Minkowski Space Research Articles

A perturbative production of massive Z bosons and fermion–antifermion pairs from the vacuum in the de Sitter Universe

In this paper we study the problem of neutral electro-weak interactions in a de Sitter geometry. We develop the formalism of reduction for the Proca field with the help of the solutions for the interacting fields and by using perturbative methods we obtain the definition of the transition amplitudes in the first order of perturbation theory. As an application to our formalism we study the generation of massive fermions and Z bosons from vacuum in the expanding de Sitter universe. Our results are the generalization to the curved geometry of the Weinberg–Salam electro-weak theory for the case of Z boson interaction with leptons. The probability is found to be a quantity that depends on the Hubble parameter and we prove that such perturbative processes are possible only for large expansion regime of the early Universe. The total probability and rate of transition are obtained for the case of large expansion and we use the dimensional regularization for extract finite results from the momenta integrals. In the Minkowski limit we obtain that the probability of particle generation from vacuum is vanishing recovering the well known result that forbids particle production in flat space-time due to the momentum-energy conservation.

Deflection angle, quasinormal modes and optical properties of a de Sitter black hole in [formula omitted] ([formula omitted], [formula omitted]) gravity

The current study aims to examine the impact of the boundary term on the bending angle of light for a static spherically symmetric black hole in the modified gravity described by the f(T,B) function. To accomplish this objective, we employ the Ishihara et al. method, which enables us to compute the deflection angle of light for a receiver and source situated at finite distances from a lens object in a non-asymptotically flat spacetime. This method considers the receiver’s viewpoint, and the resulting deflection angle diverges as the distance from the lens object increases, owing to the non-asymptotically flat spacetime. Nevertheless, the divergence can be regulated by the boundary term parameter c0. For lower values of the parameter c0, the divergence can be minimized within the finite range of the observer and source. Furthermore, we calculate the quasinormal modes of massless scalar perturbations in the black hole’s background using the asymptotic iteration method (AIM) and Padé averaged sixth-order Wentzel–Kramers–Brillouin (WKB) approximation method. Our findings indicate that the real quasinormal modes and damping rates are significantly impacted by the model parameter c0. Subsequently, we investigate two optical characteristics of the black hole, namely the shadow and the emission rate. Our results show that with an increase in the boundary term parameter c0, both the shadow’s size and the evaporation rate decrease.

Boson star with parity-odd symmetry in wormhole spacetime

In this paper, we revisit the model of bosonic matter in the form of a free complex scalar field with a nontrivial wormhole spacetime topology supported by a free phantom field. We obtain a new type of boson star with wormhole solutions, in which the complex scalar field possess full parity-odd symmetry with respect to the two asymptotically flat spacetime regions. When the size of the throat is small, the behavior of boson stars with wormhole approaches that of boson stars. When the size of the throat is intermediate, the typical spiraling dependence of the mass and the particle number on the frequency of the boson stars is replaced by a loop structure. However, as the size becomes relatively large, the loop structure will also disappear. In particular, The complex scalar field could form two boson stars with opposite phase differences with respect to the two spacetime regions in the limit of vanishing throat size. We analyze the properties of this new type of boson stars with wormhole and further show that the wormhole spacetime geometry.

Translation gauge field theory of gravity in Minkowski spacetime* *Supported by the National Nature Science Foundation of China (NSFC, 11975241)

The gravitational field with spin-2 is introduced naturally by the requirement that the Lagrangian is locally translation invariant in Minkowski spacetime. The interactions between the and spin-, 0, 1 matter fields are obtained along with the Lagrangian for the gravitational field including self-interactions. The deflection angle of light when it passes through the sun is calculated with different gauge conditions as an example. Our leading-order result is the same as that from general relativity, although the basic ideas are different. It is interesting that gravity can be described in a similar way to other fundamental interactions in Minkowski spacetime, and it may provide a new scenario for the Universe.

Homogeneous nonlinear splittings and Finsler submersions

A nonlinear splitting on a fiber bundle is a generalization of an Ehresmann connection. An example is given by the homogeneous nonlinear splitting of a Finsler function on the total manifold of a fiber bundle. We show how homogeneous nonlinear splittings and nonlinear lifts can be used to construct submersions between Euclidean, Minkowski and Finsler spaces. As an application we consider a semisimple Lie algebra and use our methods to give new examples of Finsler functions on a reductive homogeneous space.

