Related papers: What is the Shape of a Black Hole?
The 3d volume inside a spherical black hole can be defined by extending an intrinsic flat-spacetime characterization of the volume inside a 2-sphere. For a collapsed object, the volume grows with time since the collapse, reaching a simple…
It is well known that celestial bodies tend to be spherical due to gravity and that rotation produces deviations from this sphericity. We discuss what is known and expected about the shape of black holes' horizons from their formation to…
In this chapter I focus on asking and answering the following questions: (1) What is a black hole? Answer: There are three types of black holes, namely mathematical black holes, physical black holes and astrophysical black holes. An…
I survey the physics of black holes in two and three spacetime dimensions, with special attention given to an understanding of their exterior and interior properties.
The horizon (the surface) of a black hole is a null surface, defined by those hypothetical "outgoing" light rays that just hover under the influence of the strong gravity at the surface. Because the light rays are orthogonal to the spatial…
We study the property of matter in equilibrium with a static, spherically symmetric black hole in D-dimensional spacetime. It requires this kind of matter has an equation of state (\omega\equiv p_r/\rho=-1/(1+2kn), k,n\in \mathbb{N}), which…
Black holes that have nearly evaporated are often thought of as small objects, due to their tiny exterior area. However, the horizon bounds large spacelike hypersurfaces. A compelling geometric perspective on the evolution of the interior…
We investigate the energy distribution of a black hole in various spacetimes as reckoned by a distant observer using the quasi-local energy approach. In each case the horizon mass of a black hole: neutral, charged or rotating, is found to…
Astronomers have certainly observed things that are small, dark, and heavy. But are these objects really black holes in the sense of general relativity? The consensus opinion is simply "yes", and there is very little "wriggle room". We…
We briefly review some recent advances in the study of the shadows of rotating black holes in alternative theories. The size and the shape of the shadow depend on the mass and the angular momentum, and they can also depend on other…
We propose a definition of volume for stationary spacetimes. The proposed volume is independent of the choice of stationary time-slicing, and applies even though the Killing vector may not be globally timelike. Moreover, it is constant in…
What does a black hole look like? In 1+3 spacetime dimensions, the optical appearance of a black hole is a bidimensional region in the observer's sky often called the black hole shadow, as supported by the EHT observations. In higher…
Black holes in several dimensions and in several theories are studied and discussed. The theories are, general relativity, Kaluza-Klein, Brans-Dicke, Lovelock gravity and string theory.
Using a cosmological black hole model proposed recently, we have calculated the quasi-local mass of a collapsing structure within a cosmological setting due to different definitions put forward in the last decades to see how similar or…
A star surrounded by a black hole generated by it is analyzed. For an outer static observer the black hole mass (and radius) depends on his position in the gravitational field of the star. In spite of the black hole presence, the geometry…
This thesis is a review of black hole evaporation with emphasis on recent results obtained for two dimensional black holes. First, the geometry of the most general stationary black hole in four dimensions is described and some classical…
Light bending by the strong gravity around the black hole will form the so-called black hole shadow, the shape of which can shed light on the structure of the near-horizon geometry to possibly reveal novel physics of strong gravity and…
We consider the problem of determination of a volume of some bounded space-like hypersurfaces in the case of spherically symmetric spacetimes. In the case when the hypersurfaces is cut or bounded by a light-like hypersurface the problem may…
A precise formulation of the hoop conjecture for four-dimensional spacetimes proposes that the Birkhoff invariant \beta for an apparent horizon in a spacetime with mass M should satisfy \beta \le 4\pi M. The invariant \beta is the least…
Black holes are real astrophysical objects, but their interiors are hidden and can only be "observed" through mathematics. The structure of rotating black holes is typically illustrated with the help of special coordinates. But any such…