Gravity from a Modified Commutator

We show that a suitably chosen position-momentum commutator can elegantly describe many features of gravity, including the IR/UV correspondence and dimensional reduction (`holography'). Using the most simplistic example based on dimensional analysis of black holes, we construct a commutator which qualitatively exhibits these novel properties of gravity. Dimensional reduction occurs because the quanta size grow quickly with momenta, and thus cannot be "packed together" as densely as naively expected. We conjecture that a more precise form of this commutator should be able to quantitatively reproduce all of these features.Comment: 8 pages; Honorable Mention in the 2005 Gravity Research Foundation Essay Competition; v2: acknowledgments adde

The Stability of Noncommutative Scalar Solitons

We determine the stability conditions for a radially symmetric noncommutative scalar soliton at finite noncommutivity parameter $\theta$. We find an intriguing relationship between the stability and existence conditions for all level-1 solutions, in that they all have nearly-vanishing stability eigenvalues at critical $\theta m^2$. The stability or non-stability of the system may then be determined entirely by the $\phi^3$ coefficient in the potential. For higher-level solutions we find an ambiguity in extrapolating solutions to finite $\theta$ which prevents us from making any general statements. For these stability may be determined by comparing the fluctuation eigenvalues to critical values which we calculate.Comment: 12 pages, corrected typo

A Note on Cosmic (p,q,r) Strings

The spectrum of $(p,q)$ bound states of F- and D-strings has a distinctive square-root tension formula that is hoped to be a hallmark of fundamental cosmic strings. We point out that the Bogomol'nyi-Prasad-Sommerfield (BPS) bound for vortices in ${\cal N}=2$ supersymmetric Abelian-Higgs models also takes the square-root form. In contrast to string theory, the most general supersymmetric field theoretic model allows for $(p,q,r)$ strings, with three classes of strings rather than two. Unfortunately, we find that there do not exist BPS solutions except in the trivial case. The issue of whether there exist non-BPS solutions which may closely resemble the square-root form is left as an open question.Comment: 4 pages; v2: references adde

A Perturbative Approach to Neutron Stars in f(T,T)−f(T, \mathcal{T})-Gravity

We derive a Tolman-Oppenheimer-Volkoff equation in neutron star systems within the modified $f(T, \mathcal{T})$-gravity class of models using a perturbative approach. In our approach $f(T, \mathcal{T})$-gravity is considered to be a static spherically symmetric space-time. In this instance the metric is built from a more fundamental tetrad vierbein which can be used to relate inertial and global coordinates. A linear function $f = T(r) + \mathcal{T}(r) + \chi h(T, \mathcal{T}) + \mathcal{O}(\chi^{2})$ is taken as the Lagrangian density for the gravitational action. Finally we impose the polytropic equation of state of neutron star upon the derived equations in order to derive the mass profile and mass-central density relations of the neutron star in $f(T, \mathcal{T})$-gravity.Comment: arXiv admin note: text overlap with arXiv:1701.0476

Quark Stars in f(T,T)−f(T, \mathcal{T})-Gravity

We derive a working model for the Tolman-Oppenheimer-Volkoff equation for quark star systems within the modified $f(T, \mathcal{T})$-gravity class of models. We consider $f(T, \mathcal{T})$-gravity for a static spherically symmetric space-time. In this instance the metric is built from a more fundamental tetrad vierbein from which the metric tensor can be derived. We impose a linear $f(T)$ parameter parameter, namely taking $f=\alpha T(r) + \beta \mathcal{T}(r) + \varphi$ and investigate the behavior of a linear energy-momentum tensor trace, $\mathcal{T}$. We also outline the restrictions which modified $f(T, \mathcal{T})$-gravity imposes upon the coupling parameters. Finally we incorporate the MIT bag model in order to derive the mass-radius and mass-central density relations of the quark star within $f(T, \mathcal{T})$-gravity

Political Parties and Web 2.0: The Liberal Democrat Perspective

Political parties have been criticised for their limited use of interactivity via their Internet presences, largely it is suggested because they seek to control their online messages. This article will consider interactivity from the perspective of a political party, the Liberal Democrats, using their Freedom Bill online campaign as a case study. We suggest that the Liberal Democrats use ‘weak interactivity’ because of internal policymaking concerns, and their belief that as a political party they are promoting their ideas, not co-creating a new product. Thus we suggest interaction should be closer to a formal consultation than a face-to-face dialogue