Kaluza-Klein models: can we construct a viable example?

Physical Review D, 2011

In Kaluza-Klein models with an arbitrary number of toroidal internal spaces, we investigate soliton solutions which describe the gravitational field of a massive compact object. Each di-dimensional torus has its own scale factor Ci, i = 1, . . . , N , which is characterized by a parameter γi. We single out the physically interesting solution corresponding to a point-like mass. For the general solution we obtain equations of state in the external and internal spaces. These equations demonstrate that the point-like mass soliton has dust-like equations of state in all spaces. We also obtain the parameterized post-Newtonian parameters, which give the possibility to obtain the formulas for perihelion shift, deflection of light and time delay of radar echoes. Additionally, the gravitational experiments lead to a strong restriction on the parameters of the model: τ = N i=1 diγi = −(2.1 ± 2.3) × 10 −5 . The point-like mass solution with γ1 = . . . = γN = (1 + N i=1 di) −1 contradicts this restriction. The condition τ = 0 satisfies the experimental limitation and defines a new class of solutions which are indistinguishable from general relativity. We call such solutions latent solitons. Black strings and black branes with γi = 0 belong to this class. Moreover, the condition of stability of the internal spaces singles out black strings/branes from the latent solitons and leads uniquely to the black string/brane equations of state pi = −ε/2, i = 1, . . . , N , in the internal spaces and to the number of the external dimensions d0 = 3. The investigation of multidimensional static spherically symmetric perfect fluid with dust-like equation of state in the external space confirms the above results.

Physical Review D, 2008

In addition to the boosted static solution there are two other classes of stationary string-like solutions of the vacuum Einstein equation in (4+1)-dimensions. Each class is characterized by three parameters of mass, tension, and momentum flow along the fifth coordinate. We analyze the metric properties of one of the two classes, which was previously assumed to be naked singular, and show that the solution spectrum contains black string and wormhole in addition to the known naked singularity as the momentum flow to mass ratio increases. Interestingly, there does not exist new zero momentum solution in these cases.

2007

We construct 4+1 dimensional stationary spherically symmetric vacuum black string solutions which are invariant under translation along the fifth direction. The solutions are characterized by three parameters, mass, tension, and conserved momentum along the fifth direction. We analyze local and global equivalence between the stationary solution and the static solution, and discuss some of its physical properties

2022

In this paper, we obtain a static black string solution to a bilocal gravitational source in 3+1 dimensions. The solution is regular at the origin and tends asymptotically to the ordinary static uncharged black string solution of General Relativity. It can present an event horizon and allows an internal horizon depending on the value of the mass density. A mass remnant associated with a vanishing Hawking temperature is also found. In order to stabilize the solution, a perfect cosmological fluid with state parameter ω > − 1 should be present throughout space. However, energy conditions do not exclude an exotic substance nearby the black string. Finally, we present the stationary counterpart of the solution and analyze the behavior of the horizons according to the mass and angular momentum of the spinning object.

Physical Review D, 2012

We investigate nonlinear f (R) theories in the Kaluza-Klein models with toroidal compactification of extra dimensions. A point-like matter source has the dust-like equation of state in our three dimensions and nonzero equations of state in the extra dimensions. We obtain solutions of linearized Einstein equations with this matter source taking into account effects of nonlinearity of the model. There are two asymptotic regions where solutions satisfy the gravitational tests at the same level of accuracy as General Relativity. According to these asymptotic regions, there are two classes of solutions. We call these solutions asymptotic latent solitons. The asymptotic latent solitons from the first class generalize the known result of the linear theory. The asymptotic black strings and black branes are particular cases of these asymptotic solutions. The second class of asymptotic solitons exists only in multidimensional nonlinear models. The main feature for both of these classes of solutions is that the matter sources have tension in the extra dimensions.

Nuclear Physics B, 2021

We will analyze a black string in dRGT massive theory of gravity. Considering different approaches, we will study the critical behavior, phase transition and thermal stability for such a black string solution. We will also analyze the Van der Waals behavior for this system, and observe that the Van der Waals behavior depends on the graviton mass. It will be observed that the thermal fluctuations can modify the behavior of this system. We will explicitly analyze the effect of such fluctuations on the stability of this black string solution. This will be done using the Hessian matrix for this system.

Classical and Quantum Gravity, 2020

In this paper, we study some dynamical properties of neutral and charged particles around a weakly magnetized five dimensional black string. In addition, we calculate the Innermost Stable Circular Orbit (ISCO) of this metric in the presence of a magnetic field by perturbation. We also derive the escape velocity of neutral and charged particles around the black string. It has been shown that adding an extra dimension had slight influences on the effective potential and one component of effective force. The magnitude of the new constant of motion (J) affects on the shape of the potential and thereby the chance of existence of the stable circular orbits. We also found some values of J that vanishes the escape velocity for neutral particles in a specific distance from the center of the black string. In general, by comparing a black hole and a black string, we realized that the magnitude of a new constant of motion causes slight but interesting differences.

Journal of High Energy Physics, 2006

We present arguments for the existence of new black string solutions with negative cosmological constant. These higher-dimensional configurations have no dependence on the 'compact' extra dimension, and their conformal infinity is the product of time and S d−3 × R or H d−3 × R. The configurations with an event horizon topology S d−2 × S 1 have a nontrivial, globally regular limit with zero event horizon radius. We discuss the general properties of such solutions and, using a counterterm prescription, we compute their conserved charges and discuss their thermodynamics. Upon performing a dimensional reduction we prove that the reduced action has an effective SL(2, R) symmetry. This symmetry is used to construct non-trivial solutions of the Einstein-Maxwell-Dilaton system with a Liouville-type potential for the dilaton in (d − 1)-dimensions.

Physical Review D, 2001

In the five-dimensional Einstein gravity with negative cosmological constant in the presence/absence of a non-fine-tuned 3-brane, we have investigated the classical stability of black string solutions which are foliations of four-dimensional AdS/dS-Schwarzschild black holes. Such black strings are generically unstable as in the well-known Gregory-Laflamme instability. For AdS black strings, however, it turns out that they become stable if the longitudinal size of horizon is larger than the order of the AdS 4 radius. Even in the case of unstable black strings, the AdS black strings have a very different feature of string fragmentations from that in the flat brane world. Some implications of our results on the Gubser-Mitra conjecture are also discussed.

Physical Review D, 2013

The particle acceleration mechanism in S 2 × R 1 topology, namely, in the spacetime of the fivedimensional compact black string, has been studied. The expression of center-of-mass energy of the colliding neutral particles near static black string has been found. The collision of a charged particle moving at the innermost stable circular orbit with a neutral particle coming from infinity has been considered when black string is immersed in external uniform magnetic field. It has been shown that the unlimited center-of-mass energy can be approached in the case of the extremal rotation of the black string which is similar to the analogous effect in Kerr spacetime. We have also obtained that the scattering energy of particles in the center-of-mass system can take arbitrarily large values not only for extremal black string but also for the nonextremal one. It has been derived that the presence of the extra dimension can, in principle, increase the upper limit of efficiency of energy extraction from the extremely rotating black string up to 203% versus 143% which can be extracted from the extreme Kerr black hole.