Einstein's Field Equations for the Interior of a Uniformly Rotating Stationary Axisymmetric Perfect Fluid

We reduce Einstein's field equations for the interior of a uniformly rotating, axisymmetric perfect fluid to a system of six second order partial differential equations for the pressure p the energy density $\mu$ and four dependent variables.Four of these equations do not depend on p and $\mu$ and the other two determine p and $\mu$

Black Hole in a Model with Dilaton and Monopole Fields

We present an exact black hole solution in a model having besides gravity a dilaton and a monopole field. The solution has three free parameters, one of which can be identified with the monopole charge, and another with the ADM mass. The metric is asymptotically flat and has two horizons and irremovable singularity only at $r=0$. The dilaton field is singular only at $r=0$. The dominant and the strong energy condition are satisfied outside and on the external horizon. According to a formulation of the no hair conjecture the solution is "hairy". Also the well know GHS-GM solution is obtained from our solution for certain values of its parameters.Comment: Selected for Honorable Mention in the Gravity Research Foundation Essay Competition, 2006, 7 page

Contact symmetry of time-dependent Schr\"odinger equation for a two-particle system: symmetry classification of two-body central potentials

Symmetry classification of two-body central potentials in a two-particle Schr\"{o}dinger equation in terms of contact transformations of the equation has been investigated. Explicit calculation has shown that they are of the same four different classes as for the point transformations. Thus in this problem contact transformations are not essentially different from point transformations. We have also obtained the detailed algebraic structures of the corresponding Lie algebras and the functional bases of invariants for the transformation groups in all the four classes

Family Of Rotating Anisotropic Fluid Solutions which Match to Kerr's Solution

We present a family of exact rotating anisotropic fluid solutions, which satisfy all energy conditions for certain values of their parameters. The components of the Ricci tensor $R_{\mu\nu}$ the eigenvalues of the tensor $R_\mu^\nu$ and the energy-momentum tensor $T_{\mu\nu}$ of the solutions are given explicitly. All members of the family have the ring singularity of Kerr's solution and most of them one or two more singularities. The solutions can be matched to the solution of Kerr on three closed surfaces, which for proper values of the parameters of the solutions approximate oblate spheroids. All matching surfaces are thin shells. For some values of a constant the surface density in one of them is positive everywhere and in this surface and in its interior all energy conditions are satisfied.Comment: Published version in IJMP

Rotating Black Hole Solutions with Axion Dilaton and Two Vector Fields and Solutions with Metric and Fields of the Same Form

We present two rotating black hole solutions with axion $\xi$, dilaton $\phi$ and two U(1) vector fields. By applying the "Newman-Janis trick" to a metric with 3 arbitrary parameters we find a rotating metric $g_{\mu\nu}$ with 4 such parameters $(M, a, Q_E, Q_M)$, and then a solution with this $g_{\mu\nu}$ as metric. Our solution is asymptotically flat and has angular momentum $J=M a$, gyromagnetic ratio $g=2$, two horizons, the singularities of Kerr's solution, axion and dilaton singular only for $r=a\cos\theta=0$. Applying to the solution we have found the $S-$duality transformation we get a new solution, whose axion, dilaton and vector fields have one more parameter. The metric, each vector field and the $\lambda=\xi+ie^{-2\phi}$ of our solutions and the solution of : Sen for $Q_E$, Sen for $Q_E$ and $Q_M$, Kerr-Newman for $Q_E$ and $Q_M$, Kerr, Ref. 9, STW, GM-GHS, Reissner-Nordstr\"{o}m,Schwarzschild are the same function of $a$, and two functions $\rho^2=r(r+b)+a^2\cos^2\theta$ and $\Delta=\rho^2-2Mr+c$, of $a$, $b$ and two functions, and of $a$, $b$ and $d$ respectively, where $a$, $b$, $c$ and $d$ are constants. It is shown that from our solutions a number of known solutions can be obtained, which together with our solutions are listed in an Appendix. Also it is shown that all solutions which are mentioned in the paper satisfy all energy conditions, and mass formulae are obtained for them.Comment: 50 page

