Related papers: The horizon problem for prevalent surfaces
In the previous decades, the size of level sets of functions have been extensively studied in various setups involving different regularity properties and size notions. In the case of H\"older functions, the authors have provided various…
The idea of treating the horizon of a black hole as a stretched membrane with surface tension has a long history. In this work, we discuss the microscopic origin of the surface tension of the horizon in quantum pictures of spaces, which are…
The horizon is a classical concept that arises in general relativity, and is therefore not clearly defined when the source cannot be reliably described by classical physics. To any (sufficiently) localised quantum mechanical wave-function,…
This article presents the construction of a non-affine hypersurface on an $n$-simplex in $\mathbb{R}^n$. Additionally, fractal dimension of the graph of a non-affine multivariate real-valued fractal function is estimated under certain…
This article reviews the properties and limitations associated with the existence of particle, visual, and event horizons in cosmology in general and in inflationary universes in particular, carefully distinguishing them from `Hubble…
The surface Hamiltonian corresponding to the surface part of a gravitational action has $xp$ structure where $p$ is conjugate momentum of $x$. Moreover, it leads to $TS$ on the horizon of a black hole. Here $T$ and $S$ are temperature and…
We construct an explicit K3 surface over the field of rational numbers that has geometric Picard rank one, and for which there is a transcendental Brauer-Manin obstruction to weak approximation. To do so, we exploit the relationship between…
In contrast to the univariate case, several definitions are available for the notion of bounded variation for a bivariate function. This article is an attempt to study the Hausdorff dimension and box dimension of the graph of a continuous…
It is well known that the Euclidean black hole action has a boundary term at the horizon proportional to the area. I show that if the horizon is replaced by a stretched horizon with appropriate boundary conditions, a new boundary term…
The saddle point approximation to formal quantum gravitational partition functions has yielded plausible computations of horizon entropy in various settings, but it stands on shaky ground. In this paper we visit some of that shaky ground,…
A key consequence of Lorentz-violating gravity is the emergence of modified dispersion relations implying the absence of a universal maximum propagation speed. This challenges the conventional notion of the event horizon as a causal…
The fundamental gap of a domain is the difference between the first two eigenvalues of the Laplace operator. In a series of recent and celebrated works, it was shown that for convex domains in $\mathbb R^n$ and $\mathbb S^n$ with Dirichlet…
It is well-known that the convex and concave envelope of a multilinear polynomial over a box are polyhedral functions. Exponential-sized extended and projected formulations for these envelopes are also known. We consider the convexification…
This thesis explores two avenues into understanding the physics of black holes and horizons beyond general relativity, via analogue models and Lorentz violating theories. Analogue spacetimes have wildly different dynamics to general…
A fractal surface is a set which is a graph of a bivariate continuous function. In the construction of fractal surfaces using IFS, vertical scaling factors in IFS are important one which characterizes a fractal feature of surfaces…
It is folklore knowledge amongst general relativists that horizons are well behaved, continuously differentiable hypersurfaces except perhaps on a negligible subset one needs not to bother with. We show that this is not the case, by…
When solving optimization problems with multiple objective functions we are often faced with the situation that one or several objective functions are non-convex or that we can not easily show the convexity of all functions involved. In…
We establish a lower bound for the surface area of a closed, convex hypersurface in Euclidean space in terms of its displacement under continuous maps. As a result, a hypothesized lower bound for the volume of a Riemannian $n$-sphere,…
Intermediate dimensions were recently introduced to interpolate between the Hausdorff and box-counting dimensions of fractals. Firstly, we show that these intermediate dimensions may be defined in terms of capacities with respect to certain…
Event horizons are a defining feature of black holes. Consequently, there have been many efforts to probe their existence in astrophysical black hole candidates, spanning ten orders of magnitude in mass. Nevertheless, horizons remain an…