A new algorithm for anisotropic solutions

We establish a new algorithm that generates a new solution to the Einstein field equations, with an anisotropic matter distribution, from a seed isotropic solution. The new solution is expressed in terms of integrals of an isotropic gravitational potential; and the integration can be completed exactly for particular isotropic seed metrics. A good feature of our approach is that the anisotropic solutions necessarily have an isotropic limit. We find two examples of anisotropic solutions which generalise the isothermal sphere and the Schwarzschild interior sphere. Both examples are expressed in closed form involving elementary functions only.Comment: 16 pages, to appear in Pramana - J. Phy

Anisotropic static solutions in modelling highly compact bodies

Einstein field equations for anisotropic spheres are solved and exact interior solutions obtained. This paper extends earlier treatments to include anisotropic models which accommodate a wider variety of physically viable energy densities. Two classes of solutions are possible. The first class contains the limiting case $\mu\propto r^{-2}$ for the energy density which arises in many astrophysical applications. In the second class the singularity at the center of the star is not present in the energy density. The models presented in this paper allow for increasing and decreasing profiles in the behavior of the energy density.Comment: 9 pages, to appear in Pramana - J. Phy

Complete adiabatic waveform templates for a test-mass in the Schwarzschild spacetime: VIRGO and Advanced LIGO studies

Post-Newtonian expansions of the binding energy and gravitational wave flux truncated at the {\it same relative} post-Newtonian order form the basis of the {\it standard adiabatic} approximation to the phasing of gravitational waves from inspiralling compact binaries. Viewed in terms of the dynamics of the binary, the standard approximation is equivalent to neglecting certain conservative post-Newtonian terms in the acceleration. In an earlier work, we had proposed a new {\it complete adiabatic} approximant constructed from the energy and flux functions. At the leading order it employs the 2PN energy function rather than the 0PN one in the standard approximation, so that, effectively the approximation corresponds to the dynamics where there are no missing post-Newtonian terms in the acceleration. In this paper, we compare the overlaps of the standard and complete adiabatic templates with the exact waveform in the adiabatic approximation of a test-mass motion in the Schwarzschild spacetime, for the VIRGO and the Advanced LIGO noise spectra. It is found that the complete adiabatic approximants lead to a remarkable improvement in the {\it effectualness} at lower PN ($<$ 3PN) orders, while standard approximants of order $\geq$ 3PN provide a good lower-bound to the complete approximants for the construction of effectual templates. {\it Faithfulness} of complete approximants is better than that of standard approximants except for a few post-Newtonian orders. Standard and complete approximants beyond the adiabatic approximation are also studied using the Lagrangian templates of Buonanno, Chen and Vallisneri.Comment: Proceedings of the GWDAW-9, Accepted for publication in Class. Quant. Gra

Evolving wormhole geometries

We present here analytical solutions of General Relativity that describe evolving wormholes with a non-constant redshift function. We show that the matter that threads these wormholes is not necessarily exotic. Finally, we investigate some issues concerning WEC violation and human traversability in these time-dependent geometries.Comment: 12 pages latex, 3 figures, to appear in Phys. Rev. D., Title correcte

Analytic Behaviour of Competition among Three Species

We analyse the classical model of competition between three species studied by May and Leonard ({\it SIAM J Appl Math} \textbf{29} (1975) 243-256) with the approaches of singularity analysis and symmetry analysis to identify values of the parameters for which the system is integrable. We observe some striking relations between critical values arising from the approach of dynamical systems and the singularity and symmetry analyses.Comment: 14 pages, to appear in Journal of Nonlinear Mathematical Physic

Static charged perfect fluid spheres in general relativity

Interior perfect fluid solutions for the Reissner-Nordstrom metric are studied on the basis of a new classification scheme. General formulas are found in many cases. Explicit new global solutions are given as illustrations. Known solutions are briefly reviewed.Comment: 23 pages, Revtex (galley), journal version, to appear in Phys.Rev.

Cognitive‐behavioral therapy in the time of coronavirus : clinician tips for working with eating disorders via telehealth when face‐to‐face meetings are not possible

Objective The coronavirus pandemic has led to a dramatically different way of working for many therapists working with eating disorders, where telehealth has suddenly become the norm. However, many clinicians feel ill equipped to deliver therapy via telehealth, while adhering to evidence‐based interventions. This article draws together clinician experiences of the issues that should be attended to, and how to address them within a telehealth framework. Method Seventy clinical colleagues of the authors were emailed and invited to share their concerns online about how to deliver cognitive‐behavioral therapy for eating disorders (CBT‐ED) via telehealth, and how to adapt clinical practice to deal with the problems that they and others had encountered. After 96 hr, all the suggestions that had been shared by 22 clinicians were collated to provide timely advice for other clinicians. Results A range of themes emerged from the online discussion. A large proportion were general clinical and practical domains (patient and therapist concerns about telehealth; technical issues in implementing telehealth; changes in the environment), but there were also specific considerations and clinical recommendations about the delivery of CBT‐ED methods. Discussion Through interaction and sharing of ideas, clinicians across the world produced a substantial number of recommendations about how to use telehealth to work with people with eating disorders while remaining on track with evidence‐based practice. These are shared to assist clinicians over the period of changed practice