Narrow Results

Interior solution for the Fisher–Janis–Newman–Winicour (FJNW) metric is presented in an arbitrary dimensional space-time. The interior solution matches smoothly to the FJNW metric and therefore represents a globally regularized model of the FJNW solution describing a spherical source of gravitational field in the presence of a massless scalar field. The curvature invariants are derived. It is shown that the energy conditions are valid for a wide range of the metric parameters. We also obtained the Buchdahl limit in various dimensions.

In a particular variant of Kaluza–Klein theory, the so-called induced-matter theory (IMT), it is shown that any configuration of matter may be geometrically induced from a five-dimensional vacuum space. By using a similar approach we show that any distribution of charges and currents may also be induced from a five-dimensional space. Although in the case of IMT the geometry is Riemannian and the fundamental equations are the five-dimensional Einstein equations in vacuum, here we consider a Minkowskian geometry and five-dimensional Maxwell equations in vacuum.

We study the intriguing analogy between gravitational dynamics of the horizon and thermodynamics for the case of nonstationary radiating spherically symmetric black holes both in four dimensions and higher dimensions. By defining all kinematical parameters of nonstationary radiating black holes in terms of null vectors, we demonstrate that it is possible to interpret the Einstein field equations near the apparent horizon in the form of a thermodynamical identity T dS = dE+P dV.

Neutrino physics is one of the most active fields of research with important implications for particle physics, cosmology and astrophysics. On the other hand, motivated by some theories including string theory, formulation of physical theories in more than four spacetime dimensions has been the subject of increasing attention in recent years. Interaction of neutrinos with gravitational fields is one of the interesting phenomena which can lead to transition between different helicity states (spin oscillations). We study neutrino spin oscillations in Schwarzschild and RN backgrounds in higher-dimensional gravitational fields. We calculate the transition probability as a function of time and also study the dependence of the oscillation frequency on the orbital radius. The results help us to better understand the behavior of gravity and neutrinos in higher dimensions.

Gravitational collapse of radiation shells in a non-self-similar higher dimensional spherically symmetric space–time is studied. Strong curvature naked singularities form a highly inhomogeneous collapse, violating the cosmic censorship conjecture. As a special case, self similar models can be constructed.

We study the spherically symmetric collapse of a fluid with nonvanishing radial pressure in higher dimensional space–time. We obtain the general exact solution in the closed form for the equation of state (P_r = γρ), which leads to the explicit construction of the root equation governing the nature (black hole versus naked singularity) of the central singularity. A remarkable feature of the root equation is its invariance for the cases; (D, γ = 0) and (D+1, γ = -1) where D is the dimension of space–time. For the ultimate end result of the collapse, these two cases are absolutely equivalent, which is indeed a very interesting new result that brings out the interplay between dimension D of space–time and the equation of state parameter γ.

We present a simple higher dimensional FRW-type of model where the acceleration is apparently caused by the presence of the extra dimensions. Assuming an ansatz in the form of the deceleration parameter, we get a class of solutions some of which shows the desirable feature of dimensional reduction as well as reasonably good physical properties of matter. Interestingly we do not have to invoke an extraneous scalar field or a cosmological constant to account for this acceleration. One argues that the terms containing the higher dimensional metric coefficients produces an extra negative pressure that apparently drives the inflation of the 4D space with an accelerating phase. It is further found that in line with the physical requirements our model admits of a decelerating phase in the early era along with an accelerating phase at present. Further the models asymptotically mimic a steady-state-type of universe although it starts from a big-bang-type of singularity. Correspondence to Wesson's induced matter theory is also briefly discussed and, in line with it, it is argued that the terms containing the higher dimensional metric coefficients apparently creates a negative pressure which drives the inflation of the 3-space with an accelerating phase.

Homogeneous cosmological solutions are obtained in five-dimensional (5D) space–time assuming equations of state p = kρ and p₁ = γρ where p is the isotropic 3-pressure and p₁, that for the fifth dimension. Using different values for the constants k and γ many known solutions are rediscovered. Further the current acceleration of the universe has led us to investigate higher dimensional gravity theory, which is able to explain acceleration from a theoretical viewpoint without the need of introducing dark energy by hand. We also extend a recent work of Mohammedi where using a special form of the extra dimensional scale factor a new interpretation of the higher dimensional equations of motion is given and the concept of an effective 4D pressure is introduced. Interestingly the 5D matter field remains regular while the effective negative pressure is responsible for the inflation. Relaxing the assumptions of two equations of state we also present a class of solutions which provide early deceleration followed by a late acceleration in a unified manner. Relevant to point out that in this case our cosmology apparently mimics the well-known quintessence scenario fuelled by a generalized Chaplygin-type of fluid where a smooth transition from a dust dominated model to a de Sitter-like one takes place. Depending on the relative magnitude of the different constants appearing in our solutions we show that some of the cases are amenable to the desirable property of dimensional reduction.

We consider in this paper φ⁴ theory in higher dimensions. Using functional diagrammatic approach, we compute the one-loop correction to effective potential of the scalar field in five dimensions. It is shown that φ⁴ theory can be regularized in five dimensions. Temperature dependent one-loop correction and critical temperature β_c are computed and β_c depends on the fundamental scale of the theory. A brief discussion of symmetry restoration is also presented. The nature of phase transitions is examined and is of second order.

We study a class of constant scalar invariant (CSI) space–times which belong to the higher-dimensional Kundt class and which are solutions of supergravity. We review the known CSI supergravity solutions in this class and we explicitly present a number of new exact CSI supergravity solutions, some of which are Einstein.

