Dimensional Spacetime Research Articles

EFFECTS OF GRAVITY’S RAINBOW ON A RELATIVISTIC SPIN-1 OSCILLATOR

We consider a relativistic spin-1 particle with non-minimal coupling in the context of gravity’s rainbow in the three dimensional background spacetime spanned by static cosmic string. In this context, we acquire an exact solution of the associated spin-1 equation in the modified three dimensional static cosmic string-spanned background spacetime. This relativistic wave equation includes a reducible spinor and this allows us to acquire a non-perturbative expression including the modification functions in the energy domain. In the low energy limit, our results agree well with current literature and provide a basis to discuss the fundamental features of the relativistic spin-1 oscillator. Afterwards, we try to discuss the effects of gravity rainbow functions on the considered spin-1 oscillator in three different scenarios for the modification functions.

The Lamb shift in the BTZ spacetime

We study the Lamb shift of a two-level atom arising from its coupling to the conformal massless scalar field, which satisfies the Dirichlet boundary condition, in the Hartle-Hawking vacuum in the BTZ spacetime, and find that the Lamb shift in the BTZ spacetime is structurally similar to that of a uniformly accelerated atom near a perfectly reflecting boundary in (2+1)-dimensional flat spacetime. Our results show that the Lamb shift is suppressed in the BTZ spacetime as compared to that in the flat spacetime as long as the transition wavelength of the atom is much larger than AdS radius of the BTZ spacetime while it can be either suppressed or enhanced if the transition wavelength of the atom is much less than AdS radius, depending on the location of the atom. In contrast, the Lamb shift is always suppressed very close to the horizon of the BTZ spacetime and remarkably it reduces to that in the flat spacetime as the horizon is approached although the local temperature blows up there.

Decoherence and thermalization of Unruh-DeWitt detector in arbitrary dimensions

We study the decoherence and thermalization of an Unruh-DeWitt detector linearly coupled to the free massless scalar field in flat spacetime with arbitrary dimensions d ≥ 2. The initial state of the detector is chosen to be a pure state consisting of a linear superposition of ground and excited states, and we calculate the time evolution of reduced density matrix of the detector. Using perturbation method, we analytically derive the transition rate of the detector (the rate of change of the diagonal elements in the density matrix) and the decoherence rate (the rate of change of the off-diagonal elements in the density matrix). We find that the results are not the same in odd and even dimensional spacetimes, but the unitarity of the qubit is preserved in both cases. The real part of the decoherence rate is related to the transition rate, while the imaginary part may contain different forms of divergence terms in different dimensions due to the temporal order product operator and the singularities of the Wightman function for quantum field theory. We derive the recurrence formula to obtain the divergence terms in each dimension and analyze the renormalization problem.

Lifshitz symmetry: Lie algebras, spacetimes and particles

We study and classify Lie algebras, homogeneous spacetimes and coadjoint orbits (“particles”) of Lie groups generated by spatial rotations, temporal and spatial translations and an additional scalar generator. As a first step we classify Lie algebras of this type in arbitrary dimension. Among them is the prototypical Lifshitz algebra, which motivates this work and the name “Lifshitz Lie algebras”. We classify homogeneous spacetimes of Lifshitz Lie groups. Depending on the interpretation of the additional scalar generator, these spacetimes fall into three classes:1. (d+2)-dimensional Lifshitz spacetimes which have one additional holographic direction;2. (d+1)-dimensional Lifshitz-Weyl spacetimes which can be seen as the boundary geometry of the spacetimes in (1) and where the scalar generator is interpreted as an anisotropic dilation;3. and (d+1)-dimensional aristotelian spacetimes with one scalar charge, including exotic fracton-like symmetries that generalise multipole algebras.We also classify the possible central extensions of Lifshitz Lie algebras and we discuss the homogeneous symplectic manifolds of Lifshitz Lie groups in terms of coadjoint orbits.

