Dimensional Spacetime Research Articles

Lie symmetries in higher dimensional charged radiating stars

This study investigates the Lie symmetry properties of matter variables, spacetime dimension, and kinematic quantities in spherically symmetric radiating stars undergoing gravitational collapse in higher dimensional spacetimes. Our analysis explores how variations in functions and dependent variables influence the Lie algebra dimensionality and Lie symmetries of the boundary condition. Our study reveals the explicit dependence of charge and spacetime dimension in the Lie symmetry generators for the first time. We examine models with various kinematical features, such as shear, shear-free, geodesic, and non-expanding conditions with different matter variables. Using the Lie symmetries we obtain group invariant solutions to the models and observe how the kinematical features and matter variables affect the Lie symmetries. Additionally, we demonstrate the appearance of a linear equation of state. We recover known four-dimensional models from our results.

Topological photon, spin, and Euclidean group E(2)

The proposition that photon is a topological object [S. C. Tiwari, J. Math. Phys. 49, 032303 (2008)] is given rigorous foundation based on pure vector field theory independent of the electromagnetic fields. Holomorphy of 4-dimensional spacetime and the nature of topological obstructions are investigated to articulate singular vortex model for photon. The utility of the Euclidean symmetry group is discussed in detail for the proposed photon model.

Dilatonic black holes in dRGT massive gravity

Motivated by high interest in Lorentz invariant massive gravity models known as the dRGT massive gravity, we discuss the dRGT massive gravity including the coupling term between dilaton scalar field and massive graviton, and present static and spherically symmetric solutions of dilatonic black holes in four and higher dimensional spacetime. Later, we investigate phase structure of these black hole solutions, and discover that the dilatonic black hole could possess two horizons, extreme and naked singularity black holes for the suitably parameters values. Calculating the conserved and thermodynamic quantities, we check the validity of the first law of thermodynamics.

The 4-Dimensional Spacetime World Line Image Representation and the Law of Existence of Objects Inferred from it

MINKOWSKI defined the four-dimensional spacetime model (x, y, z, t) used to represent world-point and world in [1]. The spacetime light cone is an intuitive diagram, compacted one space component and replaced it by time axis, thus the spacetime light cone was based on (x, y, t). In such a way, although it made the visual expression is possible, but also the spacetime light cone exposed shortages as follows • The spacetime light cone has limited expressive ability • The relationship between two or more world lines or events cannot be expressed • Can't express different world lines correctly • Most images of spacetime light cones are wrong and no use • The image of spacetime light cone is not intuitive and is obscure in application. Because of this, we designed the 4-dimensional Spacetime World Line image representation. This new 4-dimensional Spacetime diagram presents the complete 3 space dimensions and 1 time dimension. It overcomes the weakness of spacetime light cone, gives clear and precise visual expression of the world line, is able to display multi-world lines in one figure, can clearly present the interface and development process of each of the world line, and display the interaction among them. From the 4-dimensional spacetime diagram, we deducted and proved the Law of Existence of Object, which is as such: From its birth, through its past, to the present, and into the future, an object only exists at the "present" moment.

The exact relativistic scalar quasibound states of the dyonic Kerr–Sen black hole: quantized energy, and Hawking radiation

We consider Klein–Gordon equation in the Dyonic Kerr–Sen black hole background, which is the charged rotating axially symmetric solution of the Einstein–Maxwell–Dilaton–Axion theory of gravity. The black hole incorporates electric, magnetic, dilatonic and axionic charges and is constructed in 3+1 dimensional spacetime. We begin our investigations with the construction of the scalar field’s governing equation, i.e., the covariant Klein–Gordon equation. With the help of the ansatz of separation of variables, we successfully separate the polar part, and find the exact solution in terms of Spheroidal Harmonics, while the radial exact solution is obtained in terms of the Confluent Heun function. The quantization of the quasibound state is done by applying the polynomial condition of the Confluent Heun function that gives rise to discrete complex-valued energy levels for massive scalar fields. The real part is the scalar field relativistic quantized energy, while the imaginary part represents the quasibound states’s decay. We present all of the sixteen possible exact energy solutions for both massive and massless scalars. We also present the investigation the Hawking radiation of the Dyonic Kerr–Sen black hole’s apparent horizon, via the Sigurd–Sannan method by making use of the obtained exact scalar wave functions. The radiation distribution function, and the Hawking temperature are also obtained.

