Related papers: The Vector Volume and Black Holes
We present a detailed study of the cosmological evolution in general vector-tensor theories of gravity without potential terms. We consider the evolution of the vector field throughout the expansion history of the universe and carry out a…
We explore the possibility that the present stage of accelerated expansion of the universe is due to the presence of a cosmic vector field. We show that vector theories allow for the generation of an accelerated phase without the…
The study of the additive volume of sets can be reduced to the case of one-dimensional sets. The exact values of the volume of extremal sets are given as a conjecture.
We adapt the horizon wave-function formalism to describe massive static spherically symmetric sources in a general $(1+D)$-dimensional space-time, for $D>3$ and including the $D=1$ case. We find that the probability $P_{\rm BH}$ that such…
The level of a function f on an n-dimensional space encloses a region. The volume of a region between two such levels depends on both levels. Fixing one of them the volume becomes a function of the remaining level. We show that if the…
Let $K$ be a $d$ dimensional convex body with a twice continuously differentiable boundary and everywhere positive Gauss-Kronecker curvature. Denote by $K_n$ the convex hull of $n$ points chosen randomly and independently from $K$ according…
We construct several new families of vacuum solutions that describe black holes in uniformly accelerated motion. They generalize the C-metric to the case where the energy density and tension of the strings that pull (or push) on the black…
We explore the idea that the derivative of the volume, V, of a region in R^d with respect to r equals its surface area, A, where r = d V/A. We show that the families of regions for which this formula for r is valid, which we call…
In this article we extend the variational technique for maximal volume estimation of a black hole developed by Christodoulou and Rovelli (CR) to the case of a charged BTZ black hole in 2+1 dimensions. The technique involves a study of the…
We consider the problem of picking a physically motivated vacuum state on a spherically symmetric spacetime with an extra conformal Killing vector, as opposed to an extra Killing vector as in the Schwarzschild case. Considering a conformal…
In this paper we generalize the black hole bound of arXiv:0706.2050 to de Sitter spaces, and apply it to various vacua in the landscape, with a special emphasis on slow-roll inflationary vacua. Non-trivial constraints on the lifetime and…
Christodoulou and Rovelli have shown that the maximal interior volume of a Schwarzschild black hole linearly grows with time. Recently, their conclusion has been extended to the Reissner{-}Nordstr$\ddot{\text{o}}$m and Kerr black holes.…
A presentation of the Vaidya type Schwarzschild-like black holes with flat, AdS and dS asymptotics in 4-dimensional general relativity in the form of a pointlike mass is given. True singularities are described by making the use of the Dirac…
We construct and study the vacuum polarization, $\langle \phi^{2}\rangle_{D},$ of the quantized massive scalar field with a general curvature coupling parameter in higher-dimensional static and spherically-symmetric black hole spacetimes,…
In backgrounds with compact dimensions there may exist several phases of black objects including the black-hole and the black-string. The phase transition between them raises puzzles and touches fundamental issues such as topology change,…
If the negative cosmological constant is treated as a dynamical pressure and if the volume be its thermodynamically conjugate variable then the gravitational mass can be expressed as the total gravitational enthalpy rather than the energy.…
A new intrinsic volume metric is introduced for the class of convex bodies in $\mathbb{R}^n$. As an application, an inequality is proved for the asymptotic best approximation of the Euclidean unit ball by arbitrarily positioned polytopes…
Binary black hole spacetimes with a helical Killing vector, which are discussed as an approximation for the early stage of a binary system, are studied in a projection formalism. In this setting the four dimensional Einstein equations are…
Black hole mass is a key factor in determining how a black hole interacts with its environment. However, the determination of black hole masses at high redshifts depends on secondary mass estimators, which are based on empirical…
The Kerr-Newman metric is the unique vacuum solution of the General Relativistic field equations, in which any singularities or spacetime pathologies are hidden behind horizons. They are believed to describe the spacetimes of massive…