Gravastar in the framework of symmetric teleparallel gravity

We present a novel gravastar model based on the Mazur-Mottola (2004) method with an isotropic matter distribution in \begin{document}$ f(Q) $\end{document} gravity. The gravastar, which is a hypothesized substitute for a black hole, is built using the Mazur-Mottola mechanism. This approach allows us to define the gravastar as having three stages. The first one is an inner region with negative pressure; the next region is a thin shell that is made up of ultrarelativistic stiff fluid, and we studied the proper length, energy, entropy, and surface energy density for this region. Additionally, we demonstrated the possible stability of our suggested thin shell gravastar model through the graphical study of the surface redshift. The exterior Schwarzschild geometry describes the outer region of the gravastar. In the context of \begin{document}$ f(Q) $\end{document} gravity, we discovered analytical solutions for the interior of gravastars that are free of any type of singularity and the event horizon.     

Problem of time in quantum gravity

The Problem of Time occurs because the ‘time’ of GR and of ordinary Quantum Theory are mutually incompatible notions. This is problematic in trying to replace these two branches of physics with a single framework in situations in which the conditions of both apply, e.g. in black holes or in the very early universe. Emphasis in this Review is on the Problem of Time being multi‐faceted and on the nature of each of the eight principal facets. Namely, the Frozen Formalism Problem, Configurational Relationalism Problem (formerly Sandwich Problem), Foliation Dependence Problem, Constraint Closure Problem (formerly Functional Evolution Problem), Multiple Choice Problem, Global Problem of Time, Problem of Beables (alias Problem of Observables) and Spacetime Reconstruction/Replacement Problem. Strategizing in this Review is not just centred about the Frozen Formalism Problem facet, but rather about each of the eight facets. Particular emphasis is placed upon A) relationalism as an underpinning of the facets and as a selector of particular strategies (especially a modification of Barbour relationalism, though also with some consideration of Rovelli relationalism). B) Classifying approaches by the full ordering in which they embrace constrain, quantize, find time/history and find observables, rather than only by partial orderings such as “Dirac‐quantize”. C) Foliation (in)dependence and Spacetime Reconstruction for a wide range of physical theories, strategizing centred about the Problem of Beables, the Patching Approach to the Global Problem of Time, and the role of the question‐types considered in physics. D) The Halliwell‐ and Gambini–Porto–Pullin‐type combined Strategies in the context of semiclassical quantum cosmology.     

Vassiliev invariants: A new framework for quantum gravity

We show that Vassiliev invariants of knots, appropriately generalized to the spin network context, are loop differentiable in spite of being diffeomorphism invariant. This opens the possibility of defining rigorously the constraints of quantum gravity as geometrical operators acting on the space of Vassiliev invariants of spin nets. We show how to explicitly realize the diffeomorphism constraint on this space and present proposals for the construction of Hamiltonian constraints.     

Probabilistic time and the quantum gravity interpretation

We analyze the perturbed minisuperspace models of quantum gravity through the analogy with the time-independent Schrödinger equation. We show that a time variable defined in a previous work, the probabilistic time, is the variable which yields the backreaction Einstein equations.     

New cosmological models in the framework of a gauge theory of gravity

The paper is devoted to the presentation of the new cosmological solutions obtained by the author within the framework of a gauge theory of gravitation. The models are a combination of evolving models and steady-state models.     

