相关论文: Bounds on 2m/r for static perfect fluids

In 1959 Buchdahl \cite{Bu} obtained the inequality $2M/R\leq 8/9$ under the assumptions that the energy density is non-increasing outwards and that the pressure is isotropic. Here $M$ is the ADM mass and $R$ the area radius of the boundary…

It is well known that a spherically symmetric constant density static star, modeled as a perfect fluid, possesses a bound on its mass m by its radial size R given by 2m/R \le 8/9 and that this bound continues to hold when the energy density…

A classical result by Buchdahl \cite{Bu1} shows that for static solutions of the spherically symmetric Einstein-matter system, the total ADM mass M and the area radius R of the boundary of the body, obey the inequality $2M/R\leq 8/9.$ The…

It is a famous result of relativistic stellar structure that (under mild technical conditions) a static fluid sphere satisfies the Buchdahl--Bondi bound 2M/R <= 8/9; the surprise here being that the bound is not 2M/R <= 1. In this article…

The ratio of total mass $M$ to surface radius $R$ of spherical perfect fluid ball has an upper bound, $M/R < B$. Buchdahl obtained $B = 4/9$ under the assumptions; non-increasing mass density in outward direction, and barotropic equation of…

In a previous work \cite{An1} matter models such that the energy density $\rho\geq 0,$ and the radial- and tangential pressures $p\geq 0$ and $q,$ satisfy $p+q\leq\Omega\rho, \Omega\geq 1,$ were considered in the context of Buchdahl's…

Buchdahl, by imposing a few physical assumptions on the matter, i.e., its density is a nonincreasing function of the radius and the fluid is a perfect fluid, and on the configuration, such as the exterior is the Schwarzschild solution,…

We consider spherically symmetric static solutions of the Einstein equations with a positive cosmological constant $\Lambda,$ which are regular at the centre, and we investigate the influence of $\Lambda$ on the bound of M/R, where M is the…

It is well known that a spherically symmetric compact star whose energy density decreases monotonically possesses an upper bound on its mass-to-radius ratio, $2M/R\leq 8/9$. However, field configurations typically will not be compact. Here…

The general analytical solution for the static spherically symmetric metric supported by a perfect fluid with isothermal (proportional) equation-of-state $p = w \rho$ is not known at the time of this writing, except for the trivial cases…

We prove that all spherically symmetric static spacetimes which are both regular at r=0 and satisfying the single energy condition rho + p_r + p_t >= 0 cannot contain any black hole region (equivalently, they must satisfy 2m/r <= 1…

The general analytical solution for the static spherically symmetric metric supported by a perfect fluid with proportional-equation-of-state $p = w \rho$ is not known at the time of this writing, except for the trivial cases $w=0$ and…

We consider charged spherically symmetric static solutions of the Einstein-Maxwell equations with a positive cosmological constant $\Lambda$. If $r$ denotes the area radius, $m_g$ and $q$ the gravitational mass and charge of a sphere with…

In this work we study static perfect fluid stars in 2+1 dimensions with an exterior BTZ spacetime. We found the general expression for the metric coefficients as a function of the density and pressure of the fluid. We found the conditions…

The initial state of the spherical gravitational collapse in general relativity has been studied with different methods, especially by using {\it a priori} given equations of state that describe the matter as a perfect fluid. We propose an…

In a recent paper by Giuliani and Rothman \cite{GR}, the problem of finding a lower bound on the radius $R$ of a charged sphere with mass M and charge Q<M is addressed. Such a bound is referred to as the critical stability radius.…

A family of exact relativistic stellar models is described. The family generalizes Buchdahl's n=1 polytropic solution. The matter content is a perfect fluid and, excluding Buchdahl's original model, it behaves as a liquid at low pressures…

We show that the isentropic subclass of Buchdahl's exact solution for a gaseous relativistic star is stable and gravitationally bound for all values of the compactness ratio $u [\equiv (M/R)$, where $M$ is the total mass and $R$ is the…

Sharp bounds are obtained, under a variety of assumptions on the eigenvalues of the Einstein tensor, for the ratio of the Hawking mass to the areal radius in static, spherically symmetric space-times.

An infinite class of exact static anisotropic spheres is developed. All members of the class satisfy (i) regularity (meaning no singularities), and in particular at the origin, (ii) positive but monotone decreasing energy density…