Pure-radiation gravitational fields with a simple twist and a Killing vector

Pure-radiation solutions are found, exploiting the analogy with the Euler- Darboux equation for aligned colliding plane waves and the Euler-Tricomi equation in hydrodynamics of two-dimensional flow. They do not depend on one of the spacelike coordinates and comprise the Hauser solution as a special subcase.Comment: revtex, 9 page

Expanding, axisymmetric pure-radiation gravitational fields with a simple twist

New expanding, axisymmetric pure-radiation solutions are found, exploiting the analogy with the Euler-Darboux equation for aligned colliding plane waves.Comment: revtex, 5 page

Conformal Ricci collineations of static spherically symmetric spacetimes

Conformal Ricci collineations of static spherically symmetric spacetimes are studied. The general form of the vector fields generating conformal Ricci collineations is found when the Ricci tensor is non-degenerate, in which case the number of independent conformal Ricci collineations is \emph{fifteen}; the maximum number for 4-dimensional manifolds. In the degenerate case it is found that the static spherically symmetric spacetimes always have an infinite number of conformal Ricci collineations. Some examples are provided which admit non-trivial conformal Ricci collineations, and perfect fluid source of the matter

A computational study of stimulus driven epileptic seizure abatement

This is the final version of the article. Available from Public Library of Science via the DOI in this record.Active brain stimulation to abate epileptic seizures has shown mixed success. In spike-wave (SW) seizures, where the seizure and background state were proposed to coexist, single-pulse stimulations have been suggested to be able to terminate the seizure prematurely. However, several factors can impact success in such a bistable setting. The factors contributing to this have not been fully investigated on a theoretical and mechanistic basis. Our aim is to elucidate mechanisms that influence the success of single-pulse stimulation in noise-induced SW seizures. In this work, we study a neural population model of SW seizures that allows the reconstruction of the basin of attraction of the background activity as a four dimensional geometric object. For the deterministic (noise-free) case, we show how the success of response to stimuli depends on the amplitude and phase of the SW cycle, in addition to the direction of the stimulus in state space. In the case of spontaneous noise-induced seizures, the basin becomes probabilistic introducing some degree of uncertainty to the stimulation outcome while maintaining qualitative features of the noise-free case. Additionally, due to the different time scales involved in SW generation, there is substantial variation between SW cycles, implying that there may not be a fixed set of optimal stimulation parameters for SW seizures. In contrast, the model suggests an adaptive approach to find optimal stimulation parameters patient-specifically, based on real-time estimation of the position in state space. We discuss how the modelling work can be exploited to rationally design a successful stimulation protocol for the abatement of SW seizures using real-time SW detection.This work was supported by the EPSRC (EP/K026992/1), the BBSRC, the DTC for Systems Biology (University of Manchester), and the Nanyang Technological University Singapore. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript

PB15. Neurophysiological biomarker for the clinical development of tuberous sclerosis [Abstract]

Aim To investigate the neuronal networks in children with tuberous sclerosis complex (TS) undergoing treatment with Everolimus. Methods Sleep and wake electroencephalography (EEG) before and one year after the start of the treatment with Everolimus were investigated in 13 patients with TS. To investigate functional and effective connectivity within the network generating the delta and theta activity in the background sleep and wake EEG, the methods of dynamic imaging of coherent sources (DICS) and renormalized partial directed coherence (RPDC) were applied. Results Sources before the treatment. Independent of location of the tubera and severity of epilepsy, delta activity in the background EEG pattern in patients with TS was associated with the sources in the medial prefrontal cortex, the supplementary motor area and the putamen during sleep. Theta waves during sleep were associated with sources in the prefrontal cortex, sensory cortex, hippocampus and the thalamus. The sources of delta frequency during wakefulness were identified at the posterior parietal cortex, the parahippocampal gyrus and the Broca area. Sources at theta frequency were found at the sensorymotor cortex, the prefrontal cortex, the primary visual cortex and the thalamus at awake state. Sources after the treatment. The sources one year after the start of the therapy, for both delta and delta frequencies were located in the same areas as before, however with a significantly weaker strength of coherence. The RPDC analysis at baseline showed strong bidirectional connections between described sources. The RPDC analyses after the one year of treatment showed significantly weaker unidirectional connections within the described network. At the follow up patients were grouped in two groups; group 1: five patients with >50% reduction of seizures and spike wave index, group 2: eight patients with <50% reduction of seizures and spike wave index. Interestingly, at follow up patients from the group 1 had decreased values in absolute power of the sources, coherence values and strength of connections. Whereas, patients from the group 2 had increased values in all above mentioned parameters. Conclusion The current study described the neuronal network in children with severe epilepsies due to TS. Regardless of the locations of the tubera the DICS analyses showed a complex network of cortical and subcortical sources with strong bidirectional connections. The described network was significantly weaker after one year under the treatment with Everolimus and appears to be characteristic for the children with TS and severe epilepsy

