Minkowski Space Research Articles

Covariant generalized conserved charges of General Relativity

Motivated by the current research of generalized symmetries and the construction of conserved charges in pure Einstein gravity linearized over Minkowski spacetime in Cartesian coordinates, we investigate, from a purely classical point of view, the construction of these charges in a coordinate- and frame-independent language in order to generalize them further. We show that all the charges constructed in that context are associated to the conformal Killing-Yano 2-forms of Minkowski spacetime. Furthermore, we prove that those associated to closed conformal Killing-Yano 2-forms are identical to the charges constructed by Kastor and Traschen for their dual Killing-Yano (d − 2)-forms. We discuss the number of independent and non-trivial gravitational charges that can be constructed in this way.

Fermions in loop quantum gravity and resolution of doubling problem

The fermion propagator is derived in detail from the model of fermion coupled to loop quantum gravity (LQG). As an ingredient of the propagator, the vacuum state is defined as the ground state of some effective fermion Hamiltonian under the background geometry given by a coherent state resembling the classical Minkowski spacetime. Moreover, as a critical feature of LQG, the superposition over graphs is employed to define the vacuum state. It turns out that the graph superposition leads to the propagator being the average of the propagators of the lattice field theory over various graphs so that all fermion doubler modes are suppressed in the propagator. This resolves the doubling problem in LQG. Our result suggests that the superposition nature of quantum geometry should, on the one hand, resolve the tension between fermion and the fundamental discreteness and, on the other hand, relate to the continuum limit of quantum gravity.

An asymptotic framework for gravitational scattering

Asymptotically flat spacetimes have been studied in five separate regions: future/past timelike infinity , future/past null infinity , and spatial infinity i 0. We formulate assumptions and definitions such that the five infinities share a single Bondi–Metzner–Sachs (BMS) group of asymptotic symmetries and associated charges. We show how individual ingoing/outgoing massive bodies may be ascribed initial/final BMS charges and derive global conservation laws stating that the change in total charge is balanced by the corresponding radiative flux. This framework provides a foundation for the study of asymptotically flat spacetimes containing ingoing and outgoing massive bodies, i.e. for generalized gravitational scattering. Among the new implications are rigorous definitions for quantities like initial/final spin, scattering angle, and impact parameter in multi-body spacetimes, without the use of any preferred background structure.

Exterior Stability of Minkowski Space in Generalized Harmonic Gauge

We give a short proof of the existence of a small piece of null infinity for (3+1)-dimensional spacetimes evolving from asymptotically flat initial data as solutions of the Einstein vacuum equations. We introduce a modification of the standard wave coordinate gauge in which all non-physical metric degrees of freedom have strong decay at null infinity. Using a formulation of the gauge-fixed Einstein vacuum equations which implements constraint damping, we establish this strong decay regardless of the validity of the constraint equations. On a technical level, we use notions from geometric singular analysis to give a streamlined proof of semiglobal existence for the relevant quasilinear hyperbolic equation.

Computational analysis of thin-shell with scalar field for class of new black hole solutions in metric-affine gravity

The aim of this study is to investigate the geometric structure of a thin-shell within the context of metric-affine gravity. To accomplish this, we employ a cut and paste approach to match the inner Minkowski spacetime and an outer newly calculated class of black hole solutions in metric-affine gravity. These solutions are Reissner–Nordström-like black holes with shear, spin, dilation, electric, magnetic charges, and a cosmological constant. Using the Klein–Gordon equation of motion, we analyze the dynamics of the thin-shell configuration under both massive and massless scalar fields. We find that the scalar field affects thin-shell dynamics and can lead to interesting effects such as dynamics and stability configurations. We demonstrate that the linearized radial perturbation approach employing a phantom-like equation of state, such as quintessence, dark energy, and phantom energy, reveal stable configurations of the thin-shell located beyond the expected position of the event horizon of the exterior manifold. We also find that the stability of the thin-shell depends strongly on the parameters of the black hole solutions. Our results shed light on the dynamics of thin-shells in the context of metric affine gravity with scalar fields and provide new insights into the behavior of black hole solutions in this theory. It is concluded that the thin-shell composed of quintessence and dark energy shows the more stable configuration for the choice of Reissner-Nordström-like black holes with shear, spin, and dilation charges.

