Deficit Angle Research Articles

Point-particle solution and the asymptotic flatness in 2+1D Hořava gravity

We show that the solution corresponding to the gravitational field of a point particle at rest in $2+1$ nonprojectable Ho\ifmmode \check{r}\else \v{r}\fi{}ava is exactly the same as $2+1$ general relativity with the same source. In general relativity this solution is well known, it is a flat cone whose deficit angle is proportional to the mass of the particle. To establish the system we couple the Ho\ifmmode \check{r}\else \v{r}\fi{}ava theory to a point particle with relativistic action. Motivated by this solution, we postulate the condition of asymptotic flatness exactly in the same way of $2+1$ general relativity. A remarkable feature of this condition is that the dominant mode is not fixed, but affected by the mass of the configuration. In this scheme, another important coincidence with $2+1$ general relativity under asymptotic flatness is that the energy is the same (except for some coupling constants involved), the $z=1$ term with the derivative of the lapse function does not contribute.

Internal rotation of the tibial component in total knee arthroplasty can lead to extension deficit.

Stiffness is a common problem following total knee arthroplasty (TKA). Mal-rotated components have been claimed to be the major cause of pain and limited motion after TKA. The present study investigates whether intra-operative intentional malrotation of the tibial component would change in vivo kinematics. The hypothesis is excessive internal rotation of the tibial component would result in postoperative extension deficit. Thirty-one patients were enrolled in this study. After completing bony cuts and proper soft tissue balancing, the femoral and tibial trials were impacted and fixed using small pins. Lateral radiographs were used to measure and compare intraoperative full knee extension during normal and after intentional internal rotation of the tibial component. The extension deficit angles were also compared between the posterior stabilised (PS) and cruciate retaining (CR) implants. For normal tibial component rotation, the median (interquartile range) extension deficit was 0° (4). The mean tibial trial intentional internal rotation was 21.2° (± 4.5). The median (interquartile range) extension deficit significantly increased to 6° (4) after tibial component internal rotation (p = 0.001). The use of PS spacers resulted in a significantly greater extension deficit after intentional internal rotation 9° (5) compared to that of the CR implant 1° (4) (p = 0.001). Internal rotation of the tibial component in total knee arthroplasty can lead to postoperative extension deficit. This could be attributed to interference with "screw home" mechanism that requires full external rotation of the tibia on the femur. Consequently, this deficit may cause pain and knee stiffness following TKA. III.

Topological and noninertial effects in an Aharonov–Bohm ring

In this paper, we study the influence of topological and noninertial effects on a Dirac particle confined in an Aharonov-Bohm (AB) ring. Next, we explicitly determine the Dirac spinor and the energy spectrum for the relativistic bound states. We observe that this spectrum depends on the quantum number $n$, magnetic flux $\Phi$ of the ring, angular velocity $\omega$ associated to the noninertial effects of a rotating frame, and on the deficit angle $\eta$ associated to the topological effects of a cosmic string. We verified that this spectrum is a periodic function and grows in values as a function of $n$, $\Phi$, $\omega$, and $\eta$. In the nonrelativistic limit, we obtain the equation of motion for the particle, where now the topological effects are generated by a conic space. However, unlike relativistic case, the spectrum of this equation depends linearly on the velocity $\omega$ and decreases in values as a function of $\omega$. Comparing our results with other works, we note that our problem generalizes some particular cases of the literature. For instance, in the absence of the topological and noninertial effects ($\eta=1$ and $\omega=0$) we recover the usual spectrum of a particle confined in an AB ring ($\Phi\neq{0}$) or in an 1D quantum ring ($\Phi=0$).

Isometric bending requires local constraints on free edges

While the shape equations describing the equilibrium of an unstretchable thin sheet that is free to bend are known, the boundary conditions that supplement these equations on free edges have remained elusive. Intuitively, unstretchability is captured by a constraint on the metric within the bulk. Naïvely one would then guess that this constraint is enough to ensure that the deformations determining the boundary conditions on these edges respect the isometry constraint. If matters were this simple, unfortunately, it would imply unbalanced torques (as well as forces) along the edge unless manifestly unphysical constraints are met by the boundary geometry. In this article, we identify the source of the problem: not only the local arc-length but also the geodesic curvature need to be constrained explicitly on all free edges. We derive the boundary conditions which follow. In contrast to conventional wisdom, there is no need to introduce boundary layers. This framework is applied to isolated conical defects, both with deficit as well, but more briefly, as surplus angles. Using these boundary conditions, we show that the lateral tension within a circular cone of fixed radius is equal but opposite to the radial compression, and independent of the deficit angle itself. We proceed to examine the effect of an oblique outer edge on this cone perturbatively demonstrating that both the correction to the geometry as well as the stress distribution in the cone kicks in at second order in the eccentricity of the edge.

