相关论文: When does the Hawking into Unruh mapping for globa…

The Unruh effect can be formulated as the statement that the Minkowski vacuum in a Rindler wedge has a boost as its modular flow. In recent years, other examples of states with geometrically local modular flow have played important roles in…

We study the detailed balance temperatures recorded along all classes of stationary, uniformly accelerated worldlines in four-dimensional Minkowski spacetime, namely along (i) linear uniform acceleration, (ii) cusped, (iii) circular, (iv)…

We investigate the extrinsic geometry of causal sets in $(1+1)$-dimensional Minkowski spacetime. The properties of boundaries in an embedding space can be used not only to measure observables, but also to supplement the discrete action in…

We established the equivalence between the local Hawking temperature measured by the time-like Killing observer located at some positions $r$ with finite distances from the outer horizon $r_+$ in the 5-dimensional spinning black hole space…

Complexifying space time has many interesting applications, from the construction of higher dimensional unification, to provide a useful framework for quantum gravity and to better define some local symmetries that suffer singularities in…

In special and general relativity the synchronization convention of distant clocks may be simulated with a mathematical definition of global non-inertial frames (the only ones existing in general relativity due to the equivalence principle)…

In this paper, we continue the study of the Killing symmetries of a N-dimensional generalized Minkowski space, i.e. a space endowed with a (in general non-diagonal) metric tensor, whose coefficients do depend on a set of non-metrical…

Although the Nash theorem solves the isometric embedding problem, matters are inherently more involved if one is further seeking an embedding that is well-behaved from the standpoint of submanifold geometry. More generally, consider a…

We study an Unruh-DeWitt particle detector that is coupled to the proper time derivative of a real scalar field in 1+1 spacetime dimensions. Working within first-order perturbation theory, we cast the transition probability into a…

The theory presented in this monograph establishes the first mathematically rigorous result on the global nonlinear stability of self-gravitating matter under small perturbations of an asymptotically flat, spacelike hypersurface of…

A scheme is discussed for embedding n-dimensional, Riemannian manifolds in an (n+1)-dimensional Einstein space. Criteria for embedding a given manifold in a spacetime that represents a solution to Einstein's equations sourced by a massless…

In the Minkowski space-time, a world hyper-sheet is a timelike hypersurface consisting of a one-parameter family of spacelike submanifolds. Recently, Bousso and Randall introduced the notion of caustics of world hyper-sheets in order to…

Here we present an overview of the work done over the years on the embedding of hypersurfaces in a space of higher dimension, with particular reference to the embedding of four-dimensional hypersurfaces in five-dimensional space-times. The…

In this paper we develop a global correspondence between immersed horospherically convex hypersurfaces in hyperbolic space and complete conformal metrics on domains in the sphere. We establish results on when the hyperbolic Gauss map is…

We investigate the Unruh-Fulling effect in a class of nonlocal field theories by examining both the number operator and Unruh-DeWitt detector methods. Unlike in previous literature, we use Unruh quantization to quantize the matter field.…

A simple algebraic global isometric embedding is presented for the nonrotating BTZ black hole and its counterpart of Euclidean signature. The image of the embedding, in Minkowski space of two extra dimensions, is the interection of two…

Misner spacetime is obtained by quotienting a timelike wedge of two-dimensional Minkowski spacetime by a discrete boost. The familiar Hausdorff extensions and the Hawking--Ellis non-Hausdorff extension are classical, but the passage from…

In this work, we study various properties of embedded hypersurfaces in $1+1+2$ decomposed spacetimes with a preferred spatial direction, denoted $e^{\mu}$, which are orthogonal to the fluid flow velocity of the spacetime and admit a proper…

We investigate a generalization of the so-called metric splitting of globally hyperbolic space-times to non-smooth Lorentzian manifolds and show the existence of this metric splitting for a class of wave-type space-times. Our approach is…

The definition of quasi-local mass for a bounded space-like region in space-time is essential in several major unsettled problems in general relativity. The quasi-local mass is expected to be a type of flux integral on the boundary…