Безмассовая частица Штюкельберга, решения с цилиндрической симметрией

The massless Stueckelberg field is studied in cylindrical coordinates.
 The field function consists of the scalar, 4-vector,
 and antisymmetric tensor. Physically observable components
 are the scalar and 4-vector. We apply the Stueckelberg
 tetrad-based matrix equation, generalized to arbitrary Riemannian
 space, including any curvilinear coordinates in the
 Minkowski space. We construct solutions with cylindric symmetry,
 while the operators of energy, of the third projection
 of the total angular momentum, and the third projection of
 the linear momentum are diagonalized. After separating the
 variables we derive the system of 11 first-order differential
 equations in polar coordinate. It is solved with the use of the
 Fedorov–Gronskiy method. According to this method, all 11
 functions are expressed through 3 main funcions. According
 to the known procedure we impose the differential constraints,
 which are consistent with the all 11 equations and
 allow us to transform these equations to algebraic form. This
 algebraic system is solved by standard methods. As a result,
 we obtain 5 linearly independent solutions. The problem of
 eliminating the gauge solutions will be studied in a separate
 paper.

Arrow of Time and Quantum Physics

Based on the hypothesis that the (non-reversible) arrow of time is intrinsic in any system, no matter how small, the consequences are discussed. Within the framework of local quantum physics it is shown how such a semi-group action of time can consistently be extended to that of the group of spacetime translations in Minkowski space. In presence of massless excitations, however, there arise ambiguities in the theoretical extensions of the time translations to the past. The corresponding loss of quantum information on states upon time is determined. Finally, it is explained how the description of operations in classical terms combined with constraints imposed by the arrow of time leads to a quantum theoretical framework. These results suggest that the arrow of time is fundamental in nature and not merely a consequence of statistical effects on which the Second Law is based.

Relativity with Hubble Constant as Velocity Equivalent of Position

Based on a plain belief that the cosmic space should be a unified whole with universal connection, rather than a patchwork of unconnected domain blocks, we reassess Hubble law as a short-range characterization of electromagnetic interaction and Hubble constant as velocity equivalent of position. If so, it is necessary to develop a matching transformation to work for relativity, which can ensure that the causal chain is not broken and the physical description is complete. To this end, we unify space and motion into a full-velocity concept and reshape Minkowski space into a pseudo-Minkowski one confined by an unreachable physical horizon. In the reshaped, all parts are physically allowed for unobstructed communication with each other, and the transformation that keeps physical laws including Hubble law invariant, is full-velocity Lorentz transformation, under which length contraction, time dilation and historization effect are discussed. Meanwhile, as a static solution of Einstein equation, the pseudo-Minkowski universe not only can reproduce the effective results of expansion model, but also derive the background radiation temperature and Hubble constant, etc.. Especially, it provides an analytic solution of gravitational field around mass without the singularity of event horizon.

A 4d non-BPS NS-NS microstate

We construct a two-parameter four-dimensional non-BPS NS-NS smooth microstate solution that asymptotes to flat spacetime with a linear dilaton in type II superstring theory. From the microscopic point of view, the background is made out of a certain number of decoupled (i.e. gs → 0) NS5 branes wrapping T3 × S1 × S1 with fundamental strings wrapping non-contractable cycles of S1 × S1 with integer momentum modes along them. We show that perturbative worldsheet theory in this background is given by a null-gauged WZW model. We also show that the consistency of the worldsheet theory imposes non-trivial constraints on the supergravity background.

Stimulus intensity modulates perceived tactile distance.

