Cosmological Singularity Research Articles

Relics of the quantum spacetime: from Synge’s world function as the fundamental probe of spacetime architecture to the emergent description of gravity

All our observations that characterise space and time are expressed in terms of non-local, bi-tensorial objects such as geodesic intervals between events and two-point (Green) functions. In this contribution, I highlight the importance of characterising spacetime geome-try in terms of such non-local objects, focusing particularly on two important bi-tensors that play a particular fundamental role – Synge’s World function and the van Vleck determinant. I will first discuss how these bi-tensors help capture information about spacetime geometry, and then describe their role in characterising quantum spacetime endowed with a lower bound, say ℓ 0, on spacetime intervals. Incorporating such a length scale in a Lorentz covariant manner necessitates a description of spacetime geometry in terms of above bi-tensors, and naturally replaces the conventional description based on the metric tensor gab (x) with a description in terms of a non-local bi-tensor qab (x, y). The non-analytic structure of qab (x, y) which renders a perturbative expansion in ℓ 0 meaningless, also generically leaves a non-trivial “relic” in the limit ℓ 0 → 0. I present some results where such a relic term is manifest; specifically, I will discuss how this: (i) suggests a description of gravitational dynamics different from the one based on Einstein-Hilbert lagrangian, (ii) implies dimensional reduction to 2 at small scales, (iii) connects with the notion of cosmological constant itself being a non-local vestige of the small scale structure of spacetime, (iv) helps address the issues of spacetime singularities. I will conclude by discussing the ramifications of these ideas for quantum gravity.

Black Hole Spectra from Vaz's Quantum Gravitational Collapse

AbstractIn 2014, in a famous paper Hawking strongly criticized the firewall paradox by claiming that it violates the equivalence principle and breaks the CPT invariance of quantum gravity. He proposed that the final result of the gravitational collapse should not be an event horizon, but an apparent horizon instead. On the other hand, Hawking did not give a mechanism for how this could work. In the same year, Vaz endorsed Hawking's proposal in a quantum gravitational model of dust collapse by winning the Second Prize in the 2014 Gravity Research Foundation Essay Competition. He indeed showed that continued collapse to a singularity can only be obtained if one combines two independent and entire solutions of the Wheeler‐DeWitt equation. Vaz's interpretation of the paradox was in terms of simply forbidding such a combination. This leads naturally to matter condensing on the apparent horizon during quantum collapse. In that way, an entirely new framework for black holes (BHs) has emerged. The approach of Vaz was also consistent with Einstein's idea in 1939 of the localization of the collapsing particles within a thin spherical shell. In this work we derive the BH mass and energy spectra via a Schrodinger‐like approach, by further supporting Vaz's conclusions that instead of a spacetime singularity covered by an event horizon, the final result of the gravitational collapse is an essentially quantum object, an extremely compact “dark star”. This “gravitational atom” is held up not by any degeneracy pressure but by quantum gravity in the same way that ordinary atoms are sustained by quantum mechanics. Finally, by evoking the generalized uncertainty principle, the maximum value of the density of Vaz's shell will be estimated.

Lense–Thirring effect and precession of timelike geodesics in slowly rotating black hole and naked singularity spacetimes

In this paper, we investigate the properties of the Lense-Thirring precession frequency and periastron precession of the relativistic bound orbits in slowly rotating naked singularity spacetimes. We show that the precession frequencies of a stationary test gyroscope are quite unique in slowly rotating naked singularity spacetimes, and therefore, one can easily distinguish them from the slowly rotating Kerr black hole spacetime. On the other hand, we also show that in slowly rotating Joshi-Malafarina-Narayan (JMN1) naked singularity spacetime, negative precession of the timelike bound orbits is allowed which is not possible in Kerr and slowly rotating null naked singularity spacetimes.

Dispersive censor of acoustic spacetimes with a shock-wave singularity

A dispersionless shock wave in a fluid without friction develops an acoustic spacetime singularity which is naked (not hidden by a horizon). We show that this naked nondispersive shock-wave singularity is prohibited to form in a Bose-Einstein condensate, due to the microscopic structure of the underlying ${\rm a}\!{\rm e}$ther and the resulting effective trans-Planckian dispersion. Approaching the instant of shock $t_{\rm shock}$, rapid spatial oscillations of density and velocity develop around the shock location, which begin to emerge already slightly before $t_{\rm shock}$, due to the quantum pressure in the condensate. These oscillations render the acoustic spacetime structure completely regular, and therefore lead to a removal (censoring) of the spacetime singularity. Thus, distinct from the cosmic censorship hypothesis of Penrose formulated within Einsteinian gravity, the quantum pressure in Bose-Einstein condensates censors (prohibits) the formation of a naked shock-wave singularity, instead of hiding it behind a horizon.

