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Register a new userAnalytic approximations, perturbation methods, and their applications
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The paper summarizes the parallel session B3 {em Analytic approximations, perturbation methods, and their applications} of the GR18 conference. The talks in the session reported notably recent advances in black hole perturbations and post-Newtonian approximations as applied to sources of gravitational waves.
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In this paper the double-sided Taylors approximations are studied. A short proof of a well-known theorem on the double-sided Taylors approximations is introduced. Also, two new theorems are proved regarding the monotonicity of such approximations. Then we present some new applications of the double-sided Taylors approximations in the theory of analytic inequalities.
In this work a series of methods are developed for understanding the Friedmann equation when it is beyond the reach of the Chebyshev theorem. First it will be demonstrated that every solution of the Friedmann equation admits a representation as a roulette such that information on the latter may be used to obtain that for the former. Next the Friedmann equation is integrated for a quadratic equation of state and for the Randall--Sundrum II universe, leading to a harvest of a rich collection of new interesting phenomena. Finally an analytic method is used to isolate the asymptotic behavior of the solutions of the Friedmann equation, when the equation of state is of an extended form which renders the integration impossible, and to establish a universal exponential growth law.
We present a new convenient framework for modeling Reissner-Nordstrom black hole perturbations from charged distributions of matter. Using this framework, we quantify how gravitational wave observations of compact binary systems would be affected if one or both components were charged. Our approach streamlines the (linearized) Einstein-Maxwell equations through convenient master functions that we designed to ameliorate certain disadvantages of prior strategies. By solving our improved master equations with a point source, we are able to quantify the rate of orbital energy dissipation via electromagnetic and gravitational radiation. Through adiabatic and quasicircular approximations, we apply our dissipative calculations to determine trajectories for intermediate and extreme mass-ratio inspirals. By comparing trajectories and waveforms with varied charges to those with neutral components, we explore the potential effect of electric charge on gravitational wave signals. We observe that the case of opposite charge-to-mass ratios has the most dramatic impact. Our findings are largely interpreted through the lens of the upcoming LISA mission.
We briefly review analytic approximations of thermodynamic functions of fully ionized nonideal electron-ion plasmas, applicable in a wide range of plasma parameters, including the domains of nondegenerate and degenerate, nonrelativistic and relativistic electrons, weakly and strongly coupled Coulomb liquids, classical and quantum Coulomb crystals. We present improvements to previously published approximations. Our code for calculation of thermodynamic functions based on the reviewed approximations is made publicly available.
We study higher derivative terms associated with scalar field cosmology. We consider a coupling between the scalar field and the geometry inspired by the Pais-Uhlenbeck oscillator, given by $alphapartial_{mu}partial^{mu}phipartial_{ u}partial^{ u}phi.$ We investigate the cosmological dynamics in a phase space. For $alpha>0$, we provide conditions for the stability of de Sitter solutions. In this case the crossing of the phantom divide $w_{DE}=-1$ occurs once; thereafter, the equation of state parameter remains under this line, asymptotically reaching towards the de Sitter solution from below. For $alpha<0,$ which is the portion of the parameter space where in addition to crossing the phantom divide, cyclic behavior is possible, we present regions in the parameter space where, according to Smilgas classification the ghost has benign or malicious behavior.
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