Multiverse in Karch-Randall Braneworld

In this paper, we propose a model based on wedge holography that can describe the multiverse. In wedge holography, we consider two gravitating baths, one of which has strong gravity and the other one has weak gravity. To describe a multiverse, we consider 2n Karch-Randall branes, and we propose that various d-dimensional universes are localized on these branes. These branes are embedded in (d + 1)-dimensional spacetime. The model is useful in obtaining the Page curve of black holes with multiple horizons and in the resolution of the “grandfather paradox”. We explicitly obtain the Page curves of eternal AdS black holes for n = 2 multiverse and Schwarzschild de-Sitter black hole with two horizons.

On the Dynamical Instability of Monatomic Fluid Spheres in (N + 1)-Dimensional Spacetime

In this note, I derive the Chandrasekhar instability of a fluid sphere in (N + 1)-dimensional Schwarzschild–Tangherlini spacetime and take the homogeneous (uniform energy density) solution for illustration. Qualitatively, the effect of a positive (negative) cosmological constant tends to destabilize (stabilize) the sphere. In the absence of a cosmological constant, the privileged position of (3 + 1)-dimensional spacetime is manifest in its own right. As it is, the marginal dimensionality in which a monatomic ideal fluid sphere is stable but not too stable to trigger the onset of gravitational collapse. Furthermore, it is the unique dimensionality that can accommodate stable hydrostatic equilibrium with a positive cosmological constant. However, given the current cosmological constant observed, no stable configuration can be larger than 1021M⊙. On the other hand, in (2 + 1) dimensions, it is too stable either in the context of Newtonian Gravity (NG) or Einstein’s General Relativity (GR). In GR, the role of negative cosmological constant is crucial not only to guarantee fluid equilibrium (decreasing monotonicity of pressure) but also to have the Bañados–Teitelboim–Zanelli (BTZ) black hole solution. Owing to the negativeness of the cosmological constant, there is no unstable configuration for a homogeneous fluid disk with mass 0<M≤0.5 to collapse into a naked singularity, which supports the Cosmic Censorship Conjecture. However, the relativistic instability can be triggered for a homogeneous disk with mass 0.5<M≲0.518 under causal limit, which implies that BTZ holes of mass MBTZ>0 could emerge from collapsing fluid disks under proper conditions. The implicit assumptions and implications are also discussed.

A space-time calculus based on symmetric 2-spinors

In this paper we present a space-time calculus for symmetric spinors, including a product with a number of index contractions followed by symmetrization. As all operations stay within the class of symmetric spinors, no involved index manipulations are needed. In fact spinor indices are not needed in the formalism. It is also general because any covariant tensor expression in a 4-dimensional Lorentzian spacetime can be translated to this formalism. The computer algebra implementation SymSpin as part of xAct for Mathematica is also presented.

Margulis multiverse: Infinitesimal rigidity, pressure form and convexity

In this article we construct the pressure forms on the moduli spaces of higher dimensional Margulis spacetimes without cusps and study their properties. We show that the Margulis spacetimes are infinitesimally determined by their marked Margulis invariant spectra. We use this fact to show that the restrictions of the pressure form give Riemannian metrics on the constant entropy sections of the quotient moduli space. We also show that constant entropy sections of the moduli space with fixed linear parts bound convex domains.

Deflection in higher dimensional spacetime and asymptotically non-flat spacetimes

Using a perturbative technique, in this work we study the deflection of null and timelike signals in the extended Einstein–Maxwell spacetime, the Born–Infeld gravity and the charged Ellis–Bronnikov (CEB) spacetime in the weak field limit. The deflection angles are found to take a (quasi-)series form of the impact parameter, and automatically takes into account the finite distance effect of the source and observer. The method is also applied to find the deflections in CEB spacetime with arbitrary dimension. It’s shown that to the leading non-trivial order, the deflection in some n-dimensional spacetimes is of the order . We then extended the method to spacetimes that are asymptotically non-flat and studied the deflection in a nonlinear electrodynamical scalar theory. The deflection angle in such asymptotically non-flat spacetimes at the trivial order is found to be not π anymore. In all these cases, the perturbative deflection angles are shown to agree with numerical results extremely well. The effects of some nontrivial spacetime parameters as well as the signal velocity on the deflection angles are analyzed.