THE MAIN CONCEPTIONS FOR LANGUAGE 1 AND LANGUAGE 2 ACQUIRING

Socio-biology is the Darwinian framework of aimless natural selection for random changes in matter in motion derives an atheistic position from But from the first cosmic singularity to free will, explanatory gaps in the sociobiological account of religion invite God's foot at the door. Yoga about the anatomical connection between humans and God By interpreting the Taoist, Taoist, and Kabbalistic descriptions not as primitive, poetic tropes, but as internal receptions of little-known, enigmatic, epigenetically repressed structures, Leissner fibers and called the nervous system. I propose a new theistic sociobiological theory of religion. A valid belief in this theory could epigenetically awaken repressed Leissner fiber genes and initiate empirical testing of the theory.

Regular black holes and horizonless ultra-compact objects in Lorentz-violating gravity

There is growing evidence that Hořava gravity may be a viable quantum theory of gravity. It is thus legitimate to expect that gravitational collapse in the full, non-projectable version of the theory should result in geometries that are free of space-time singularities. Previous analyses have shown that such geometries must belong to one of the following classes: simply connected regular black holes with inner horizons; non-connected black holes “hiding” a wormhole mouth (black bounces); simply connected or non-connected horizonless compact objects. Here, we consider a singular black hole in the low-energy limit of non-projectable Hořava gravity, i.e. khronometric theory, and describe examples of its possible “regularisations”, covering all of the viable classes. To our knowledge, these examples constitute the first instances of black holes with inner universal horizons, of black bounces and of stars with a de Sitter core in the context of Lorentz-violating theories of gravity.

Resolution of Cosmological Singularity in Hořava–Lifshitz Cosmology

The standard ΛCDM model, despite its agreement with observational data, still has some issues unaddressed, such as the problem of initial singularity. Solving that problem usually requires modifications of general relativity. However, there appeared the Hořava–Lifshitz (HL) theory of gravity, in which equations governing cosmological evolution include a new term scaling similarly as the dark radiation term in the Friedmann equations, enabling a bounce of the universe instead of initial singularity. This review describes past works on the stability of such a bounce in different formulations of HL theory, an initial detailed balance scenario, and further projectable versions containing higher than quadratic terms to the original action.

Bouncing cosmology in modified gravity with higher-order curvature terms

A bouncing scenario of a flat homogeneous and isotropic universe is explored by using the reconstruction technique for the power-law parametrization of the Hubble parameter in a modified gravity theory with higher-order curvature and trace of the energy-momentum tensor terms. It is demonstrated that bouncing criteria are satisfied so that the cosmological initial singularity can be avoided. In addition, it is shown that the equation of state parameter crosses the line of the phantom divide. In the present scenario, the universe is filled with perfect fluid around the bouncing point, in which the universe becomes highly unstable and a big bounce can be realized. Furthermore, it is found that extremal acceleration occurs at the bouncing point.

Three dimensional regular black string via loop corrections

It is well known that some spacetime singularities of low energy effective action can be resolved by the effective loop corrections. However, the known potentials for the loop corrections fail to regulate the singularity of three dimensional black string. An alternative method is to introduce an extra flat spatial direction and boost away the singularity by using the O(d, d) rotation with the special Kalb-Ramond field. In this paper, we investigate a new set of non-local dilaton potentials for the effective loop corrections. The result shows that the singularity of three dimensional black string can be consistently resolved by the loop corrections.

Irrefutable Proof of The Non-Existence of a ‎Gravitational ‎Singularity at The Centre of a ‎Black Hole

Astronomical observations confirm that gravitational force decreases with the square of the distance. If the gravitational ‎force in the centre of Sagittarius A* were close to infinity and would decrease with the square of the distance, our Milky Way ‎could not exist as we observe it. This fact is irrefutable proof that there is no gravitational singularity in the centre of ‎Sagittarius A* and in general, there is no gravitational singularity in the centre of a black hole.‎

THE TORN DIRECTION OF ASIAN LITERATURE

Socio-biology is the Darwinian framework of aimless natural selection for random changes in matter in motion derives an atheistic position from But from the first cosmic singularity to free will, explanatory gaps in the sociobiological account of religion invite God's foot at the door. Yoga about the anatomical connection between humans and God By interpreting the Taoist, Taoist, and Kabbalistic descriptions not as primitive, poetic tropes, but as internal receptions of little-known, enigmatic, epigenetically repressed structures, Leissner fibers and called the nervous system. I propose a new theistic sociobiological theory of religion. A valid belief in this theory could epigenetically awaken repressed Leissner fiber genes and initiate empirical testing of the theory.

Quantum resolution of the cosmological singularity without new physics

We study a quantum Hot Big Bang in the connection representation, with a matter constant of motion m whose conjugate defines time. Superpositions in m induce a unitary inner product. The wave function reveals a resolution of the singularity problem without new physics or supplementary boundary conditions. Backtracking in time, the probability peak eventually halts at a maximum curvature, its height dropping thereafter while a symmetric contracting peak rises. The Big Bang is replaced by a superposition of contracting and expanding regular Universes. We contrast these findings with the situation in the metric representation, where boundary conditions at the singularity are needed for unitary evolution.