Efficiency of magnetic Penrose process in higher dimensional Myers-Perry black hole spacetimes

Efficiency of magnetic Penrose process in higher dimensional Myers-Perry black hole spacetimes

Charging Kerr-Schild spacetimes in higher dimensions

Charging Kerr-Schild spacetimes in higher dimensions

Fermion localization on the brane in Ricci-inverse gravity

This study aims to analyze the effects of modified gravity via anti-curvature tensor on a gravitational model set up within a 5-dimensional space–time, focusing on brane-world scenarios. The anti-curvature tensor introduces innovative configuration that is equal to the inverse of the Ricci tensor. In this analysis, we consider f(R,A)=(R+αA), where the coupling parameter α influences both vacuum regions outside the brane and the core region within it. Through analysis, this study uncovers alterations in fermion localization, particularly impacting left-chirality fermion. To quantify fermion localization, probabilistic metrics such as Shannon entropy and relative probability are employed, demonstrating a heightened level of certainty as α values increase. These findings shed significant light on the dynamics of extra-dimensional models, providing valuable insights into the realms of particle physics and cosmology.

The Casimir Effect in Finite-Temperature and Gravitational Scenarios

In this paper, we review some recent findings related to the Casimir effect. Initially, the thermal corrections to the vacuum Casimir energy density are calculated, for a quantum scalar field, whose modes propagate in the (3+1)-dimensional Euclidean spacetime, subject to a nontrivial compact boundary condition. Next, we analyze the Casimir effect induced by two parallel plates placed in a weak gravitational field background. Finally, we review the three-dimensional wormhole solutions sourced by the Casimir density and pressures associated with the quantum vacuum fluctuations of the Yang-Mills field.

Vacuum energy, temperature corrections and heat kernel coefficients in (D + 1)-dimensional spacetimes with nontrivial topology

Vacuum energy, temperature corrections and heat kernel coefficients in (<i>D</i> + 1)-dimensional spacetimes with nontrivial topology

A new perspective on Kaluza–Klein theories

Assuming that the geometry of spacetime is uniquely determined by the energy–momentum tensor of matter alone, i.e. without any interactions, enables us to construct the Lagrangian from which the metric of higher dimensional spacetime follows. From the geodesic equations that follow, it becomes clear that the incorrect mass of elementary particles predicted by Kaluza–Klein theories arises from the assumption that in the absence of gravity the solution to the Einstein field equations reduces to the Minkowski metric. From construction of a consistent theory of 4D electromagnetism, we find that this assumption does not only result in the incorrect mass of elementary particles, but also the incorrect value of the cosmological constant. This suggests that these incorrect predictions, which are often regarded as major flaws of Kaluza–Klein theories, just reflect the inconsistency of the assumption that the solution to Einstein field equations reduces to Minkowski metric in the absence of gravity and Weyl invariance which is the symmetry of gauge theories in 4D spacetime. Abandoning this assumption results in modification of general relativity. We show that the unified description of fundamental interactions naturally incorporates the Higgs mechanism. For non-Abelian gauge fields, we find that the manifold comprising the extra dimensions has to be a group manifold and show that the standard model is realized in 16D spacetime. We show that charge and spin are the same concept, but what makes them different is that the former follows from symmetry of 4D spacetime while the latter follows from symmetry of the internal space.

