Related papers: Birkhoff Theorem and Matter
According to general relativity, black holes are incomplete, which prevents developing a complete physical description of their dynamical formation and evolution once quantum effects are taken into account. Theories beyond general…
We present a tetrad-based method for solving the Einstein field equations for spherically-symmetric systems and compare it with the widely-used Lema\^itre-Tolman-Bondi (LTB) model. In particular, we focus on the issues of gauge ambiguity…
Self-similar spacetimes are of importance to cosmology and to gravitational collapse problems. We show that self-similarity or the existence of a homothetic Killing vector field for spherically symmetric spacetimes implies the separability…
We present an effective theory to describe the quantization of spherically symmetric vacuum in loop quantum gravity. We include anomaly-free holonomy corrections through a canonical transformation of the Hamiltonian of general relativity,…
Although the standard viewpoint in theoretical physics is that the unification of quantum theory and general relativity requires the quantization of gravity and spacetime, there is not consensus about whether spacetime must fundamentally…
We continue our work on the study of spherically symmetric loop quantum gravity coupled to two spherically symmetric scalar fields, one which acts as a clock. As a consequence of the presence of the latter, we can define a true Hamiltonian…
In this paper, we study the structure of Birkhoff spectra for hyperbolic dynamical systems. Given a H\"older observable \(f\) on a basic set \(\Lambda\), we obtain the following results: First, we characterize when the Birkhoff spectrum of…
Kastner's (Philosophy of Science 70, 2003, pp. 145--163) recent objections to the counterfactual usage of the time-symmetric Aharonov-Bergmann-Lebowitz rule by the author, especially her claims that the resulting time-symmetric quantum…
In Newtonian gravity (NG) it is known that the gravitational field anywhere inside a spherically symmetric distribution of mass is determined only by the enclosed mass. This is also widely believed to be true in general relativity (GR), and…
The arguments leading to the introduction of the massive Nonsymmetric Gravitational action are reviewed \cite{Moffat:1994,Moffat:1995b}, leading to an action that gives asymptotically well-behaved perturbations on GR backgrounds. Through…
There is undetermined potential function $V(\phi)$ in the action of mimetic gravity which should be resolved through physical means. In general relativity(GR), the static spherically symmetric(SSS) solution to the Einstein equation is a…
A new type of singularity theorem, based on spatial averages of physical quantities, is presented and discussed. Alternatively, the results inform us of when a spacetime can be singularity-free. This theorem provides a decisive…
The paper extends Birkhoff's theorem on doubly stochastic matrices to some countable families of discrete probability spaces with nonempty intersections. We join every two elements lying in the same probability space by an edge and…
Birkhoff's theorem is discussed in the frame of f(R) gravity by using its scalar-tensor representation. Modified gravity has become very popular at recent times as it is able to reproduce the unification of inflation and late-time…
The f(T) theory, a generally modified teleparallel gravity, has been proposed as an alternative gravity model to account for the dark energy phenomena. Following our previous work [Xin-he Meng and Ying-bin Wang, EPJC(2011),…
A combination of qualitative analysis and numerical study indicates that vacuum $T^2$ symmetric spacetimes are, generically, oscillatory.
f(T) gravity, a generally modified teleparallel gravity, has become very popular in recent times as it is able to reproduce the unification of inflation and late-time acceleration without the need of a dark energy component or an inflation…
In terms of Sturm's theorem, we reexamine a marginal stable circular orbit (MSCO) such as the innermost stable circular orbit (ISCO) of a timelike geodesic in any spherically symmetric and static spacetime. MSCOs for some of exact solutions…
This paper investigates the global properties of a class of spherically symmetric spacetimes. The class contains the maximal development of asymptotically flat spherically symmetric initial data for a wide variety of coupled Einstein-matter…
The classic Birkhoff- von Neumann theorem states that the set of doubly stochastic matrices is the convex hull of the permutation matrices. In this paper, we study a generalisation of this theorem in the type $II_1$ setting. Namely, we…