Anisotropic Scaling Non-Relativistic Holography: A Symmetry Perspective

We study the holographic dual of the two-dimensional non-relativistic field theory with anisotropic scaling from a symmetry perspective. We construct a new four-dimensional metric with two-dimensional global anisotropic scaling isometry. The four-dimensional spacetime is homogeneous and is a solution of Einstein gravity with quadratic-curvature extension. We consider this spacetime dual to the vacuum of the boundary field theory. By introducing a proper solution phase space, we find that the asymptotic symmetry of the gravity theory is the two-dimensional local anisotropic conformal symmetry, which recovers precisely the results from the dual non-relativistic field theory side.

Non-supersymmetric vacua and self-adjoint extensions

Internal intervals spanned by finite ranges of a conformal coordinate z and terminating at a pair of singularities are a common feature of many string compactifications with broken supersymmetry. The squared masses emerging in lower-dimensional Minkowski spaces are then eigenvalues of Schrödinger-like operators, whose potentials have double poles at the ends of the intervals. For one-component systems, the possible self-adjoint extensions of Schrödinger operators are described by points in AdS3 × S1, and those corresponding to independent boundary conditions at the ends of the intervals by points on the boundary of AdS3. The perturbative stability of compactifications to Minkowski space time depends, in general, on these choices of self-adjoint extensions. We apply this setup to the orientifold vacua driven by the “tadpole potential” V=T {e}^{frac{3}{2}phi } and find, in nine dimensions, a massive scalar spectrum, a unique choice of boundary conditions with stable tensor modes and a massless graviton, and a wide range of choices leading to massless and/or massive vector modes.

Conharmonically Flat Spacetimes in FRW Cosmological Model

Conharmonically Flat Spacetimes in FRW Cosmological Model

The Relevance of Time in Biological Scaling.

Various phenotypic traits relate to the size of a living system in regular but often disproportionate (allometric) ways. These "biological scaling" relationships have been studied by biologists for over a century, but their causes remain hotly debated. Here, I focus on the patterns and possible causes of the body-mass scaling of the rates/durations of various biological processes and life-history events, i.e., the "pace of life". Many biologists have regarded the rate of metabolism or energy use as the master driver of the "pace of life" and its scaling with body size. Although this "energy perspective" has provided valuable insight, here I argue that a "time perspective" may be equally or even more important. I evaluate various major ways that time may be relevant in biological scaling, including as (1) an independent "fourth dimension" in biological dimensional analyses, (2) a universal "biological clock" that synchronizes various biological rates/durations, (3) a scaling method that uses various biological time periods (allochrony) as scaling metrics, rather than various measures of physical size (allometry), as traditionally performed, (4) an ultimate body-size-related constraint on the rates/timing of biological processes/events that is set by the inevitability of death, and (5) a geological "deep time" approach for viewing the evolution of biological scaling patterns. Although previously proposed universal four-dimensional space-time and "biological clock" views of biological scaling are problematic, novel approaches using allochronic analyses and time perspectives based on size-related rates of individual mortality and species origination/extinction may provide new valuable insights.

Spin-0 fields and the NP-constants close to spatial infinity in Minkowski spacetime

Newman–Penrose (NP) constants of massless spin-0 fields propagating in Minkowski spacetime are computed close to spatial and null infinity by means of Friedrich’s i0-cylinder. Assuming a certain regularity condition on the initial data ensuring that the field extends analytically to critical sets, it is shown that the NP constants at future I+ and past null infinity I− are independent of each other. In other words, the classical NP constants at I± stem from different parts of the initial data given on a Cauchy hypersurface. In contrast, it is shown that, using a slight generalization of the classical NP constants, the associated quantities (i0-cylinder NP constants) do not require the regularity condition being satisfied and give rise to conserved quantities at I± that are determined by the same piece of initial data, which, in turn, correspond to the terms controlling the regularity of the field. Additionally, it is shown how the conservation laws associated with the NP constants can be exploited to construct, in flat space, heuristic asymptotic-system expansions, which are sensitive to the logarithmic terms at the critical sets.