Magnetic monopoles with no strings attached: a portal to the dark side of dual electrodynamics

It has long been known that in the absence of electric charges and currents, Maxwell’s electromagnetism in 4 dimensional vacuum Minkowski space-time is invariant under SO(2) dual transformations that mix its electric and magnetic fields. Extending this symmetry to include the coupling to electrically charged matter, requires a dual coupling to magnetically charged matter as well, leading to Maxwell equations for SO(2) dual electrodynamics. Based on a doubled ensemble of SO(2) dual 4-vector gauge potentials which does away with the need of Dirac string singularities for magnetic monopoles, a local Lagrangian action principle for SO(2) dual electromagnetism is known, which manifestly displays all the required space-time and internal symmetries, and reduces to the experimentally well established Maxwell electrodynamics in the absence of magnetic charges and currents. Applying the same considerations for the matter action of electrically and magnetically charged point particles, a unique SO(2) dual generalised Lorentz force is identified for SO(2) dual electrodynamics, truly different from the usual SO(2) dual invariant choice motivated by simplicity, but yet made arbitrarily and which does not derive from some action principle. This generalised Lorentz force involves a single real and new coupling constant of unknown value, without the requirement of a Dirac–Schwinger–Zwanziger quantisation condition for electric and magnetic charges of dyons. A physical consequence for SO(2) dual electrodynamics of this coupling constant if nonvanishing, is to open a channel, or portal between the otherwise mutually totally “dark” sectors of electric and magnetic charges for electromagnetic interactions.

Breaking of the universal nature of the central charge criticality in AdS black holes in Gauss-Bonnet gravity

In this paper, we have studied the thermodynamics of Gauss-Bonnet black holes in D-dimensional $AdS$ spacetime. Here, the cosmological constant ($\Lambda$), Newton's gravitational constant ($G$) and the Gauss-Bonnet parameter ($\alpha$) are varied in the bulk, and a mixed first law is rewritten considering central charge ($C$) (of dual boundary conformal theory) and its conjugate variable utilising the gauge-gravity duality. A novel universal nature of central charge near the critical point of black hole phase transition in Einstein's gravity has been observed in \cite{mann1}. We observe that this universal nature breaks when such phase transition is considered for black holes in the Gauss-Bonnet gravity. Apart from this, treating the Gauss-Bonnet parameter as a thermodynamic variable as suggested in \cite{kastori} in light of the consistency between first law and the Smarr relation leads to modified thermodynamic volume (conjugate to variable cosmological constant), adding to a new understanding of the Van der Waals gas like behaviour of the black holes in higher dimensional and higher curvature gravity theories. Our analysis considers a general $D$ dimensional background. We have then imposed a greater focus in the analysis of the phase structure of the five dimensional Gauss-Bonnet spacetime. Our analysis also shows that the general universal nature of the critical value of the central charge (which was present in four dimensional $AdS$ spacetime), breaks down in case of five dimensional $AdS$ spacetime even in the absence of Gauss-Bonnet gravity. This finding indicates the universal nature of the central charge may be a special feature of the four dimensional $AdS$ spacetime only.

Whittaker modules and quasi-Whittaker modules for the Schrödinger algebra in (2 + 1)-dimensional spacetime

In this paper, we classify simple (quasi)-Whittaker modules for the Schrödinger Lie algebra s2 in (2+1)-dimensional space-time. Moreover, we show that a simple sn-module is a Whittaker module if and only if it is a locally finite sn+-module, and it is a quasi-Whittaker module if and only if it is a locally finite hn-module. Also, we determine the center of U(s2) and U(s2/Cz).

