Related papers: Buchdahl compactness limit and gravitational field…
The aim of the research is to look into a new solution for isotropic compact stars in the context of the $f(R,\,T)$ theory of gravity. We used the Buchdahl [H.A. Buchdahl, Phys. Rev. {\bf 116} (1959) 1027] metric potentials as input to deal…
In this paper, we have presented a compact object model in the framework of Einstein-Gauss-Bonnet gravity (EGB) with a linear equation of state considering a metric potential proposed for Buchdahl (1959). The new obtained models satisfy all…
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…
Upper limits for the mass-radius ratio are derived for arbitrary general relativistic matter distributions in the presence of a cosmological constant. General restrictions for the red shift and total energy (including the gravitational…
We study the self-force acting on a static charged point-like particle near a Schwarzschild black hole. We obtain the point-like particle as a limit of a spacetime describing a big neutral black hole with a small charged massive object…
The Schr\"odinger equation for a charged particle in the field of a nonrelativistic electric quadrupole in two dimensions is known to be separable in spherical coordinates. We investigate the occurrence of bound states of negative energy…
In this note, I argue that tidal effects generically limit the kinetic energy of a single massive elementary particle in the vicinity of a compact object. As the kinetic energy is increased, the differences in the tidal potential over a…
It was shown long back in \cite{Dadhich97} that a non-extremal black hole cannot be converted into an extremal one by test particle adiabatic accretion. The Buchdahl star is the most compact object without horizon and is defined by $\Phi(R)…
One of the macroscopically measurable effects of gravity is the tidal deformability of astrophysical objects, which can be quantified by their tidal Love numbers. For planets and stars, these numbers measure the resistance of their material…
In a very interesting paper, Andr\'easson has recently proved that the gravitational mass of a spherically symmetric compact object of radius $R$ and electric charge $Q$ is bounded from above by the relation…
General relativity is a non-linear theory with the distinguishing feature that gravitational field energy also acts as gravitational charge density. In the well-known Schwarzschild solution describing field of an isolated massive body at…
An interpretation of general relativity is developed in which the energy used to lift a body in a static gravitational field increases its rest mass. Observers at different gravitational potentials would experience different mass reference…
Buchdahl star is the most compact object without an event horizon and is an excellent candidate for a black hole mimicker. Unlike black holes, rotating Buchdahl star can be over-extremal with respect to the black hole, sustaining a larger…
In Einstein gravity, matter with an arbitrarily small density can be a black hole. Pressure in the star diverges if size of the star is smaller than 9/8 of the Schwarzschild radius, implying the gravitational collapse into a black hole. By…
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…
In their original study of conformal gravity, a candidate alternate gravitational theory, Mannheim and Kazanas showed that in any empty vacuum region exterior to a localized static spherically symmetric gravitational source, the geometry…
A new class of relativistic stellar structure equations which include the effects of an energy-dependent Newton coupling is presented. Significant modifications in the mass-radius relation for neutron stars are possible only if the running…
We consider the bound-state energy levels of a spin-1/2 fermion in the gravitational field of a near-black hole object. In the limit that the metric of the body becomes singular, all binding energies tend to the rest-mass energy (i.e. total…
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…
The finite part of the self-force on a static scalar test-charge outside a Schwarzschild black hole is zero. By direct construction of Hadamard's elementary solution, we obtain a closed-form expression for the minimally coupled scalar field…