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Bearing the thermodynamic arguments together with the two definitions of mass in mind, we try to find metrics with spherical symmetry. We consider the adiabatic condition along with the Gong-Wang mass, and evaluate the $g_{rr}$ element…
For the Edwards-Anderson model we introduce an integral representation for the surface pressure (per unit surface) in terms of a quenched moment of the bond-overlap on the surface. We find upper and lower bounds uniformly in the volume and…
We develop the General Theory of Relativity in a formalism with extended causality that describes physical interaction through discrete, transversal and localized pointlike fields. The homogeneous field equations are then solved for a…
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 consider a spherical thick shell immersed in two different spherically symmetric space-times. Using the fact that the boundaries of the thick shell with two embedding space-times must be nonsingular hypersurfaces, we develop a scheme to…
Compton wavelength and Schwarzschild radius are considered here as limiting cases of a unified length scale. Using this length, it is shown that the Dirac equation and the Einstein equations for a point mass are limiting cases of an…
The cosmological constant is estimated by considering the surface tension of supervoids in a void-dominated cosmic fluid by which we can get a possible source of dark energy. Looking at voids as bubbles, we define the concept of surface…
Based on the relativistic mean field theory and the Thomas-Fermi approximation, we study the surface properties of compressed, superheavy atoms. By compressed, superheavy atom we mean an atom composed by a superheavy nuclear core…
We consider the dynamics of timelike spherical thin matter shells in vacuum. A general formalism for thin shells matching two arbitrary spherical spacetimes is derived, and subsequently specialized to the vacuum case. We first examine the…
Kerr-Schild solutions to the vacuum Einstein equations are considered from the viewpoint of integral equations. We show that, for a class of Kerr-Schild fields, the stress-energy tensor can be regarded as a total divergence in Minkowski…
With the back reaction of the vacuum energy-momentum tensor consistently taken into account, we study static spherically symmetric black-hole-like solutions to the semi-classical Einstein equation. The vacuum energy is assumed to be given…
In this paper, we discuss gravitational collapse of spherically symmetric spacetimes. We derive a general formalism by taking two arbitrary spherically symmetric spacetimes with $g_{00}=1$. Israel's junction conditions are used to develop…
A definition of surface gravity at the apparent horizon of dynamical spherically symmetric spacetimes is proposed. It is based on a unique foliation by ingoing null hypersurfaces. The function parametrizing the hypersurfaces can be…
We formulate an analogue transverse first law for general closed marginally trapped surfaces in arbitrary spacetimes. The construction is intrinsically quasi-local and is attached directly to an individual marginally trapped surface, rather…
Wrinkling is the phenomenon of out-of-plane deformation patterns in thin walled structures, as a result of a local compressive (internal) loads in combination with a large membrane stiffness and a small but non-zero bending stiffness.…
We consider the three-dimensional incompressible free-boundary Euler equations in a bounded domain and with surface tension. Using Lagrangian coordinates, we establish a priori estimates for solutions with minimal regularity assumptions on…
We consider a freely falling holographic screen for the Schwarzschild and Reissner-Nordstr\"om black holes and evaluate the entropic force \`a la Verlinde. When the screen crosses the event horizon, the temperature of the screen agrees to…
A special-relativistic scalar-vector theory of gravitation is presented which mimics an important class of solutions of Einstein's gravitational field equations. The theory includes solutions equivalent to Schwarzschild, Kerr,…
We study a three-dimensional system of self-propelled Brownian particles interacting via the Lennard-Jones potential. Using Brownian Dynamics simulations in an elongated simulation box, we investigate the steady states of vapour-liquid…
Mathematically rigorous derivation of the hadron matter equation of state within the induced surface and curvature tensions approach is worked out. Such an equation of state allows one to go beyond the Van der Waals approximation for the…