Dilatonic interpolation between Reissner-Nordstrom and Bertotti-Robinson spacetimes with physical consequences

We give a general class of static, spherically symmetric, non-asymptotically flat and asymptotically non-(anti) de Sitter black hole solutions in Einstein-Maxwell-Dilaton (EMD) theory of gravity in 4-dimensions. In this general study we couple a magnetic Maxwell field with a general dilaton potential, while double Liouville-type potentials are coupled with the gravity. We show that the dilatonic parameters play the key role in switching between the Bertotti-Robinson and Reissner-Nordstr\"om spacetimes. We study the stability of such black holes under a linear radial perturbation, and in this sense we find exceptional cases that the EMD black holes are unstable. In continuation we give a detailed study of the spin-weighted harmonics in dilatonic Hawking radiation spectrum and compare our results with the previously known ones. Finally, we investigate the status of resulting naked singularities of our general solution when probed with quantum test particles.Comment: 27 pages, 4 figures, to appear in CQG

Emergence of good conduct, scaling and Zipf laws in human behavioral sequences in an online world

We study behavioral action sequences of players in a massive multiplayer online game. In their virtual life players use eight basic actions which allow them to interact with each other. These actions are communication, trade, establishing or breaking friendships and enmities, attack, and punishment. We measure the probabilities for these actions conditional on previous taken and received actions and find a dramatic increase of negative behavior immediately after receiving negative actions. Similarly, positive behavior is intensified by receiving positive actions. We observe a tendency towards anti-persistence in communication sequences. Classifying actions as positive (good) and negative (bad) allows us to define binary 'world lines' of lives of individuals. Positive and negative actions are persistent and occur in clusters, indicated by large scaling exponents alpha~0.87 of the mean square displacement of the world lines. For all eight action types we find strong signs for high levels of repetitiveness, especially for negative actions. We partition behavioral sequences into segments of length n (behavioral `words' and 'motifs') and study their statistical properties. We find two approximate power laws in the word ranking distribution, one with an exponent of kappa-1 for the ranks up to 100, and another with a lower exponent for higher ranks. The Shannon n-tuple redundancy yields large values and increases in terms of word length, further underscoring the non-trivial statistical properties of behavioral sequences. On the collective, societal level the timeseries of particular actions per day can be understood by a simple mean-reverting log-normal model.Comment: 6 pages, 5 figure

Microstructural damage of the posterior corpus callosum contributes to the clinical severity of neglect

One theory to account for neglect symptoms in patients with right focal damage invokes a release of inhibition of the right parietal cortex over the left parieto-frontal circuits, by disconnection mechanism. This theory is supported by transcranial magnetic stimulation studies showing the existence of asymmetric inhibitory interactions between the left and right posterior parietal cortex, with a right hemispheric advantage. These inhibitory mechanisms are mediated by direct transcallosal projections located in the posterior portions of the corpus callosum. The current study, using diffusion imaging and tract-based spatial statistics (TBSS), aims at assessing, in a data-driven fashion, the contribution of structural disconnection between hemispheres in determining the presence and severity of neglect. Eleven patients with right acute stroke and 11 healthy matched controls underwent MRI at 3T, including diffusion imaging, and T1-weighted volumes. TBSS was modified to account for the presence of the lesion and used to assess the presence and extension of changes in diffusion indices of microscopic white matter integrity in the left hemisphere of patients compared to controls, and to investigate, by correlation analysis, whether this damage might account for the presence and severity of patients' neglect, as assessed by the Behavioural Inattention Test (BIT). None of the patients had any macroscopic abnormality in the left hemisphere; however, 3 cases were discarded due to image artefacts in the MRI data. Conversely, TBSS analysis revealed widespread changes in diffusion indices in most of their left hemisphere tracts, with a predominant involvement of the corpus callosum and its projections on the parietal white matter. A region of association between patients' scores at BIT and brain FA values was found in the posterior part of the corpus callosum. This study strongly supports the hypothesis of a major role of structural disconnection between the right and left parietal cortex in determining 'neglect'