Making two particle detectors in flat spacetime communicate quantumly

A communication protocol with nonzero quantum capacity is found when the two communicating parts are particle detector models in (3+1)-dimensional spacetime. In particular, as detectors, we consider two harmonic oscillators interacting with a scalar field, whose evolution is generalized for whatever background spacetime and whatever spacetime smearing of the detectors. We then specialize to Minkowski spacetime and an initial Minkowski vacuum, considering a rapid interaction between the field and the two detectors, studying the case where the receiver is static and the sender is moving. The possibility to have a quantum capacity greater than zero stems from a relative acceleration between the detectors. Indeed, no reliable quantum communication is possible when the two detectors are static or moving inertially with respect to each other, but a reliable quantum communication can be achieved between a uniformly accelerated sender and an inertial receiver. Published by the American Physical Society 2024

Gauge theory on ρ-Minkowski space-time

We construct a gauge theory model on the 4-dimensional ρ-Minkowski space-time, a particular deformation of the Minkowski space-time recently considered. The corresponding star product results from a combination of Weyl quantization map and properties of the convolution algebra of the special Euclidean group. We use noncommutative differential calculi based on twisted derivations together with a twisted notion of noncommutative connection. The twisted derivations pertain to the Hopf algebra of ρ-deformed translations, a Hopf subalgebra of the ρ-deformed Poincaré algebra which can be viewed as defining the quantum symmetries of the ρ-Minkowski space-time. The gauge theory model is left invariant under the action of the ρ-deformed Poincaré algebra. The kinetic part of the action is found to coincide with the one of the usual (commutative) electrodynamics.

The linearized Einstein equations with sources

On vacuum spacetimes of general dimension, we study the linearized Einstein vacuum equations with a spatially compactly supported and (necessarily) divergence-free source. We prove that the vanishing of appropriate charges of the source, defined in terms of Killing vector fields on the spacetime, is necessary and sufficient for solvability within the class of spatially compactly supported metric perturbations. The proof combines classical results by Moncrief with the solvability theory of the linearized constraint equations with control on supports developed by Corvino–Schoen and Chruściel–Delay.

Scattering and absorption by extra-dimensional black holes with GUP

In this paper, we consider the Schwarzschild-Tangherlini black hole to investigate the process of scalar wave scattering by the black hole in a spacetime of (d+1) dimensions and also with the generalized uncertainty principle (GUP). In this scenario, we analytically determine the phase shift and explore the effect of extra dimensions by calculating the differential scattering and absorption cross-section by applying the partial wave method at low and high-frequency limits. We show at high dimensions that the absorption is not zero as the mass parameter approaches zero.

Can the induced increase in the angular velocity prevent the overspinning of BTZ black holes?

Previously we showed that nearly extremal Bañados–Teitelboim–Zanelli (BTZ) black holes can be overspun by test bodies and fields, following the work of Rocha and Cardoso for the extremal case. The naked singularities in AdS space-times correspond to states rotating faster than light in the Ads/CFT correspondence. Therefore, overspinning turns out to be a drastic problem in a (2 + 1) dimensional AdS space-time, where one cannot invoke backreaction effects. Here, we consider the induced increase in the angular velocity of the event horizon which modifies the condition to allow the absorption of the perturbations satisfying the null energy condition. We show that its magnitude is sufficiently large to prevent the absorption of the challenging modes both for test bodies and scalar fields. We bring a solution to the notorious overspinning problem which does not involve any reference to self-energy or gravitational radiation

Unconstrained Lagrangian formulation for bosonic continuous spin theory in flat spacetime of arbitrary dimension

We have discovered two unconstrained forms of free Lagrangian for continuous spin(CS) theory in arbitrary flat spacetime dimension for bosonic case. These Lagrangians, unlike that by Schuster and Toro, do not include delta functions and are conventional. The first form consists of five kinds of totally symmetric helicity fields and one kind of gauge parameter. By introducing auxiliary creation and annihilation operators, each is combined into a state vector in Fock space, including all ranks one by one. The Lagrangian imposes no constraints, such as trace conditions, on these fields or the gauge parameter field. Additionally, the Lagrangian does not contain higher-order derivative terms. In the limit as CS parameter μ approaches zero, it naturally reproduces a Lagrangian for helicity fields in higher spin(HS) theory, known as unconstrained quartet formulation. Permitting third-order derivatives, we also obtain the second unconstrained form of Lagrangian that can be written in terms of three kinds of fields, including μ, similar to the formulation by Francia and Sagnotti. Partial gauge fixing and partial use of equations of motion (EOM) on this Lagrangian yield a Fronsdal-like Lagrangian with a single double-traceless field, including μ. By imposing further gauge fixing on the field in the EOM with respect to divergence and trace, we confirm the reproduction of the modified Wigner equations already known in literature.

