Considering a Skyrme model with a peculiar gauging of the symmetry, monopole-like solutions exist through a topological lower bound. However, it was recently shown that these objects cannot form bound states in the limit of vanishing Skyrme coupling. Here we consider these monopoles in scalar-tensor gravity. A numerical study of the equations reveals that neither the coupling to gravity nor to ...

We consider renormalizability of topologically massive gravity in three space-time dimensions. With a usual parametrization of the metric tensor, we establish the statement that topologically massive gravity is in fact renormalizable. In this proof, we make use of not only a recently found, new infrared regularization method of scalar mode but also a covariant ultraviolet regulator with a speci...

We want to correct the misunderstandings on the tetrad (or veilbeins in general) appeared in many text books or review articles. The tetrad should be defined without any condition. eμa = ∂μXa with local Lorentz coordinates Xa ia wrong in many sences: it gives the condition ∂μeνa = ∂νeμa, which leads us to the trivial result that the cyclic coefficients vanish identically and to the null Riemann...

cp heat capacity dx distance between two points after time t dX original infinitesimal distance between two points D stretching tensor Di dissipation number ĝ gravity vector h depth of convecting layer H(r) two-particle correlation function P dynamic pressure Ra thermal Rayleigh number t time T temperature ui components of the velocity tensor v velocity w upward velocity a thermal expansivity _...

In diffusion tensor imaging (DTI) an effective diffusion tensor in each voxel is measured by using a set of diffusion-weighted images (DWIs) in which diffusion gradients are applied in a multiplicity of oblique directions. However, to estimate the diffusion tensor accurately, one must account for the effects of all imaging and diffusion gradient pulses on each signal echo, which are embodied in...

The possibility of the cosmic string creation by the vacuum fluctuations of quantum fields in the self-consistent semiclassical theory of gravity is discussed. We use the approximate method for obtaining vacuum expectation value of the renormalized stress-energy tensor of conformally invariant quantum fields in static cylindrically symmetric spacetimes. We have obtained the particular solutions...

The early Universe might have undergone phase transitions at energy scales much higher than the one corresponding to the Grand Unified Theories (GUT) scales. Then, at these higher energy scales, the transition at which gravity separated from all other interactions, the Planck era, more massive strings called supermassive cosmic strings, could be produced, with energy of about 10GeV . The dynami...

I discuss the relation between arbitrarily high-order theories of gravity and scalartensor gravity at the level of the field equations and the action. I show that (2n+4)-order gravity is dynamically equivalent to Brans-Dicke gravity with an interaction potential for the Brans-Dicke field and n further scalar fields. This scalar-tensor action is then conformally equivalent to the Einstein-Hilber...

Einstein-Hilbert (EH) action can be separated into a bulk and a surface term, with a specific (‘‘holographic’’) relationship between the two, so that either can be used to extract information about the other. The surface term can also be interpreted as the entropy of the horizon in a wide class of spacetimes. Since EH action is likely to just the first term in the derivative expansion of an eff...

We show that the only shrinking gradient solitons with vanishing Weyl tensor are quotients of the standard ones Sn, S × R, and Rn. This gives a new proof of the Hamilton-Ivey-Perel’man classification of 3dimensional shrinking gradient solitons. We also show that gradient solitons with constant scalar curvature and suitably decaying Weyl tensor when noncompact are quotients of Hn, H × R, Rn, S ×...