On the Traversable Yukawa–Casimir Wormholes

Wormholes require negative energy, and therefore an exotic matter source. Since Casimir’s energy is negative, it has been speculated as a good candidate to source those objects a long time ago. However, only very recently a full solution for 3+1 dimensions has been found by Garattini, thus the Casimir energy can be a source of traversable wormholes. We have recently shown that this can be generalized to higher dimensional spacetimes. Lately, Garattini sought to analyze the effects of Yukawa-type terms on shape functions and obtained promising results. However, his approach breaks down the usual relation between the energy density and the radial pressure of the Casimir field. In this work, we study the effects of the same three Yukawa-type corrective factors on the shape function of the Casimir wormhole keeping the usual way to obtain the radial pressure from the energy density. We show that, in addition to being able to construct traversable wormholes that satisfy all the necessary conditions, it is possible to obtain adequate constraints on the constants to recover the standard case with no double limit used by Garatinni. We show that, for some values of the Yukawa parameter, it is possible to generate a repulsive gravitational wormhole. Finally, we analyze the stability of the solutions and find the upper bounds for the Yukawa factor.

Connection dynamics of reduced five-dimensional Kaluza-Klein theory and its deparametrization

The connection dynamics of the 5-dimensional Kaluza-Klein theory reduced on 4-dimensional spacetime is obtained by performing the Hamiltonian analysis and canonical transformations. Deparametrization is achieved in the spherically symmetric model of the theory without introducing additional matter fields beyond the 5-dimensional gravity. Thus the physical time evolution and the physical spatial coordinate can be provided by the geometrical degrees of freedom in the higher dimensional spacetime.

Development of singularities in the relativistic Euler equations

The purpose of this paper is to study the phenomenon of singularity formation in large data problems for C 1 C^1 solutions to the Cauchy problem of the relativistic Euler equations. The classical theory established by [P. D. Lax [J. Math. Phys. 5 (1964), pp. 611–613] shows that, for 2 × 2 2\times 2 hyperbolic systems, the break-down of C 1 C^1 solutions occurs in finite time if initial data contain any compression in some truly non-linear characteristic field under some additional conditions, which include genuine non-linearity and the strict positivity of the difference between two corresponding eigenvalues. These harsh structural assumptions mean that it is highly non-trivial to apply this theory to archetypal systems of conservation laws, such as the (1+1)-dimensional relativistic Euler equations. Actually, in the (1+1)-dimensional spacetime setting, if the mass-energy density ρ \rho does not vanish initially at any finite point, the essential difficulty in considering the possible break-down is coming up with a way to obtain sharp enough control on the lower bound of ρ \rho . To this end, based on introducing several key artificial quantities and some elaborate analysis on the difference of the two Riemann invariants, we characterized the decay of mass-energy density lower bound in time, and ultimately made some concrete progress. On the one hand, for the C 1 C^1 solutions with large data and possible far field vacuum to the isentropic flow, we verified the theory obtained by P. D. Lax in 1964. On the other hand, for the C 1 C^1 solutions with large data and strictly positive initial mass-energy density to the non-isentropic flow, we exhibit a numerical value N N , thought of as representing the strength of an initial compression, above which all initial data lead to a finite-time singularity formation. These singularities manifest as a blow-up in the gradient of certain Riemann invariants associated with corresponding systems.

Another look at the Balázs-Quastel-Seppäläinen theorem

We study the KPZ equation with a 1 + 1 − 1+1- dimensional spacetime white noise, started at equilibrium, and give a different proof of the main result of Balázs, Quastel, and Seppäläinen [J. Amer. Math. Soc. 24 (2011), pp. 683–708], i.e., the variance of the solution at time t t is of order t 2 / 3 t^{2/3} . Instead of using a discrete approximation through the exclusion process and the second class particle, we utilize the connection to directed polymers in random environment. Along the way, we show the annealed density of the stationary continuum directed polymer equals to the two-point covariance function of the stationary stochastic Burgers equation, confirming the physics prediction of Maes and Thiery [J. Stat. Phys. 168 (2017), pp. 937–963].