General formalism of the quantum equivalence principle

A consistent theory of quantum gravity will require a fully quantum formulation of the classical equivalence principle. Such a formulation has been recently proposed in terms of the equality of the rest, inertial and gravitational mass operators, and for non-relativistic particles in a weak gravitational field. In this work, we propose a generalization to a fully relativistic formalism of the quantum equivalence principle, valid for all background space-times, as well as for massive bosons and fermions. The principle is trivially satisfied for massless particles. We show that if the equivalence principle is broken at the quantum level, it implies the modification of the standard Lorentz transformations in flat space-time and a corresponding modification of the metric in curved space-time by the different mass ratios. In other words, the observed geometry would effectively depend on the properties of the test particle. Testable predictions of potential violations of the quantum equivalence principle are proposed.

Weak gravitational lensing and shadow cast by rotating black holes in axionic Chern–Simons theory

We investigate the impact of the axionic coupling parameter on the bending angle of light and the shadow cast by slowly rotating black holes in Chern–Simons modified gravity. We utilize the Ishihara et al. method to derive the deflection angle of light for an observer and source located at finite distances from a lens object in an asymptotically flat spacetime, using the Gauss–Bonnet theorem. The deflection angle exhibits an increasing trend up to a certain point, followed by a decrease as a function of the impact parameter, with the presence of the axion matter field causing the observed increase. Additionally, we calculate the Einstein ring radius as a direct application of the weak deflection angle. We also investigate the effect of the axion matter field on the time delay of light and analyze its impact on the shadow cast by slowly rotating black holes. Our findings reveal a significant effect of the axionic coupling parameter on the black hole’s shadow.

Evolving embedded traversable wormholes in [formula omitted] gravity: A comparative study

The objective of this paper is to unveil the evolving traversable wormhole solutions within the perspective of modified f(R,G) gravity, where R is Ricci scalar and G is Gauss Bonnet term. In order to accomplish this, we develop a wormhole shape function using the Karmarkar condition for traversable static wormhole geometry, that links two asymptotically flat spacetime regions and meets the necessary requirements. The embedding diagram in two and three-dimensional Euclidean space is also discussed in order to demonstrate the wormhole configurations. For our current study, we choose two realistic and viable f(R,G) gravity models to discuss the wormhole geometry. For the traversable wormhole configurations the energy conditions must be satisfied at the throat. For this purpose, we check the energy conditions and observed that these conditions are satisfied near the throat of the wormhole space in modified f(R,G) gravity. Further, the intriguing part of this research is to perform a comparative analysis of the evolving wormhole geometries of our considered models with the help of three-dimensional graphical representation along with their regions. Moreover, we also describe the stability of obtained wormholes solutions by employing the equilibrium condition. It can be observed that our shape function acquired through the Karmarkar technique yields validated wormhole configurations with even less exotic matter correlating to the proper choice of f(R,G) gravity models. As a nutshell, we can infer that our findings fulfill all of the criterion for the presence of traversable wormhole, ensuring that our study is viable and consistent.

A description of classical and quantum cosmology for a single scalar field torsion gravity

In the background of homogeneous and isotropic flat FLRW spacetime, both classical and quantum cosmologies have been studied for teleparallel dark energy (DE) model. Using Noether symmetry analysis, not only the symmetry vector but also the coupling function in the Lagrangian and the potential of the scalar field have been determined. Also symmetry analysis identifies a cyclic variable in the Lagrangian along the symmetry vector and as a result the Lagrangian simplifies to a great extent so that classical solution is obtained. Subsequently, in quantum cosmology Wheeler–DeWitt (WD) equation has been constructed and the quantum version of the conserved momenta corresponding to Noether symmetry identifies the periodic part of the wave function of the universe and as a result the WD equation becomes solvable. Finally, quantum description shows finite nonzero probability at the classical big bang singularity.

Colliding gravitational waves and singularities

We have investigated a model of colliding plain gravitational waves, proposed by Szekeres, whose structure of singularities is determined. We have evaluated a total energy of matter as a volume integral of the energy–momentum tensor (EMT), whose contributions arise only at these singularities. The total matter energy is conserved before a collision of two plane gravitational waves but decreases during the collision and becomes zero at the end of the collision. We thus interpret that this model of colliding plane gravitational waves is a space–time describing a pair annihilation of plan gravitational waves. We have also calculated a matter conserved charge proposed by the present author and his collaborators. The matter charge is indeed conserved but is zero due to a cancelation between two plain gravitational waves. This seems natural since nothing remains after a pair annihilation, and gives a hint on a physical interpretation of the conserved charge, which we call the gravitational charge. By modifying the space–time for the pair annihilation, we newly construct two types of a scattering plane gravitational wave and a pair creation of plane gravitational waves, and combining all, a Minkowski vacuum bottle, a Minkowski space–time surrounded by two moving plane gravitational waves.

