Different Regions Of Spacetime Research Articles

The Interplay of Fantasy and Physics in King’s The Dark Tower: The Gunslinger: A Physicist’s Perspective

The paper aims to explore the existence of many worlds and their interconnections in Stephen King’s The Dark Tower: The Gunslinger. It draws on theoretical physicist Brian Greene’s concept of parallel universes. It also draws on the theoretical concept of Albert Einstein and Nathan Rosen as they have discussed in ‘Einstein-Rosen Bridge Theory’. This theory is commonly known as wormholes that connect different regions of space-time, enabling the journey from one world to another and back. Greene's theoretical underpinnings, proposing a vast ensemble of universes with distinct properties, find expressions in the narrative. King's narrative, exemplified by, among others, Jake's revival in Mid-World after a presumed death in a New York car accident, explicitly embraces the idea of parallel universes, each with unique physical laws that influence the concepts such as life and death. The narrative unfolds across disparate worlds, echoing Greene’s theoretical mapping of parallel universes, each governed by its unique set of physical laws and realities. In the narrative, the exploration of multiverse concepts employs fiction's imaginative license to investigate interconnected universes and the potential for transcendent journeys through the cosmic fabric. The theoretical backdrop finds resonance in the novel where characters navigate within the four-dimensional continuum, mirroring the speculative nature of multiverse theories. By intertwining the world of fantasy with the hypotheses of physics, the paper discusses the connections between seemingly disparate realms. This perspective bridges literature and theoretical physics, offering a compelling exploration of the speculative landscapes of parallel universes.

A study of traversable wormhole solutions in extended teleparallel theory of gravity with matter coupling

This study is devoted to explore the physical aspects of wormhole geometry under embedded class-1 spacetime in f(T,tau ) gravity, where tau denotes the trace of the energy-momentum tensor and T is the torsion. We derive the embedded class-1 solutions by considering spherically symmetric static spacetime. The shape function is calculated in the framework of embedded class-1 spacetime. It is necessary to mention here that the calculated shape function can be used in other modified theories of gravity. To complete this study, we take diagonal and off-diagonal tetrad, and try to build a comparison by considering the validity region of energy conditions in embedded class-1 spacetime. The embedded surface diagram is given to understand the connection between the two different regions of spacetime. The validity regions of all the energy conditions are calculated. A detailed graphical analysis is provided for validity regions of all the energy conditions. The presence of exotic matter is confirmed in both the cases as the null energy condition is violated.

Inhomogeneous cosmology in an anisotropic Universe

This thesis presents computer simulations of the formation of super-structures in the Universe by solving the equations of Einstein’s theory of gravity: General Relativity. This differs from the usual approach which uses Newton’s law of gravity. We find that different regions of spacetime expand at different rates, but the effect is not sufficient to explain the measured accelerating expansion of the Universe, currently attributed to dark energy. Local differences are also not sufficient to explain the recently measured discrepancy between small-scale and large-scale expansion rates of the Universe. However, they could affect our observations as our instruments become more precise.

Charged wormholes in f(R,T)-extended theory of gravity

Wormholes (WHs) are a solution for General Relativity field equations which characterize a passage or tunnel that connects two different regions of spacetime and is filled by some sort of exotic matter that does not satisfy the energy conditions. On the other hand, it is known that in extended theories of gravity, the extra degrees of freedom once provided may allow the energy conditions to be obeyed and, consequently, the matter content of the WH to be nonexotic. In this work, we obtain, as a novelty in the literature, solutions for charged WHs in the [Formula: see text]-extended theory of gravity. We show that the presence of charge in these objects may be a possibility to respect some stability conditions for their metric. Also, remarkably, the energy conditions are respected in the present approach. In addition, we argue that our framework can be very useful to study the possibility of evolving [Formula: see text] and [Formula: see text]-dimensional WH spacetime within the context of nonlinear electrodynamics, which open a new window to probe the physical quantities in a WH-type solution.

Junction conditions in extended Teleparallel gravities

In the context of extended Teleparallel gravity theories, we address the issue of junction conditions required to guarantee the correct matching of different regions of spacetime. In the absence of shells/branes, these conditions turn out to be more restrictive than their counterparts in General Relativity as in other extended theories of gravity. In fact, the general junction conditions on the matching hypersurfaces depend on the underlying theory and a new condition on the induced tetrads in order to avoid delta-like distributions in the field equations. This result imposes strict consequences on the viability of standard solutions such as the Einstein-Straus-like construction. We find that the continuity of the scalar torsion is required in order to recover the usual General Relativity results.