A sum-over-histories account of an EPR(B) experiment

We analyze a variant of the EPRB experiment within a framework for quantum mechanics that rests on a radical interpretation of the sum over histories. Within this framework, reality is (just as classically) a single history, e.g. a definite collection of particles undergoing definite motions; and quantum dynamics appears as a kind of stochastic law of motion for that history, a law formulated in terms of non-classical probability-amplitudes. No state vectors enter this framework, and their attendant nonlocality is therefore absent as well.1. That is, before pair creations and annihilations were discovered. (The electronic and nuclear spins might also be regarded as new aspects of their kinematics. But perhaps spin is better construed, within the sum-over-histories framework, as a quality of a more dynamical character, namely as a generalized sort of probability-amplitude.)2. A possible escape would be the so-called Everett interpretation, in which the collapse never occurs, but its effects are supposed to be recovered via a more careful analysis of closed systems in which measurement-like processes take place. Among other things, this approach tends to lead either to the view that nothing really happens [1] or to the view that everything really happens [2] (which perhaps is not that different from the former view).3. For example, the rule, collapse occurs along the past light cone (in the Heisenberg picture), appears to be consistent.4. And Bell's inequality shows thatany theory formulated in terms of an instantaneous state evolving in time would encounter the same trouble. Indeed, the trouble shows up even more glaringly if one adapts Bell's argument to spin-1 systems, using the results of Kochen and Specker[10]. In order to use the Kochen-Specker results in the EPR manner one needs a scheme for measuring the relevant observables, but this can be accomplished by means of suitably concatenated Stern-Gerlach analyzers with recombining beams [13]. Then, as Allen Stairs has pointed out [14], even the perfect correlations become impossible to reproduce, and no reference to probability theory is needed to establish a contradiction with locality. Recently, an analogous experiment using three spin 1/2 particles instead of two spin 1 particles has also been given [15].5. No technical problem obstructs an extension to fermionic fields (indeed the functional integral formalism for Quantum Field Theory is probably the most popular at present), but the realistic interpretation of the individual histories seems to get lost. One way out would be if all fermions were composites or collective excitations of fields quantized according to bosonic commutation relations. Another would be if the particle formulation were taken as basic, with the complementary field formulation being merely a mathematical artifice (at least for fermions).6. In the approach of Gell-Mann-Hartle and Griffiths for example, only a small subset of the possible partitions is granted meaning, in such a way that all interference terms are suppressed and quantum probabilities reduce to classical ones.7. In stating these rules we consider an idealized situation in which the spatio-temporal indeterminacy of particle-locationwithin a given one of our trajectories is ignored; or if you prefer, you can take the experiment as only a Gedanken one affording a simplified illustration of how EPR-like correlations are understood within the sum-over-histories framework. In this connection recall also that the semiclassical propagator is in fact exact for a free particle.8. This can be interpreted either as part of the specification of the initial conditions, or (as suggested by a referee) merely as an example of relativization of probabilities.9. Thus a state vector may be defined as an equivalence-class of sets of partial histories.10. One such generalization applies to open systems, for example to a particle in contact with a heat reservoir. For this example see [11], wherein the two-way path formalism of §5 above is used, and the influence of the reservoir results in an effective dynamics for the particle in which the forward and backward portions of its world-line are coupled to each other by a certain interaction term in the amplitude. In this type of situation a density-operator (though not a state vector ) can still be introduced, but it no longer summarizes all the relevant information about the past (and correspondingly its evolution lacks the Markov property that(t + dt) is determined by(t) alone). For quantum gravity, it may be that not even such a non-Markov will be exactly definable, and only the global probabilities themselves will make sense.11. Ironically it is just this property of the amplitudes which, as mentioned above, makes possible the introduction of the state vectors whose collapse then introduces such a strong appearance ofnonlocality into the theory.     

Quantum gravity,the origin of time and time's arrow

The local Lorentz and diffeomorphism symmetries of Einstein's gravitational theory are spontaneously broken by a Higgs mechanism by invoking a phase transition in the early universe, at a critical temperature T_c below which the symmetry is restored. The spontaneous breakdown of the vacuum state generates an external time, and the wave function of the universe satisfies a time-dependent Schrödinger equation, which reduces to the Wheeler-deWitt equation in the classical regime for T<T_c, allowing a semiclassical WKB approximation to the wave function. The conservation of energy is spontaneously violated for T>T_c, and matter is created fractions of seconds after the big bang, generating the matter in the Universe. The time direction of the vacuum expectation value of the scalar Higgs field generates a time asymmetry, which defines the cosmological arrow of time and the direction of increasing entropy as the Lorentz symmetry is restored at low temperatures.     