Dynamical evolution of electromagnetic perturbation in the background of a scalar hairy black hole in Horndeski theory

We have investigated dynamical evolution of electromagnetic perturbation in a scalar hairy black hole spacetime, which belongs to solutions in Horndeski theory with a logarithmic cubic term. Our results show that the parameter [Formula: see text] affects the existence of event horizon and modifies the asymptotical structure of spacetime at spatial infinity, which imprints on the quasinormal frequency of electromagnetic perturbation. Moreover, we find that the late-time tail of electromagnetic perturbation in this background depends also on the parameter [Formula: see text] due to the existence of solid angle deficit. These imply that the spacetime properties arising from the logarithmic cubic term in the action play important roles in the dynamical evolutions of the electromagnetic perturbation in the background of a scalar hairy black hole.

Deflection angle of light for an observer and source at finite distance from a rotating global monopole

By using a method improved with a generalized optical metric, the deflection of light for an observer and source at finite distance from a lens object in a stationary, axisymmetric and asymptotically flat spacetime has been recently discussed [Ono, Ishihara, Asada, Phys. Rev. D 96, 104037 (2017)]. In this paper, we study a possible extension of this method to an asymptotically nonflat spacetime. We discuss a rotating global monopole. Our result of the deflection angle of light is compared with a recent work on the same spacetime but limited within the asymptotic source and observer [Jusufi et al., Phys. Rev. D 95, 104012 (2017)], in which they employ another approach proposed by Werner with using the Nazim's osculating Riemannian construction method via the Randers-Finsler metric. We show that the two different methods give the same result in the asymptotically far limit. We obtain also the corrections to the deflection angle due to the finite distance from the rotating global monopole. Near-future observations of Sgr A * will be able to put a bound on the global monopole parameter $\ensuremath{\beta}$ as $1\ensuremath{-}\ensuremath{\beta}<{10}^{\ensuremath{-}3}$ for a rotating global monopole model, which is interpreted as the bound on the deficit angle $\ensuremath{\delta}<8\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$ [rad].

Quasitopological magnetic brane coupled to nonlinear electrodynamics

In this paper, we are eager to construct a new class of (n+1)-dimensional static magnetic brane solutions in quasi-topological gravity coupled to nonlinear electrodynamics such as exponential and logarithmic forms. The solutions of this magnetic brane are horizonless and have no curvature. For \rho near r_{+}, the solution f(\rho) is dependent to the values of parameters q and n and for larger \rho, it depends on the coefficients of Love-Lock and quasi-topological gravities \lambda, \mu and c. The obtained solutions also have a conic singularity at r=0 with a deficit angle that is only dependent to the parameters q, n and \beta. We should remind that the two forms of nonlinear electrodynamics theory have similar behaviors on the obtained solutions. At last, by using the counterterm method, we obtain conserved quantities such as mass and electric charge. The value of the electric charge for this static magnetic brane is obtained zero.

Universes Inside a Black Hole with the de Sitter Interior

We outline the basic ideas and analyze the possibilities of the quantum birth of universes inside regular black holes with the de Sitter interior replacing a singularity. We compare different cases and show that the most plausible case is the birth of a flat universe from an initial quantum fluctuation with a small admixture of radiation and strings with the negative deficit angle, which provides the existence of a potential barrier needed for quantum tunneling.

Surface tension of membranes depending on the boundary shape

In this paper, we study the boundary effect on the surface (or frame) tension of elastic membrane surface models. The frame tension generally depends only on the projected area of the boundary over which the surface spans. However, from a spin model analogy, the frame tension is expected to be dependent also on the boundary shape at the continuous transition point. We confirm this expectation using the following fixed-connectivity and tethered surface models: the surface model of Helfrich and Polyakov and a surface model with deficit angle term. We also discuss the reason why this expectation is worthwhile to study.

The Letelier spacetime with quintessence: Solution, thermodynamics and Hawking radiation

We obtain the solution corresponding to a static and spherically symmetric black hole with a cloud of strings (Letelier spacetime) immersed in a quintessential fluid. We discuss some aspects of its thermodynamics and complete proceeding studies in the spacetime of Schwarzschild with quintessence and a solid deficit angle, which is mathematically analogous to the solution we obtained. We also present a discussion about Hawking radiation of particles, in the background under consideration and compare with related studies in the literature.

