Related papers: Lane-Emden stars, selfgravitating disks and the So…
We establish an improved form of the classical logarithmic Sobolev inequality for the Gaussian measure restricted to probability densities which satisfy a Poincar\'e inequality. The result implies a lower bound on the deficit in terms of…
Polytropic stars are useful tools for learning about stellar structure without the complexity of comprehensive stellar models. These models rely on a certain power-law correlation between the star's pressure and density. This paper proposes…
Models are presented for the polytropic equation of state of self-gravitating, quiescent interstellar gas clouds. A detailed analysis, including chemistry, thermal balance, and radiative transfer, is performed for the physical state of the…
The disks that surround young stars are mostly composed of molecular gas, which is harder to detect and interpret than the accompanying dust. Disk mass measurements have therefore relied on large and uncertain extrapolations from the dust…
The trace-free Einstein equations contain one equation less than the complete field equations. In a static and spherically symmetric spacetime, the number of field equations is thus reduced to two. The equation of pressure isotropy of…
We introduce a new approach to a century old assumption which enhances not only planetary interior calculations but also high pressure material physics. We show that the polytropic index is the derivative of the bulk modulus with respect to…
We show the existence of a new class of initially smooth spherically symmetric self-similar solutions to the non-isentropic Euler-Poisson system. These solutions exhibit supersonic gravitational implosion in the sense that the density…
We estimate the masses of disks of galaxies using the marginal gravitational stability criterion and compare them with the photometrical disk mass evaluations. The comparison reveals that the stellar disks of most of spiral galaxies we…
This paper is devoted to study cylindrically symmetric stellar filaments in self-interacting Brans-Dicke gravity. For this purpose, we construct polytropic filamentary models through generalized Lane-Emden equation in Newtonian regime. The…
We studied global nonaxisymmetric hydrodynamic instabilities in an extensive collection of hot, self-gravitating polytropic disk systems, systems that covered a wide expanse of the parameter space relevant to protostellar and protoplanetary…
The initial data sets for the five-dimensional Einstein equation have been examined. The system is designed such that the black hole ($\simeq S^3$) or the black ring ($\simeq S^2\times S^1$) can be found. We have found that the typical…
We investigate the minimum planet mass that produces observable signatures in infrared scattered light and submm continuum images and demonstrate how these images can be used to measure planet masses to within a factor of about two. To this…
It has recently been observed that there are no disc galaxies with masses less than 10^9 M_solar and this cutoff has not been explained. It is shown here that this minimum mass can be predicted using a model that assumes that 1) inertia is…
The classical model of an isolated selfrgavitating gaseous star is given by the Euler-Poisson system with a polytropic pressure law $P(\rho)=\rho^\gamma$, $\gamma>1$. For any $1<\gamma<\frac43$, we construct an infinite-dimensional family…
A fundamental assumption in the so-called "global polytropic model" is hydrostatic equilibrium for a system of planets or statellites. By solving the Lane-Emden differential equation for such a system in the complex plane, we find…
This paper is an investigation of the stability of some ideal stars. It is in- tended as a study in General Relativity, with emphasis on the coupling to matter, eventually aimed at a better understanding of very strong gravitational fields…
The inner structure of a star or a primordial interstellar cloud is a major topic in classical and relativistic physics. The impact that General Relativistic principles have on this structure has been the subject of many research papers. In…
Simulations in general relativity show that the outcome of collapse of a marginally unstable, uniformly rotating star spinning at the mass-shedding limit depends critically on the equation of state. For a very stiff equation of state, which…
We constrain the post-Newtonian gravity parameter gamma on kiloparsec scales by comparing the masses of 15 elliptical lensing galaxies from the Sloan Lens ACS Survey as determined in two independent ways. The first method assumes only that…
It is shown how the well-known formula for the gravitational energy of self-gravitating regular polytropes of finite mass can be obtained in an elementary way by using Gauss's divergence theorem and the Chandrasekhar virial tensor, without…