We have considered five-dimensional massive scalar field coupled to gravity and evaluated the one-loop effective potential in higher dimensions. It is demonstrated that nonminimally coupled φ⁴ theory can be regularized in five dimensions. Temperature dependent one-loop correction and critical temperature β_c are computed. The phase transitions in the early universe depend on the space–time curvature R and scalar gravitational coupling ξ. A brief discussion of symmetry restoration is also presented and the nature of phase transitions in the early universe is found to be of second order.

Black holes are among the most exciting phenomena predicted by General Relativity and play a key role in fundamental physics. Many interesting phenomena involve dynamical black hole configurations in the high curvature regime of gravity. In these lecture notes I will summarize the main numerical relativity techniques to explore highly dynamical phenomena, such as black hole collisions, in generic D-dimensional space–times. The present notes are based on my lectures given at the NR/HEP2 spring school at IST/Lisbon (Portugal) from March 11–14, 2013.

Studies of scattering amplitudes for electric and magnetic charges have identified previously overlooked multiparticle representations of the Poincaré group in four dimensions. Such representations associate nontrivial quantum numbers (known as pairwise helicities) with asymptotically separated pairs of particles, and thus cannot be described as tensor products of one-particle states. We extend this construction to sources and spacetimes of higher dimension. We first establish the dynamical origin of pairwise helicity in $p$-form electrodynamics coupled to mutually nonlocal branes. We then interpret this pairwise helicity as a quantum number under an SO(2) pairwise little group associated with pairs of distinct branes. We further characterize the “higher” little groups that could in principle be used to induce multiparticle or multi-brane representations of the Lorentz group.

Localization of electrons in the internal frame of reference is well established in one dimension in the presence and absence of Coulomb interaction. We start from quasi-one-dimensional (Q1D) ring and show the possibility of such a transition by going to a regime where it can be shown for electrons that just interact via Fermi statistics. We then give a proof that when the Q1D ring is made infinitely wide, then there will be such a localization even when Coulomb interaction is included. Finally, we also comment on dimensions greater than two.

The result that near the melting point three-dimensional crystals have an octahedronic structure is generalized to higher flat non-compact dimensions.

We investigate the occurrence and nature of a naked singularity in the gravitational collapse of an inhomogeneous dust cloud described by a self-similar higher dimensional Tolman–Bondi space–time. Bound, marginally bound and unbound space–times are analyzed. The degree of inhomogeneity of the collapsing matter necessary to form a naked singularity is given.

We extend to higher dimensions a recent work of Bonnor, which generalizes the Einstein–Straus model utilizing the inhomogeneous Tolman–Bondi universe in place of the homogeneous Friedmann one. Following Israel's junction conditions, the criteria of matching between the higher dimensional Schwarzschild-like interior and the Tolman–Bondi-like exterior is obtained. We also give a new exact solution for a five-dimensional TB type of metric and use it to study the dynamical behavior of the vacuole boundary. Furthermore the transformation relations which transform the inhomogeneous TB metric to the homogeneous Friedmann model are explicitly given for any arbitrary dimensions. The frequency shift of radiation coming from the boundary surface is calculated and it is found that, depending on initial conditions both redshift and blue-shift are possible for an expanding vacuole. This is at variance with Bonnor's result where only redshift is possible under similar situation. It is also observed that higher dimensional models are less stable against perturbation than the usual 4D ones.

We investigate the occurrence of naked singularities in the gravitational collapse of an inhomogeneous dust cloud in an expanding de Sitter background — a piece of Tolman–Bondi–de Sitter space–time. It turns out that the collapse proceed in the same way as in the Minkowski background, i.e., the strong curvature naked singularities form and thus violate the cosmic censorship conjecture. Our result unambiguously support the fact that the asymptotic flatness of space–time is not a necessary ingredient for the development of naked singularities.

Exact cosmological solutions are obtained for a five-dimensional inhomogeneous fluid distribution along with a Brans–Dicke type of scalar field. The set includes varied forms of matter field including ρ+p = 0, where p is the 3D isotropic pressure. Depending on the signature of 4-space curvature, our solutions admit of indefinite expansion in the usual 3-space and dimensional reduction of the fifth dimension. Due to the presence of the scalar field, the case p = -ρ does not yield an exponential expansion of the scale factor, which strikingly differs from our earlier investigations without scalar field. The effective four-dimensional values of entropy and matter are calculated and possible consequences of entropy and matter generation in the 4D world as a result of dimensional reduction of the extra space are also discussed. It is encouraging to point out that aside from the well known big bang singularity, our inhomogeneous cosmology is spatially regular everywhere. Further, our model seems to suggest an alternative mechanism pointing to a smooth pass over from a primordial, inhomogeneous cosmological phase to a 4D homogeneous one.

Limits are imposed upon the possible rate of change of extra spatial dimensions in a decrumpling model Universe with time variable spatial dimensions (TVSD) by considering the time variation of (1+3)-dimensional Newton's constant. Previous studies on the time variation of (1+3)-dimensional Newton's constant in TVSD theory had not include the effects of the volume of the extra dimensions and the effects of the surface area of the unit sphere in D-space dimensions. Our main result is that the absolute value of the present rate of change of spatial dimensions to be less than about 10^-14 yr^-1. Our results would appear to provide a prima facie case for ruling the TVSD model out. We show that based on observational bounds on the present variation of Newton's constant, one would have to conclude that the spatial dimension of the Universe when the Universe was "at the Planck scale" to be less than or equal to 3.09. If the dimension of space when the Universe was "at the Planck scale" is constrained to be fractional and very close to 3, then the whole edifice of TVSD model loses credibility.