We consider a cosmological model based upon a non-canonical noncommutative extension of the Heisenberg-Weyl algebra to address the thermodynamical stability and the singularity problem of both the Schwarzschild and the Kantowski-Sachs black holes. The interior of the black hole is modelled by a noncommutative extension of the Wheeler-DeWitt equation. We compute the temperature and entropy of a Kantowski-Sachs black hole and compare our results with the Hawking values. Again, the noncommutativity in the momenta sector allows us to have a minimum in the potential, which is relevant in order to apply the Feynman-Hibbs procedure. For Kantowski-Sachs black holes, the same model is shown to generate a non-unitary dynamics, predicting vanishing total probability in the neighborhood of the singularity. This result effectively regularizes the Kantowski-Sachs singularity and generalizes a similar result, previously obtained for the case of Schwarzschild black hole.
We illustrate the recently proposed generalized unimodular gravity using simple examples of the Friedmann, Kantowski-Sachs and Schwarzschild geometries and show that it can be further generalized and reveal some unexpected and interesting effects.
The dynamics of the vacuum Kantowski-Sachs space-time are studied in the so-called limiting curvature mimetic gravity theory. It is shown that in this theory the vacuum Kantowski-Sachs space-time is always singular. While the departures from general relativity due to the limiting curvature mimetic theory do provide an upper bound on the magnitude of the expansion scalar, both its rate of oscillations and the magnitude of the directional Hubble rates increase without bound and cause curvature invariants to diverge. Also, since the radial scale factor does not vanish in finite (past) time, in th…
In the context of scalar-torsion theory we investigate the evolution of the cosmological anisotropies for a Kantowski-Sachs background geometry. We study the phase-space of the gravitational field equations by determining the admitted stationary points and study their stability properties. For the potential function of the non-minimally coupled scalar field we assume the exponential and the power-law functions. Finally, we make use of Poincare variables in order to investigate the existence of stationary points at the infinity regime of the dynamics.
Exact and analytic solutions in Einstein-Aether scalar field theory with Kantowski-Sachs background space are determined. The theory of point symmetries is applied to determine the functional form of the unknown functions which defines the gravitational model. Conservation laws are applied to reduce the order of the field equations and write the analytic solution. Moreover, in order to understand the physical behaviour of the cosmological model a detailed analysis of the asymptotic behaviour for the gravitational field equations is performed.
We study quantum cosmology of the $2D$ Jackiw-Teitelboim (JT) gravity with $Λ>0$ and calculate the Hartle-Hawking (HH) wave function for this model in the minisuperspace framework. Our approach is guided by the observation that the JT dynamics can be mapped exactly onto that of the Kantowski-Sachs (KS) model describing a homogeneous universe with spatial sections of $S^1\times S^2$ topology. This allows us to establish a JT-KS correspondence between the wave functions of the models. We obtain the semiclassical Hartle-Hawking wave function by evaluating the path integral with appropriate bounda…
It is shown that like Bianchi I, V and IX models, a Kantowski-Sachs cosmological model also allows a unitary evolution on quantization. It has also been shown that this unitarity is not at the expense of the anisotropy. Non-unitarity, if there is any, cannot escape notice in this as the evolution is studied against a properly oriented time parameter fixed by the evolution of the fluid. Furthermore, we have constructed a wave-packet by superposing different energy eigenstates, thereby establishing unitarity in a non-trivial way, which is a stronger result than an energy eigenstate trivially giv…
In this paper we study the quantum cosmological Kantowski-Sachs model and solve the Wheeler-DeWitt equation in minisuperspace to obtain the wave function of the corresponding universe. The perfect fluid is described by the Schutz's canonical formalism, which allows to attribute dynamical degrees of freedom to matter. The time is introduced phenomenologically using the fluid's degrees of freedom. In particular, we adopt a stiff matter fluid. The viability of this model is analyzed and discussed.
The Kantowski-Sachs cosmological model sourced by a Skyrme field and a cosmological constant is considered in the framework of General Relativity. Assuming a constant radial profile function for the hedgehog ansatz, the Skyrme contribution to Einstein equations is shown to be equivalent to an anisotropic fluid. Using dynamical system techniques, a qualitative analysis of the cosmological equations is presented. Physically interesting features of the model such as isotropization, bounce and recollapse are discussed.