Universality in logarithmic temperature corrections to near-extremal rotating black hole thermodynamics in various dimensions

The low-temperature thermodynamics of near-extremal rotating black holes has recently been revisited to incorporate one-loop contributions that are dominant in this regime. We discuss these quantum corrections to the gravitational path integral for asymptotically Anti de-Sitter black holes in four and five dimensions. In four dimensions we explicitly consider Kerr-AdS4, Kerr-Newman-AdS4 and the rotating black hole in N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 4 gauged supergravity with two scalars and two electric charges turned on. In five dimensions we explicitly address the asymptotically flat Myers-Perry black hole and the Kerr-AdS5 black hole. In every case we find that tensor modes contribute 32logTHawking\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\frac{3}{2}\\log {T}_{\ extrm{Hawking}} $$\\end{document} to the low-temperature thermodynamics. We identify the root cause of this universality in two facts: (i) the universal presence of a SL(2, ℝ) subgroup of isometries in the near-horizon geometry and (ii) a set of cancellations in the Lichnerowicz operator. We show that these two conditions hold for near-extremal black holes in asymptotically flat and asymptotically AdS spacetimes of various dimensions.

The nonlinear stability of (n + 1)-dimensional FLRW spacetimes

We prove nonlinear Lyapunov stability of a family of “([Formula: see text])”-dimensional cosmological models of general relativity locally isometric to the Friedman–Lemaître–Robertson–Walker (FLRW) spacetimes including a positive cosmological constant. In particular, we show that the perturbed solutions to the Einstein–Euler field equations around a class of spatially compact FLRW metrics (for which the spatial slices are compact negative Einstein spaces in general and hyperbolic for the physically relevant [Formula: see text] case) arising from regular Cauchy data remain uniformly bounded and decay to a family of metrics with constant negative spatial scalar curvature. To accomplish this result, we employ an energy method for the coupled Einstein–Euler field equations in constant mean extrinsic curvature spatial harmonic (CMCSH) gauge. In order to handle Euler’s equations, we construct energy from a current that is similar to the one derived by Christodoulou [The Formation of Shocks in 3-dimensional Fluids, EMS Monographs in Mathematics, Vol. 2 (European Mathematical Society, 2007)] (and which coincides with Christodoulou’s current on the Minkowski space) and show that this energy controls the desired norm of the fluid degrees of freedom. The use of a fluid energy current together with the CMCSH gauge condition casts the Einstein–Euler field equations into a coupled elliptic–hyperbolic system. Utilizing the estimates derived from the elliptic equations, we first show that the gravity-fluid energy functional remains uniformly bounded in the expanding direction. Using this uniform boundedness property, we later obtain sharp decay estimates if a positive cosmological constant [Formula: see text] is included, which confirms that the accelerated expansion of the physical universe that is induced by the positive cosmological constant is sufficient to control the nonlinearities in the case of small data. A few physical consequences of this stability result are discussed.

Casimir energy for Lorentz-violating scalar field with helical boundary condition in d spatial dimensions

Delving into spring-like helical configurations, such as DNA within our cells, motivates physicists to inquire about the effects of such structures in the realm of quantum field theory, specifically unraveling their manifestation of effectiveness in Casimir energy. To explore this, we initiated our investigation with the Casimir effect and proceeded to calculate the Casimir energy, along with its thermal and radiative corrections, for massive and massless Lorentz-violating scalar fields across (d+1)-dimensional spacetime. Adhering to the principle that the renormalization program should be consistent with the boundary conditions applied to the quantum fields was paramount. Accordingly, one-loop correction to the Casimir energy for both massive and massless scalar fields under helical boundary conditions by employing a position-dependent counterterm was performed. Our results, spanning across spatial dimensions, exhibited convergence and coherence with established physical grounds. Additionally, we presented the Casimir energy density using graphical plots for systems featuring time-like and space-like Lorentz violations across all spatial dimensions, followed by a comprehensive discussion of the obtained results.