Inertia modified by electromagnetic Abelian gauge transformations

This paper is about inertia modified by electromagnetic Abelian gauge transformations. We will establish an experiment proposal in order to control the gravitational acceleration constant near the surface of the planet. We will achieve this goal by establishing a change in electromagnetic gauge in a region of flat spacetime. The change in gauge will be generated by the Aharonov–Bohm effect through the use of a solenoid. The spacetime boosts outside the solenoid caused by the change in electromagnetic gauge will counteract the gravitational acceleration constant [Formula: see text] attenuating its local value as seen from the planet surface reference frames. Therefore, we will be able to establish local control of gravity on electrically charged particles like electrons in synchrotron motion outside the solenoid.

Understanding thermal nature of de Sitter spacetime via inter-detector interaction

We investigate the interaction potential of two static detectors (atoms) at the same radial but different azimuthal coordinates in the de Sitter invariant vacuum. We show that for two detectors very far away from the cosmological horizon, the interaction potential is different from that of two static ones in a thermal bath in Minkowski spacetime at a temperature equal to the Gibbons-Hawking temperature, suggesting that de Sitter spacetime in regard to its thermal nature basically differs from a thermal bath in Minkowski spacetime. For two detectors very close to the cosmological horizon, the interaction potential behaves as ∼[TUρ4ln⁡(4TUρ)]−1 with TU and ρ the Unruh temperature associated with the proper acceleration and the proper separation of the detectors, which deviates dramatically from ∼(TUρ4)−1, the behavior of the interaction potential of two synchronously uniformly accelerated detectors in Minkowski spacetime, indicating that thermal nature of de Sitter spacetime also differs essentially from the Unruh thermal bath.

Quantum energy inequalities along stationary worldlines

Quantum energy inequalities (QEIs) are lower bounds on the averaged energy density of a quantum field. They have been proved for various field theories in general curved spacetimes but the explicit lower bound is not easily calculated in closed form. In this paper we study QEIs for the massless minimally coupled scalar field in four-dimensional Minkowski spacetime along stationary worldlines—curves whose velocity evolves under a 1-parameter Lorentz subgroup—and find closed expressions for the QEI bound, in terms of curvature invariants of the worldline. Our general results are illustrated by specific computations for the six prototypical stationary worldlines. When the averaging period is taken to infinity, the QEI bound is consistent with a constant energy density along the worldline. For inertial and uniformly linearly accelerated worldlines, this constant value is attained by the Minkowski and Rindler vacuums respectively. It is an open question as to whether the bounds for other stationary worldlines are attained by other states of interest.

An interlacing result for Hermitian matrices in Minkowski space

In this paper we will look at the well known interlacing problem, but here we consider the result for Hermitian matrices in the Minkowski space, an indefinite inner product space with one negative square. More specific, we consider the n×n matrix A=[Ju−u⁎a] with a∈R, J=J⁎ and u∈Cn−1. Then A is H-selfadjoint with respect to the matrix H=In−1⊕(−1). The canonical form for the pair (A,H) plays an important role and the sign characteristic coupled to the pair is also discussed.

The on-shell expansion: from Landau equations to the Newton polytope

We study the application of the method of regions to Feynman integrals with massless propagators contributing to off-shell Green’s functions in Minkowski spacetime (with non-exceptional momenta) around vanishing external masses, {p}_i^2to 0 . This on-shell expansion allows us to identify all infrared-sensitive regions at any power, in terms of infrared subgraphs in which a subset of the propagators become collinear to external lightlike momenta and others become soft. We show that each such region can be viewed as a solution to the Landau equations, or equivalently, as a facet in the Newton polytope constructed from the Symanzik graph polynomials. This identification allows us to study the properties of the graph polynomials associated with infrared regions, as well as to construct a graph-finding algorithm for the on-shell expansion, which identifies all regions using exclusively graph-theoretical conditions. We also use the results to investigate the analytic structure of integrals associated with regions in which every connected soft subgraph connects to just two jets. For such regions we prove that multiple on-shell expansions commute. This applies in particular to all regions in Sudakov form-factor diagrams as well as in any planar diagram.