We use a path-integral approach to study the tunneling wave function in quantum cosmology with spatial topology $S^{1}\times S^{2}$ and positive cosmological constant (the Kantowski-Sachs model). If the initial scale factors of both $S^1$ and $S^2$ are set equal to zero, the wave function describes (semiclassically) a universe originating at a singularity. This may be interpreted as indicating that an $S^1\times S^2$ universe cannot nucleate out of nothing in a non-singular way. Here we explore an alternative suggestion by Halliwell and Louko that creation from nothing corresponds in this mode…
The system under study is the $Λ$-Kantowski-Sachs universe. Its canonical quantization is provided based on a recently developed method: the singular minisuperspace Lagrangian describing the system, is reduced to a regular (by inserting into the dynamical equations the lapse dictated by the quadratic constraint) possessing an explicit (though arbitrary) time dependence; thus a time-covariant Schrödinger equation arises. Additionally, an invariant (under transformations $t=f(\tilde{t})$) decay probability is defined and thus ``observers'' which correspond to different gauge choices obtain, by d…
The quantum mechanics of Schwarzschild-de Sitter black holes is of great recent interest because of their peculiar thermodynamic properties as well as their realization in modern dark energy cosmology which indicates the presence of a small positive cosmological constant. We study Schwarzschild-de Sitter black holes and also the Kantowki-Sachs Cosmology using quantum computing. In these cases in addition to the Hamiltonian there is a Mass operator which plays an important role in describing the quantum states of the black hole and Kantowski-Sachs cosmology. We compute the spectrum of these ope…
We apply the Regge-Wheeler formalism to study axial and polar gravitational waves in Kantowski-Sachs universe. The background field equations and the linearised perturbation equations for the modes are derived in presence of matter. To find analytical solutions, we analyze the propagation of waves in vacuum spacetime. The background field equations in absence of matter are solved by assuming the expansion scalar to be proportional to the shear scalar. Using the method of separation of variables, the axial perturbation parameter $ h_0(t, r) $ is obtained from its wave equation. The other pertur…
We investigate Kantowski-Sachs models in Einstein-æther theory with a perfect fluid source using the singularity analysis to prove the integrability of the field equations and dynamical system tools to study the evolution. We find an inflationary source at early times, and an inflationary sink at late times, for a wide region in the parameter space. The results by A. A. Coley, G. Leon, P. Sandin and J. Latta (JCAP 12, 010, 2015), are then re-obtained as particular cases. Additionally, we select other values for the non-GR parameters which are consistent with current constraints, getting a very…
The loop quantum dynamics of Kantowski-Sachs spacetime and the interior of higher genus black hole spacetimes with a cosmological constant has some peculiar features not shared by various other spacetimes in loop quantum cosmology. As in the other cases, though the quantum geometric effects resolve the physical singularity and result in a non-singular bounce, after the bounce a spacetime with small spacetime curvature does not emerge in either the subsequent backward or the forward evolution. Rather, in the asymptotic limit the spacetime manifold is a product of two constant curvature spaces. …
We show that the Kantowski--Sachs model of a Schwarzschild black hole interior can be slightly generalized in order to accommodate spatial metrics of different orientations, and in this formulation the equations of motion admit a variable redefinition that makes the system regular at the singularity. This system will then traverse the singularity in a deterministic way (information will be conserved through it), and evolve into a time-reversed and orientation-flipped Schwarzschild white hole interior.
A Kantowski-Sachs model with a modified quantization prescription is considered. Such quantization rules, inspired by the so-called Generalized Uncertainty Principle (GUP), correspond to a modified commutation relation between minisuperspace variables and their conjugate momenta. For a wide range of the modification parameter, this approach differentiates from the standard results by the presence of a potential well in the corresponding Wheeler-DeWitt equation. This then produces the appearance of a set of wave functions, with corresponding discrete energy spectrum.
We show that as in the case of isotropic models, the `Dirac Algorithm' and `Modified Horowitz' Formalism' lead to identical phase-space structure of the Hamiltonian for the gravitational action with curvature squared terms, in anisotropic space-time, viz, Bianchi-I, Bianchi-III and Kantowski-Sachs models too.
The classical Einstein-Standard Model system with conformally invariant coupling of the Higgs field to gravity is investigated in nearly Schwarzschild black holes. We show that, in the presence of Kantowski-Sachs symmetries, there is a finite critical value of the mean curvature such that on spacelike hypersurfaces with greater mean curvature the Higgs sector does not have any symmetry breaking vacuum state. Hence, according to the Standard Model of particle physics, the gauge and spinor fields do not have rest mass and electric charge. Therefore, particles falling into a nearly Schwarzschild …
Anisotropic cosmologies are studied in the case where the matter source is given by the Skyrme model which is an effective description of low energy QCD. The dynamical evolution of the Kantowski-Sachs and Bianchi-I universes are analyzed in depth. In both situations in order for solutions to exist and at the same time to avoid finite time future singularities, bounds on the value of the cosmological constant and on the values of the Skyrme couplings must be set. The upper bound on the cosmological constant, which depends also on the initial conditions is closely related to the fact that the ba…
This paper analyzes the supersymmetric solutions to five and six-dimensional minimal (un)gauged supergravities for which the bilinear Killing vector constructed from the Killing spinor is null. We focus on the spacetimes which admit an additional ${\rm SO}(1,1)$ boost symmetry. Upon the toroidal dimensional reduction along the Killing vector corresponding to the boost, we show that the solution in the ungauged case describes a charged, nonextremal black hole in a Friedmann-Lemaître-Robertson-Walker (FLRW) universe with an expansion driven by a massless scalar field. For the gauged case, the so…