Several features of tactile stimuli modulate the perceived distance between touches. In particular, distances are perceived as farther apart when the time interval between them is longer, than when it is shorter. Such effects have been interpreted as a form of 'psychological relativity', analogous to Einstein's conception of a four-dimensional space-time. We investigated whether similar effects occur for stimulus features other than time, specifically stimulus intensity. We hypothesised that perceived distance would be increased when the two stimuli differed in intensity, since they would then be farther apart in a multi-dimensional feature space. Participants made verbal estimates of the perceived distance between two touches on their left hand. Intensity was manipulated such that both stimuli could be intense, both could be light, or one could be intense and the other light. We found no evidence for change in perceived tactile distance when stimuli intensity mis-matched. In contrast, there were clear effects of average stimulus intensity on perceived distance. Intense stimuli were judged as farther apart than light stimuli, and mixed stimuli were intermediate. These results are consistent with theories of general magnitude representation, which argue that multiple dimensions of magnitude are dependent on a shared underlying representation of domain-general magnitude.

Optimal blowup stability for supercritical wave maps

We study corotational wave maps from (1+4)-dimensional Minkowski space into the 4-sphere. We prove the stability of an explicitly known self-similar wave map under perturbations that are small in the critical Sobolev space.

Investigation of space-times through W2-curvature tensor in [formula omitted] gravity

The W2-curvature tensor is an important geometric invariant with relativistic significance, introduced in the early 1970s by Pokhariyal and Mishra, which can be identified in class 4 in the classification of skew-symmetric operators. In this work, we investigate 4-dimensional space-times admitting W2-curvature tensor in f(R,G) modified theory of gravity. It is proved that the W2-curvature flat perfect fluid space-times obeying f(R,G) gravity represent inflation. Also, it is shown that the isotropic pressure and the energy density of such space-times are constant. It is to be noted that in such space-times the considered energy conditions are consistently satisfied if the scalar curvature is positive. Next, we study perfect fluid space-times admitting divergence free W2-curvature tensor in f(R,G) gravity. Amongst other results, we prove that if the energy-momentum tensor of such space-times is bi-recurrent, then either the space-times represent inflation or their isotropic pressure and energy density are constants.

Particle dynamics around the Einstein–Maxwell–Yang–Mills black hole

The presence of matter in general relativity can cause spacetime to curve. This paper investigates the spacetime properties of the Einstein–Maxwell–Yang–Mills (EMYM) black hole by discussing the geodesic motion of neutral and charged particles. By studying the Lagrangian of these particles, equations of motion and effective potential are obtained in the asymptotic flat and (A)dS spacetimes. Moreover, for the motion of a neutral particle, it is found that there exist stable elliptic/hyperbolic orbits and unstable orbits with different energies by discussing the effective potential and the phase-plane analysis. However, for the motion of a charged particle, there exists an equilibrium point that separates these orbits. In addition, the effects of the system parameters on the potential are analyzed, including the masses of the black hole and charged particles, charges, the cosmological constant, and the strength of the external magnetic field.

Exploring the 0− bound state with dressed quarks in Minkowski space

The Bethe-Salpeter equation for a pseudoscalar bound-system, with i) a ladder kernel with massive gluons, ii) dynamically-dressed quark mass function and iii) an extended quark-gluon vertex, is solved in Minkowski space by using the Nakanishi integral representation of the Bethe-Salpeter amplitude. The quark dressing is implemented through a phenomenological ansatz, which was tuned by lattice QCD calculations of the quark running mass. The latter were also used for assigning the range of the gluon mass and the parameter featuring the extended color density. This framework allows to investigate the gluon dynamics that manifest itself in the quark dressing, quark-gluon vertex and the binding, directly in the physical space. We present the first results for low-density pseudoscalar systems in order to elucidate the onset of the interplay between the above mentioned gluonic phenomena, and we discuss both static and dynamical quantities, like valence longitudinal and transverse distributions.

