture of gravitational turbulence are discussed.

Cosmological singularities and 2-dimensional dilaton gravity

We study Big-Bang or -Crunch cosmological singularities in 2-dimensional dilaton-gravity-scalar theories, in general obtained by dimensional reduction of higher dimensional theories. The dilaton potential encodes information about the asymptotic data defining the theories, and encompasses various families such as flat space, AdS, conformally AdS as arising from nonconformal branes, and more general nonrelativistic theories. We find a kind of universal near singularity behaviour independent of the dilaton potential, giving universal interrelations between the exponents defining the time behaviour near the cosmological singularity. More detailed analysis using a scaling ansatz enables finding various classes of cosmological backgrounds, recovering known examples such as the AdS Kasner singularity as well finding as new ones. We give some comments on the dual field theory from this point of view.

Bekenstein's Entropy Bound-Particle Horizon Approach to Avoid the Cosmological Singularity.

The cosmological singularity of infinite density, temperature, and spacetime curvature is the classical limit of Friedmann’s general relativity solutions extrapolated to the origin of the standard model of cosmology. Jacob Bekenstein suggests that thermodynamics excludes the possibility of such a singularity in a 1989 paper. We propose a re-examination of his particle horizon approach in the early radiation-dominated universe and verify it as a feasible alternative to the classical inevitability of the singularity. We argue that this minimum-radius particle horizon determined from Bekenstein’s entropy bound, necessarily quantum in nature as a quantum particle horizon (QPH), precludes the singularity, just as quantum mechanics provided the solution for singularities in atomic transitions as radius . An initial radius of zero can never be attained quantum mechanically. This avoids the spacetime singularity, supporting Bekenstein’s assertion that Friedmann models cannot be extrapolated to the very beginning of the universe but only to a boundary that is ‘something like a particle horizon’. The universe may have begun in a bright flash and quantum flux of radiation and particles at a minimum, irreducible quantum particle horizon rather than at the classical mathematical limit and unrealizable state of an infinite singularity.

Charged black holes in Einsteinian cubic gravity and nonuniqueness

Black holes are the simplest objects in the universe. They correspond to extreme deformations of spacetime geometry, and can exist even devoid of matter. In general relativity, (electro)vacuum black holes are uniquely determined by their mass, charge and angular momentum. This feature follows from a uniqueness theorem, which can be evaded if one considers higher dimensions or matter fields coupled to gravity. Here we find that Einsteinian cubic gravity, a well-motivated modification of Einstein gravity that includes third-order curvature corrections in accordance with low-energy effective theory expectations, admits black hole solutions with charge greater than mass, when minimally coupled to a Maxwell field. Moreover, we find that, in this regime, there can be two asymptotically flat black holes with the same charge and mass, posing the first example of vacuum black hole nonuniqueness in four dimensions that is free from pathologies. Examination of these black hole's thermodynamics reveals that when two branches coexist only the larger black hole is thermodynamically stable, while the smaller branch has negative specific heat. Einsteinian cubic gravity unveils two further surprising features. The charged black holes do not possess an inner horizon, in contrast with the usual Reissner-Nordstr\"om spacetime, thus avoiding the need to resort to strong cosmic censorship to uphold determinism. In addition to black holes, there exists a one-parameter family of naked singularity spacetimes sharing the same mass and charge as the former, but not continuously connected with them. These naked singularities exist in the under-extremal regime, being present even in pure (uncharged) Einsteinian cubic gravity.

Shadow of a naked singularity without photon sphere

It is generally believed that the shadows of either a black hole or naked singularity arise due to photon spheres developing in these spacetimes. Here we propose a new spherically symmetric naked singularity spacetime solution of Einstein equations which has no photon sphere, and we show that the singularity casts a shadow in the absence of the photon sphere. We discuss some novel features of this shadow and the lightlike geodesics in this spacetime. We compare the shadow of the naked singularity here with shadows cast by Schwarzschild black hole and the first type of Joshi-Malafarina-Narayan (JMN1) naked singularity, where for the last two spacetimes the shadow is formed due to the presence of a photon sphere. It is seen, in particular, that the size of shadow of the singularity is considerably smaller than that of a black hole. Our analysis shows that the shadow of this naked singularity is distinguishable from the shadow of a Schwarzschild black hole and the JMN1 naked singularity. These results are useful and important in the context of recent observations of shadow of the M87 galactic center.

The self-consistent field method and macroscopic Einstein equations for the early universe

The complete theory of cosmological evolution's macroscopic description is constructed with a help of self-consistent field. The theory includes a subsystem of linear equations of perturbations' evolution and nonlinear macroscopic Einstein equations and equations of a scalar field. We provide examples of system's solution which show the principal difference of the cosmological models of the early Universe built on homogenous and locally fluctuating scalar fields. {\bf Keywords}: macroscopic gravitation, self-consistent field, cosmological model, scalar fields, averaging of local fluctuations, asymptotical behavior, cosmological singularity.

Dragging of inertial frames in the composed black-hole-particle system and the weak cosmic censorship conjecture

We analyze a gedanken experiment in which a spinning particle that also possesses an extrinsic orbital angular momentum is captured by a spinning Kerr black hole. The gravitational spin-orbit interaction decreases the energy of the particle, thus allowing one to test the validity of the Penrose weak cosmic censorship conjecture in extreme situations that have not been analyzed thus far. It is explicitly shown that, to leading order in the black-hole-particle interactions, the linearized test particle can over-spin the black hole, thus exposing its inner spacetime singularity to external observers. However, we prove that the general relativistic effect of dragging of inertial frames by the orbiting particle contributes to the energy budget of the system a non-linear black-hole-particle interaction term that ultimately ensures the validity of the Penrose cosmic censorship conjecture in this type of gedanken experiments.

A gravitational collapse singularity theorem consistent with black hole evaporation

The global hyperbolicity assumption present in gravitational collapse singularity theorems is in tension with the quantum mechanical phenomenon of black hole evaporation. In this work I show that the causality conditions in Penrose's theorem can be almost completely removed. As a result, it is possible to infer the formation of spacetime singularities even in the absence of predictability and hence compatibly with quantum field theory and black hole evaporation.

Ergosphere and shadow of a rotating regular black hole

The spacetime singularities in classical general relativity predicted by the celebrated singularity theorems are formed at the end of gravitational collapse. Quantum gravity is the expected theory to resolve the singularity problem but we are now far from it. Therefore attention has shifted to models of regular black holes free from the singularities. A spherically symmetric regular toy model was obtained by Dymnikova (1992) which we demonstrate as an exact solution of Einstein's field equations coupled to nonlinear electrodynamics for a Lagrangian with parameter b related to magnetic charge. We construct rotating counterpart of this solution which encompasses the Kerr black hole as a special case when charge is switched off (b=0). Event Horizon Telescope has released the first image of supermassive black hole M87⁎, revealing the structure near black hole horizon. The rotating regular black hole's shadow may be useful to determine strong field regime. We investigate ergosphere and black hole shadow of rotating regular black hole to infer that their sizes are sensitive to charge b and have a richer chaotic structure. In particular, rotating regular black hole possess larger size, but less distorted shadows when compared with Kerr black holes. We find one to one correspondence between ergosphere and shadow of the black hole.