Quantum dynamics of gravitational massive shell

The quantum dynamics of a self-gravitating thin matter shell in vacuum has been considered. Quantum Hamiltonian of the system is positive definite. Within chosen set of parameters, the quantum shell bounces above the horizon. Considered quantum system does not collapse to the gravitational singularity of the corresponding classical system.

Quantum dynamics corresponding to the chaotic BKL scenario

We quantize the solution to the Belinski– Khalatnikov–Lifshitz (BKL) scenario using the integral quantization method. Quantization smears the gravitational singularity, preventing its localization in the configuration space. The latter is defined in terms of spatial and temporal coordinates, which are treated on the same footing that enables the respective covariance of general relativity. The relative quantum perturbations grow as the system evolves towards the gravitational singularity. The quantum randomness amplifies the deterministic classical chaos of the BKL scenario. Additionally, our results suggest that the generic singularity of general relativity can be avoided at a quantum level, giving support to the expectation that quantum gravity has a good chance of being a regular theory.

Big rip in shift-symmetric Kinetic Gravity Braiding theories

We revise the future fate of a group of scalar-tensor theories known as kinetic gravity braiding models. As it is well-known, these theories can safely drive the expansion of the universe towards a future de Sitter state if the corresponding Lagrangian is invariant under constant shifts in the scalar field. However, this is not the only possible future state of these shift-symmetric models as we show in this letter. In fact, future cosmic singularities characterized by a divergence of the energy density can also appear in this framework. We present an explicit example where a big rip singularity is the only possible future fate of the cosmos.

Quantization of a black-hole gravity: geometrodynamics and the quantum

Quantum gravity is effective in domains where both quantum effects and gravity are essential, such as in the vicinity of space-time singularities. This paper will investigate the quantization of a black-hole gravity, particularly the region surrounding the singularity at the origin of the coordinate system. Describing the system with a Hamiltonian formalism, we apply the covariant integral quantization method to find the Wheeler–DeWitt equation of the model. We find that the quantized system has a discrete energy spectrum in the region inside the event horizon. Through the Kantowski–Sachs metric, it is possible to correlate the entropic time, which gives the dynamics for this model, to the cosmic time in a non-trivial way. Different configurations for the phase space of a Schwarzschild black hole are obtained in a semi-classical analysis. For lower-energy states, the quantum corrections result in singularity removal and wormhole formation.

Regular black holes, universes without singularities, and phantom-scalar field transitions

We consider a procedure of elimination of cosmological singularities similar to that suggested in the recent paper by Simpson and Visser for the construction of regular black holes. It is shown that by imposing a nonsingular cosmological evolution with a bounce in a flat Friedmann universe filled with a minimally coupled scalar field, we obtain a transition between the standard scalar field and its phantom counterpart. In this case, the potential of the scalar field has a nonanalyticity of the cusp type. This result is also readily reproduced in the case of an anisotropic Bianchi I universe. We have also found a spherically symmetric static solution of the Einstein equations, free of singularities and sustained by a scalar field.

Energy does not have a Gravitational Mass (Flaw of the Einstein’s gravitational theory)

According to the Einstein’s gravitational theory, the zero-point energy in the vacuum will collapse the universe into a gravitational singularity if the cut-off frequency of the zero-point field is the Plank frequency. But, according to the ZPF gravity theory proposed by the author, the energy dose not have a gravitational mass as claimed by the Einstein’s gravitational theory. From which, it is considered that Einstein’s gravitational theory is not correct.

Universal estimates and Liouville theorems for superlinear problems without scale invariance

<p style='text-indent:20px;'>We revisit rescaling methods for nonlinear elliptic and parabolic problems and show that, by suitable modifications, they may be used for nonlinearities that are not scale-invariant even asymptotically and whose behavior can be quite far from power like.</p><p style='text-indent:20px;'>In this enlarged framework, by adapting the doubling-rescaling method from [<xref ref-type="bibr" rid="b37">37</xref>, <xref ref-type="bibr" rid="b38">38</xref>], we show that the equivalence found there between universal estimates and Liouville theorems remains valid. In the parabolic case we also prove a Liouville type theorem for a rather large class of non scale-invariant nonlinearities. This leads to a number of new results for non scale-invariant elliptic and parabolic problems, concerning space or space-time singularity estimates, initial and final blow-up rates, universal and a priori bounds for global solutions, and decay rates in space and/or time.</p><p style='text-indent:20px;'>We illustrate our approach by a number of examples, which in turn give indication about the optimality of the estimates and of the assumptions.</p>

Spacetime singularities and curvature blow-ups

The singularity theorems of Penrose, Hawking, and Geroch predict the existence of incomplete inextendible causal geodesics in a wide range of physically adequate spacetimes modeling the gravitational collapse of stars and the expanding universe. Here, using results on spacetime extensions, it is shown that if a suitable low regular form of the strong cosmic censor hypothesis holds, then parallelly propagated blow-up of either the tidal force or frame-drag part of the curvature must occur in “generic” timelike geodesically incomplete maximal Cauchy developments.