A note on the Kaluza–Klein theory

We show that the Kaluza–Klein (KK) theory contains a fundamental problem: The four-dimensional metric tensor and the electromagnetic potential vector assumed in the KK theory belong to four-dimensional vector spaces that are not integrable in general, resulting that the four-dimensional physical variables and the corresponding field equations derived from the five-dimensional Einstein field equation (i.e. the four-dimensional Einstein field equation and the Maxwell equations) are not defined on a four-dimensional submanifold. That is, the four-dimensional spacetime assumed in the KK theory does not exist. No satisfactory solutions are found within the KK formalism. Perhaps the best approach to fix the problem is giving up the KK theory and looking for a new unified scheme for gravitational and electromagnetic interactions in the framework of a spacetime with extra dimensions, as having already been explored in some literature.

Black hole extremality in nonlinear electrodynamics: a lesson for weak gravity and Festina Lente bounds

We study black hole extremality in nonlinear electrodynamics motivated by the Weak Gravity Conjecture (WGC) and the Festina Lente (FL) bound. For illustration, we consider the Euler-Heisenberg model and the Dirac-Born-Infeld model in asymptotically flat spacetime, de Sitter spacetime, and anti-de Sitter spacetime. We find that in all cases the extremal condition enjoys a certain monotonicity expected by the WGC. This provides evidence for the conjecture beyond the leading order corrections to the Einstein-Maxwell theory. We also study how light charged particles modify the mass-charge relation of Nariai black holes in de Sitter spacetime and discuss possible implications for the FL bound. Besides, we point out an interesting similarity between our black hole analysis and gravitational positivity bounds on scattering amplitudes.

Curvature estimates for spacelike graphic hypersurfaces in Lorentz–Minkowski space R1n+1$\mathbb {R}^{n+1}_{1}$

AbstractIn this paper, we can obtain curvature estimates for spacelike admissible graphic hypersurfaces in the ‐dimensional Lorentz–Minkowski space , and through which the existence of spacelike admissible graphic hypersurfaces, with prescribed 2‐nd Weingarten curvature and Dirichlet boundary data, defined over a strictly convex domain in the hyperbolic plane of center at origin and radius 1, can be proven.

On the conserved quantities in an Einstein-scalar system

The generalization of ten conserved quantities (Newman–Penrose constants) defined in asympotically flat vacuum spacetimes to asymptotically flat Einstein-scalar spacetimes is studied. It is found that these quantites, when suitably modified, are also conserved in a Einstein-scalar system.

On the spectrum and structure constants of short operators in N=4 SYM at strong coupling

We study short operators in planar mathcal{N} = 4 SYM at strong coupling, for general spin and SO(6) symmetric traceless representations. At strong coupling their dimension grows like Delta sim 2sqrt{delta }{lambda}^{1/4} and their spectrum of degeneracies can be analysed by considering the massive spectrum of type II strings in flat space-time. We furthermore compute their structure constants with two arbitrary chiral primary operators. This is done by considering the four-point correlator of arbitrary chiral primary operators at strong coupling in planar mathcal{N} = 4 SYM, including the supergravity approximation plus the infinite tower of stringy corrections that contributes in the flat space limit. Our results are valid for generic rank n symmetric traceless representations of SO(6) and in particular for n ≫ 1, as long as n ≪ λ1/4.

On torsion axial vector and gravitational energy in Lewis–Papapetrou space-time in the theory of teleparallel gravity

The teleparallel version of Lewis–Papapetrou space-time is investigated. For this space-time, the true discussion of the geometric and physical properties is given. We show that the value of the space-like torsion-axial vector does not depend on the choice of tetrad field. Consequently, the spin procession of the Dirac particle and the corresponding Hamiltonian have physical meaning. The energy and momentum densities for such space-time are calculated. We show that when choosing two sets of tetrad fields, the dependence and independence of the aforementioned quantities on the tetrad field depend on the Lorentz factor, which links the two sets of tetrad fields.