Related papers: The Vector Volume and Black Holes

We advocate for a holographic definition of thermodynamic pressure and volume for black holes based on quasi-local gravitational thermodynamics. When a black hole is enclosed by a finite timelike boundary, York's quasi-local first law…

The investigation about the volume of a black hole is closely related to the quantum nature of the black hole. The entropy is a significant concept for this. A recent work by Majhi and Samanta [Phys. Lett. B 770 (2017) 314] after us…

We argue that the main feature behind novel properties of higher-dimensional black holes, compared to four-dimensional ones, is that their horizons can have two characteristic lengths of very different size. We develop a long-distance…

We review recent developments on the thermodynamics of black holes in extended phase space, where the cosmological constant is interpreted as thermodynamic pressure and treated as a thermodynamic variable in its own right. In this approach,…

In this paper, we give a definition of volume for subsets in the space of arcs of an algebraic variety, and study its properties. Our main result relates the volume of a set of arcs on a Cohen-Macaulay variety to its jet-codimension, a…

The classical spacetime is usually described by a differentiable manifold with infinitely many degrees of freedom. Occasionally though, it is useful to consider an approximation whose number of degrees of freedom is finite. There are…

In the first part of this talk, I consider some exact string solutions in curved spacetimes. In curved spacetimes with a Killing vector (timelike or spacelike), the string equations of motion and constraints are reduced to the Hamilton…

Traditional treatments of the first law of black hole thermodynamics do not include a discussion of pressure and volume. We give an overview of recent developments proposing a definition of volume that can be used to extend the first law to…

We calculate the maximum interior volume, enclosed by the event horizon, of a ($1+D$)-dimensional Schwarzschild black hole. Taking into account the mass change due to Hawking radiation, we show that the volume increases towards the end of…

We introduce a 'quasi-topological` term [1] in D=1+1 dimensions and the entropy for black holes is calculated [2]. The source of entropy in this case is justified by a non-null stress-energy tensor.

Some basic theorems on Killing vector fields are reviewed. In particular, the topic of a constant-curvature space is examined. A detailed proof is given for a theorem describing the most general form of the metric of a homogeneous isotropic…

For a type of non-minimally coupled vector-tensor theories with Abelian gauge symmetry breaking in four-dimensional spacetime and correspondingly asymptotic non-AdS black hole solutions including a cosmological constant, we construct the…

A brief, and certainly not exhaustive, survey is provided of some recent results and conjectures in four and higher spacetime dimensions, such as the Hoop Conjecture, relating the geometry of event horizons to dynamical quantities such as…

We discuss black hole spacetimes with a geometrically defined quasi-local horizon on which the curvature tensor is algebraically special relative to the alignment classification. Based on many examples and analytical results, we conjecture…

We present a numerical relativity study of the accretion properties of a non-spinning black hole in a cosmology driven by a scalar field. The simulations are carried out with a modified moving-puncture gauge condition suitable for…

A certain vector-tensor (VT) theory of gravitation was tested in previous papers. In the background universe, the vector field of the theory has a certain energy density, which is appropriate to play the role of vacuum energy (cosmological…

In geometric inequalities ADM mass plays more fundamental role than the concept of quasi-local mass. This paper is to demonstrate that using the quasi-local mass some new insights can be acquired. In spherically symmetric spacetimes the…

An action principle for spacetimes with the topology of an Euclidean black-hole is given. The gravitational field is described by the ordinary volume degrees of freedom plus additional surface fields at the horizon. The surface degrees of…

Generalized vector-tensor theories of gravity have drawn attention for admitting hairy black hole solutions, thereby circumventing the standard no-hair theorems. It remains an open question, however, how such black holes may form starting…

We study a graded vector space of polynomials associated to a square matrix, defined by a finite difference condition along the rows. We show this space coincides with one defined by directional derivatives, and prove it is…