On the absence of the usual weak-field limit, and the impossibility of embedding some known solutions for isolated masses in cosmologies withf(R)dark energy

The problem of matching different regions of spacetime in order to construct inhomogeneous cosmological models is investigated in the context of Lagrangian theories of gravity constructed from general analytic functions f(R), and from non-analytic theories with f(R)=R^n. In all of the cases studied, we find that it is impossible to satisfy the required junction conditions without the large-scale behaviour reducing to that expected from Einstein's equations with a cosmological constant. For theories with analytic f(R) this suggests that the usual treatment of weak-field systems as perturbations about Minkowski space may not be compatible with late-time acceleration driven by anything other than a constant term of the form f(0), which acts like a cosmological constant. In the absence of Minkowski space as a suitable background for weak-field systems, one must then choose and justify some other solution to perform perturbative analyses around. For theories with f(R)=R^n we find that no known spherically symmetric vacuum solutions can be matched to an expanding FLRW background. This includes the absence of any Einstein-Straus-like embeddings of the Schwarzschild exterior solution in FLRW spacetimes.

Quantum interferometric visibility as a witness of general relativistic proper time.

Current attempts to probe general relativistic effects in quantum mechanics focus on precision measurements of phase shifts in matter–wave interferometry. Yet, phase shifts can always be explained as arising because of an Aharonov–Bohm effect, where a particle in a flat space–time is subject to an effective potential. Here we propose a quantum effect that cannot be explained without the general relativistic notion of proper time. We consider interference of a 'clock'—a particle with evolving internal degrees of freedom—that will not only display a phase shift, but also reduce the visibility of the interference pattern. According to general relativity, proper time flows at different rates in different regions of space–time. Therefore, because of quantum complementarity, the visibility will drop to the extent to which the path information becomes available from reading out the proper time from the 'clock'. Such a gravitationally induced decoherence would provide the first test of the genuine general relativistic notion of proper time in quantum mechanics.

Entropy localization and extensivity in the semiclassical black hole evaporation

I aim to quantify the distribution of information in the Hawking radiation and inside the black hole in the semiclassical evaporation process. The structure of relativistic quantum field theory does not allow one to define a localized entropy unambiguously, but rather forces one to consider the shared information (mutual information) between two different regions of space-time. Using this tool, I first show that the entropy of a thermal gas at the Unruh temperature underestimates the actual amount of (shared) information present in a region of the Rindler space. Then, I analyze the mutual information between the black hole and the late time radiation region. A well-known property of the entropy implies that this is monotonically increasing with time. This means that in the semiclassical picture it is not possible to recover the eventual purity of the initial state in the final Hawking radiation through subtle correlations established during the whole evaporation period, no matter the interactions present in the theory. I find extensivity of the entropy as a consequence of a reduction to a two dimensional conformal problem in a simple approximation. However, the extensivity of information in the radiation region in a full four dimensional calculation seems not to be guaranteed on general grounds. I also analyze the localization of shared information inside the black hole finding that a large amount of it is contained in a small, approximately flat region of space-time near the point where the horizon begins. This gives place to large violations of the entropy bounds. I show that this problem is not eased by backscattering effects and argue that a breaking of conformal invariance is necessary to delocalize the entropy. Finally, I indicate that the mutual information could lead to a way to understand the Bekenstein-Hawking black hole entropy which does not require a drastic reduction in degrees of freedom in order to regulate the entanglement entropy. On the contrary, a large number of field degrees of freedom at high energies giving place to a Hagedorn transition implements a natural distance cutoff in the mutual information, which may in consequence turn out to be bounded.

Consistent histories, the quantum Zeno effect, and time of arrival

We present a decomposition of the general quantum mechanical evolution operator, that corresponds to the path decomposition expansion, and interpret its constituents in terms of the quantum Zeno effect (QZE). This decomposition is applied to a finite dimensional example and to the case of a free particle in the real line, where the possibility of boundary conditions more general than those hitherto considered in the literature is shown. We reinterpret the assignment of consistent probabilities to different regions of spacetime in terms of the QZE. The comparison of the approach of consistent histories to the problem of time of arrival with the solution provided by the probability distribution of Kijowski shows the strength of the latter point of view.

Combining Cauchy and characteristic numerical evolutions in curved coordinates

In numerical relativity there would seem to be considerable advantages in combining Cauchy and characteristic methods in different regions of spacetime. Numerical experiments demonstrate, for the model problem of the scalar wave equation in flat space using general null coordinates, that there are no unforseen problems with the interface between the two regions.

Double Laplace Transformation in Mixed Boundary-Initial Value Problems

A comprehensive treatment of the application of the double Laplace transform to the combined boundary-initial value problem for systems of linear, hyperbolic, partial differential equations with constant coefficients is given. The treatment is restricted to two independent variables x and t. A discussion of the relations among the boundary and initial conditions necessary for a well-formulated problem is given, and it is shown that the solution subject to these restrictions does satisfy the boundary and initial conditions. An extensive examination of the solution in different regions of space-time is given, and the connection between this solution and the more common ``normal-mode'' solution proportional to exp[ikx − iωl(k)t] or exp[ikl(ω)x − iωt] is discussed. A generalized wave equation is used throughout the paper for illustration.