Some effects of non-conservative gravity on cosmic string configurations

We investigate some consequences of a specific non-conservation of the energy-momentum tensor for the physics of certain cosmic string configurations. This non-conservation was induced by a new gravitational theory recently introduced as an attempt to incorporate dissipative systems in the description of gravity. This model of gravity is endowed with a variational principle, where an action dependence on the geometric sector is assumed. For the Abelian Higgs string we derive the dynamical equations and provide the numerical solutions describing the behavior of the Higgs and gauge fields and the profile of the metric functions for different cases of the parameter that characterizes the model. Additionally, from this numerical approach we find how the inner structure of the cosmic string is affected by this underlying gravitational theory, by analyzing the deviations both on the mass per unit length and the deficit angle of the string. Next, we proceed with an analytical treatment obtaining the solution close to the string axis and also the corresponding vacuum solution. Our analytical results are also complemented with the study of a thick cosmic string model, where the defect is endowed with a finite core. In this case we have obtained the proper interior solution which, joined together with the vacuum metric outside, provides an exact solution for the exterior geometry which generalizes previous results and leads to a decreasing of the mass per unit length of the cosmic string.

Direct detection of universal expansion by holonomy in the McVittie spacetime

In general relativity the parallel transfer of a vector around a closed curve in spacetime, or along two curves which together form a closed loop, usually results in a nonzero deficit angle between the vector's initial and final positions. We show that such holonomy in the McVittie spacetime, which represents a gravitating object imbedded in an expanding universe, can in principle be used to directly detect the expansion of the universe, for example by measuring changes in the components of a gyroscopic spin axis. Although such changes are of course small, they are large enough (\D S \sim 10^{-7}) that they could conceivably be measured if the real universe behaved like the McVittie spacetime. The real problem is that virialization will lead to domains decoupled from the global expansion on a scale much larger than that of the solar system, making such an experiment infeasible probably even in principle. Nevertheless the effect is of interest in relation to ongoing discussions, dating back at least to Einstein and Straus, which concern the relationship between the expansion of the universe and local systems.

Cosmic string and black hole limits of toroidal Vlasov bodies in general relativity

We numerically investigate limits of a two-parameter family of stationary solutions to the Einstein-Vlasov system. The solutions are toroidal and have non-vanishing angular momentum. As one tunes to more relativistic solutions (measured for example by an increasing redshift) there exists a sequence of solutions which approaches the extreme Kerr black hole family. Solutions with angular momentum larger than the square of the mass are also investigated, and in the relativistic limit the near-field geometry of such solutions is observed to become conical in the sense that there is a deficit angle. Such solutions may provide self-consistent models for rotating circular cosmic strings.

Vacuum fluctuations and boundary conditions in a global monopole

We study the vacuum fluctuations of a massless scalar field $\hat{\Psi}$ on the background of a global monopole. Due to the nontrivial topology of the global monopole spacetime, characterized by a solid deficit angle parametrized by $\eta^2$, we expect that $\left<\hat{\Psi}^2\right>_{\text{ren}}$ and $\left<\hat{T}_{\mu\nu}\right>_{\text{ren}}$ are nonzero and proportional to $\eta^2$, so that they annul in the Minkowski limit $\eta\to0$. However, due to the naked singularity at the monopole core, the evolution of the scalar field is not unique. In fact, they are in one to one correspondence with the boundary conditions which turn into self-adjoint the spatial part of the wave operator. We show that only Dirichlet boundary condition corresponds to our expectations and gives zero contribution to the vacuum fluctuations in Minkowski limit. All other boundary conditions give nonzero contributions in this limit due to the nontrivial interaction between the field and the singularity.

Transition processes of a static multilevel atom in the cosmic string spacetime with a conducting plane boundary

We investigate the transition processes of a static multilevel atom in interaction with a fluctuating vacuum quantum electromagnetic field in the cosmic string spacetime in the presence of an infinite, perfectly conducting plane. Using the formalism proposed by DDC, we find that the presence of the boundary modifies both vacuum fluctuations and radiation reaction contributions to the atomic spontaneous emission rate. Our results indicate that the total decay rate and the boundary-induced contribution both depend upon the atom-string distance, the atom-plate separation, the extent of the polar angle deficit induced by the string, and the atomic polarization direction. By adjusting these parameters, the atomic decay rate can be either enhanced or weakened significantly by the boundary. Moreover, the presence of the boundary can distinguish certain polarization directions that bring about the same decay rate in the case of a free cosmic string spacetime. Theoretically, our work suggests a more flexible means to adjust and control the radiative processes of atoms.