Common time in a four-dimensional symmetry framework

Following the ideas of Poincaré, Reichenbach, and Grunbaum concerning the convention of setting up clock systems, we analyze clock systems and light propagation within the framework of four-dimensional symmetry. It is possible to construct a new four-dimensional symmetry framework incorporatingcommon time: observers in different inertial frames of reference use one and the same clock system, which is located in any one of the frames. Consequently, simultaneity has a meaning independent of position and independent of frame of reference. A further consequence is that the two-way speeds of light alone are isotropic in any frame. By the choice of clock system there will be one frame in which the one-way speed of light is isotropic. This frame can be arbitrarily chosen. The difference between one-way speeds and two-way speeds of light signals is considered in detail.Work supported by the NRC, NASA, and the U.S. DOE.     

A predictive framework for quantum gravity and black hole to white hole transition

The apparent incompatibility between quantum theory and general relativity has long hampered efforts to find a quantum theory of gravity. The recently proposed positive formalism for quantum theory purports to remove this incompatibility. We showcase the power of the positive formalism by applying it to the black hole to white hole transition scenario that has been proposed as a possible effect of quantum gravity. We show how the characteristic observable of this scenario, the bounce time, can be predicted within the positive formalism, while a traditional S-matrix approach fails at this task. Our result also involves a conceptually novel use of positive operator valued measures.     

Phase transition in conformal gravity with cosmological time background

We study phase transitions and calculate the critical temperature in conformal gravity and we show also that a phase transition occurs with merons only in the cosmological time background.     

On the resolution of time problem in quantum gravity induced from unconstrained membranes

The relativistic theory of unconstrained p-dimensional membranes (p-branes) is further developed and then applied to the embedding model of induced gravity. Space-time is considered as a 4-dimensional unconstrained membrane evolving in an N-dimensional embedding space. The parameter of evolution or the evolution time is a distinct concept from the coordinate time t=x⁰. Quantization of the theory is also discussed. A covariant functional Schrödinger equation has a solution for the wave functional such that it is sharply localized in a certain subspace P of space-time, and much less sharply localized (though still localized) outside P. With the passage of evolution the region P moves forward in space-time. Such a solution we interpret as incorporating two seemingly contradictory observations: (i) experiments clearly indicate that space-time is a continuum in which events are existing; (ii) not the whole 4-dimensional space-time, but only a 3-dimensional section which moves forward in time, is accessible to our immediate experience. The notorious problem of time is thus resolved in our approach to quantum gravity. Finally we include sources into our unconstrained embedding model.     

The role of singular spinor fields in a torsional gravity,Lorentz-violating,framework

In this work, we consider a generalization of quantum electrodynamics including Lorentz violation and torsional-gravity, in the context of general spinor fields as classified in the Lounesto scheme. Singular spinor fields will be shown to be less sensitive to the Lorentz violation, as far as couplings between the spinor bilinear covariants and torsion are regarded. In addition, we prove that flagpole spinor fields do not admit minimal coupling to the torsion. In general, mass dimension four couplings are deeply affected when singular—flagpoles—spinors are considered, instead of the usual Dirac spinors. We also construct a mapping between spinors in the covariant framework and spinors in Lorentz symmetry breaking scenarios, showing how one may transliterate spinors of different classes between the two cases. Specific examples concerning the mapping of Dirac spinor fields in Lorentz violating scenarios into flagpole and flag-dipole spinors with full Lorentz invariance (including the cases of Weyl and Majorana spinors) are worked out.     

Initial-data formulation of tetrad gravity utilizing York's extrinsic time approach

An ability to analyze the geometrodynamic degrees of freedom and initial-data formulation is central to the canonical quantization of gravity. In the metric theory of gravity York provided the most powerful technique to analyze the dynamic degrees of freedom and to solve the initial-data problem. In this paper we extend York's analysis to tetrad gravity. Such an extension is necessary for the quantization of gravity when coupled to a half-integer-spin field. We present a comparative analysis of the geometric information carried by (1) a 3-metric of an initial hypersurface and (2) the spacelike triad of a time-gauged tetrad. We apply the tetrad initial-data formulation to Ashtekar's connection variables, and provide a comparison with other alternative choices of canonical tetrad variables.