A positive cosmological constant as a geometrical artifact

In this paper, we revisit the classical mechanism to produce [Formula: see text]-dimensional spacetimes via Kaluza–Klein compactification. We made the assumption that the [Formula: see text]-dimensional bulk geometry [Formula: see text] admits a Homothetic Vector Field (HVF) [Formula: see text] relaxing the existence of a zero i.e. [Formula: see text] holds on [Formula: see text] and the homothetic bivector [Formula: see text]. Under these circumstances, we identify the origin of a positive cosmological constant in the [Formula: see text]-dimensional spacetime as the homothetic factor representing a geometrical artifact of late time state of the [Formula: see text]-dimensional bulk spacetime.

Unitary constraints on semiclassical Schwarzschild black holes in the presence of island

We reconsider $D\ensuremath{\ge}4$ dimensional asymptotically flat eternal Schwarzschild black hole and focus on the situation where the inner boundary of the radiation region is chosen to be near the horizon (i.e., $\ensuremath{\beta}\ensuremath{\ll}1$). The tension between the near-horizon condition and the short-distance approximation emerges in large dimensions in [K. Hashimoto, N. Iizuka, and Y. Matsuo, J. High Energy Phys. 06 (2020) 085]. We remove this tension by introducing a more proper near horizon condition; thus, the resulting island solution is well-behaved in any $D\ensuremath{\ge}4$ dimensional spacetime. Interestingly, a novel constraint is obtained in this situation as required by the existence of the island solution, which directly leads to the constraints on the size of the Schwarzschild black hole, the position of the inner boundary for the radiation region, or the value of $c\ifmmode\cdot\else\textperiodcentered\fi{}{\stackrel{\texttildelow{}}{G}}_{N}$ in any $D\ensuremath{\ge}4$ dimension. When considering the large $D$ limit, the constraint on the size of the Schwarzschild black hole obtained in this situation is in agreement with the result given in [F. Holdt-Sordrensen, D. A. McGady, and N. Wintergerst, Phys. Rev. D 102, 026016 (2020)]. We interpret these as the unitary constraints implied by the presence of island in semiclassical gravity.

Canonical Quantization of Yang-Mills Theory in Curved Space-time

The framework of canonical quantization of quantum field is given by Lagrangian (not Lagrangian density) formulation to avoid the problem of transfer physical quantities from 4–dimensional space–time to 3–dimensional position space (3–dimensional hypersurface with normal vector dt).

Induced Vacuum Energy Density of Quantum Charged Scalar Matter in the Background of an Impenetrable Magnetic Tube with the Neumann Boundary Condition

We consider the vacuum polarization of a charged scalar matter field outside the tube with magnetic flux inside. The tube is impenetrable for quantum matter, and the perfectly rigid (Neumann) boundary condition is imposed at its surface. We write expressions for the induced vacuum energy density for the case of a space with arbitrary dimension and for an arbitrary value of the magnetic flux. We do the numerical computation for the case of a half-integer flux value in the London flux units and the (2 + 1)-dimensional space-time. We show that the induced vacuum energy of the charged scalar matter field is induced, if the Compton wavelength of the matter field exceeds the transverse size of the tube considerably. We show that the vacuum energy is periodic in the value of the magnetic flux of the tube, providing a quantumfield-theoretical manifestation of the Aharonov–Bohm effect. The dependencies of the induced vacuum energy upon the distance from the center of the tube for different values of its thickness are obtained. The results are compared to those obtained earlier in the case of the perfectly reflecting (Dirichlet) boundary condition. It is shown that the value of the induced vacuum energy density in the case of the Neumann boundary condition is greater than in the case of the Dirichlet boundary condition.