Does the Isotropy of the CMB Imply a Homogeneous Universe? Some Generalised EGS Theorems

We demonstrate that the high isotropy of the Cosmic Microwave Background (CMB), combined with the Copernican principle, is not sufficient to prove homogeneity of the universe -- in contrast to previous results on this subject. The crucial additional factor not included in earlier work is the acceleration of the fundamental observers. We find the complete class of irrotational perfect fluid spacetimes admitting an exactly isotropic radiation field for every fundamental observer and show that are FLRW if and only if the acceleration is zero. While inhomogeneous in general, these spacetimes all possess three-dimensional symmetry groups, from which it follows that they also admit a thermodynamic interpretation. In addition to perfect fluids models we also consider multi-component fluids containing non-interacting radiation, dust and a quintessential scalar field or cosmological constant in which the radiation is isotropic for the geodesic (dust) observers. It is shown that the non-acceleration of the fundamental observers forces these spacetimes to be FLRW. While it is plausible that fundamental observers (galaxies) in the real universe follow geodesics, it is strictly necessary to determine this from local observations for the cosmological principle to be more than an assumption. We discuss how observations may be used to test this.Comment: replaced with final version. Added discusion and ref

Slowly Rotating Homogeneous Stars and the Heun Equation

The scheme developed by Hartle for describing slowly rotating bodies in 1967 was applied to the simple model of constant density by Chandrasekhar and Miller in 1974. The pivotal equation one has to solve turns out to be one of Heun's equations. After a brief discussion of this equation and the chances of finding a closed form solution, a quickly converging series solution of it is presented. A comparison with numerical solutions of the full Einstein equations allows one to truncate the series at an order appropriate to the slow rotation approximation. The truncated solution is then used to provide explicit expressions for the metric.Comment: 16 pages, uses document class iopart, v2: minor correction

A simple theorem to generate exact black hole solutions

Under certain conditions imposed on the energy-momentum tensor, a theorem that characterizes a two-parameter family of static and spherically symmetric solutions to Einstein's field equations (black holes), is proved. A discussion on the asymptotics, regularity, and the energy conditions is provided. Examples that include the best known exact solutions within these symmetries are considered. A trivial extension of the theorem includes the cosmological constant {\it ab-initio}, providing then a three-parameter family of solutions.Comment: 14 pages; RevTex; no figures; typos corrected; references adde

A Lorentz-Poincar\'e type interpretation of the Weak Equivalence Principle

The validity of the Weak Equivalence Principle relative to a local inertial frame is detailed in a scalar-vector gravitation model with Lorentz-Poincar\'e type interpretation. Given the previously established first Post-Newtonian concordance of dynamics with General Relativity, the principle is to this order compatible with GRT. The gravitationally modified Lorentz transformations, on which the observations in physical coordinates depend, are shown to provide a physical interpretation of \emph{parallel transport}. A development of ``geodesic'' deviation in terms of the present model is given as well.Comment: v1: 9 pages, 2 figures, v2: version to appear in International Journal of Theoretical Physic

Bondi-Sachs metrics and Photon Rockets

We study the Bondi-Sachs rockets with nonzero cosmological constant. We observe that the acceleration of the systems arises naturally in the asymptotic symmetries of (anti-) de Sitter spacetimes. Assuming the validity of the concepts of energy and mass previously introduced in asymptotically flat spacetimes, we find that the emission of pure radiation energy balances the loss of the Bondi mass in certain special families of the Bondi-Sachs rockets, so in these there is no gravitational radiation.Comment: 12 pages, to appear in General Relativity and Gravitatio