Compact objects in scalar-tensor theories after GW170817

The recent observations of neutron star mergers have changed our perspective on scalar-tensor theories of gravity, favouring models where gravitational waves travel at the speed of light. In this work we consider a scalar-tensor set-up with such a property, belonging to a beyond Horndeski system, and we numerically investigate the physics of locally asymptotically flat black holes and relativistic stars. We first determine regular black hole solutions equipped with horizons: they are characterized by a deficit angle at infinity, and by large contributions of the scalar to the geometry in the near horizon region. We then study configurations of incompressible relativistic stars. We show that their compactness can be much higher than stars with the same energy density in General Relativity, and the scalar field profile imposes stringent constraints on the star properties. These results can suggest new ways to probe the efficiency of screening mechanisms in strong gravity regimes, and can help to build specific observational tests for scalar-tensor gravity models with unit speed for gravitational waves.

Designing patterns using triangle-quad hybrid meshes

We present a framework to generate mesh patterns that consist of a hybrid of both triangles and quads. Given a 3D surface, the generated patterns fit the surface boundaries and curvatures. Such regular and near regular triangle-quad hybrid meshes provide two key advantages: first, novel-looking polygonal patterns achieved by mixing different arrangements of triangles and quads together; second, a finer discretization of angle deficits than utilizing triangles or quads alone. Users have controls over the generated patterns in global and local levels. We demonstrate applications of our approach in architectural geometry and pattern design on surfaces.

Electromagnetic Vacuum Densities Induced by a Cosmic String

We investigate the influence of a generalized cosmic string in (D+1)-dimensional spacetime on the local characteristics of the electromagnetic vacuum. Two special cases are considered with flat and locally de Sitter background geometries. The topological contributions in the vacuum expectation values (VEVs) of the squared electric and magnetic fields are explicitly separated. Depending on the number of spatial dimensions and on the planar angle deficit induced by the cosmic string, these contributions can be either negative or positive. In the case of the flat bulk, the VEV of the energy–momentum tensor is evaluated as well. For the locally de Sitter bulk, the influence of the background gravitational field essentially changes the behavior of the vacuum densities at distances from the string larger than the curvature radius of the spacetime.

Some results on a black hole with a global monopole in Poincar\xe9 gravity

The aim of this work is to study the thermodynamics and spin current of a system corresponding to a black hole containing a global monopole in the context of Poincaré gravity theory which is an extension of general relativity, in the sense that the intrinsic angular momentum of matter is also a source of gravitational interaction. Thus, in this work we find the solution corresponding to the spacetime under consideration by taking into account that the action which describes this system contains terms corresponding to the curvature and torsion. The metric obtained is a function of mass, solid angle deficit and the coupling constants of the quadratic terms of the curvature and torsion. In this model, the stability of the system is studied through the analysis of the Hawking temperature and the specific heat. In this context it was also studied the critical temperatures of the system considering positive or negative cosmological constant. In the vicinity of the black hole with a global monopole, where there is a logarithmic correction due to the relationship between the torsion and curvature fields, some analysis were done. We also study the AdS/dS limit where the black hole is analyzed from the topological point of view. Although the effect of spin current density at low energies is negligible, in the vicinity of strong gravitational fields it can generate an appreciable effect due to spin gravity coupling.

Magnetic solutions in Einstein-massive gravity with linear and nonlinear fields

The solutions of U(1) gauge-gravity coupling is one of the interesting models for analyzing the semi-classical nature of spacetime. In this regard, different well-known singular and nonsingular solutions have been taken into account. The paper at hand investigates the geometrical properties of the magnetic solutions by considering Maxwell and power Maxwell invariant (PMI) nonlinear electromagnetic fields in the context of massive gravity. These solutions are free of curvature singularity, but have a conic one which leads to presence of deficit/surplus angle. The emphasize is on modifications that these generalizations impose on deficit angle which determine the total geometrical structure of the solutions, hence, physical/gravitational properties. It will be shown that depending on the background spacetime [being anti de Sitter (AdS) or de Sitter (dS)], these generalizations present different effects and modify the total structure of the solutions differently.