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Related papers: The tetralogy of Birkhoff theorems

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This work reveals a fundamental link between general covariance and Birkhoff's theorem. We extend Birkhoff's theorem from general relativity to a broad class of generally covariant gravity theories formulated in the Hamiltonian framework.…

General Relativity and Quantum Cosmology · Physics 2025-12-30 Cong Zhang , Zhoujian Cao

Shape Dynamics is a theory of gravity that replaces refoliation invariance for spatial Weyl invariance. Those solutions of the Einstein equations that have global, constant mean curvature slicings, are mirrored by solutions in Shape…

General Relativity and Quantum Cosmology · Physics 2015-06-15 Henrique Gomes

In Schwarzschild spacetime the value $r=3m$ of the radius coordinate is characterized by three different properties: (a) there is a ``light sphere'', (b) there is ``centrifugal force reversal'', (c) it is the upper limiting radius for a…

General Relativity and Quantum Cosmology · Physics 2010-11-19 Wolfgang Hasse , Volker Perlick

We show succinctly that all metric theories with second order field equations obey Birkhoff's theorem: their spherically symmetric solutions are static.

General Relativity and Quantum Cosmology · Physics 2010-11-05 S. Deser , J. Franklin

We study static, spherically symmetric vacuum solutions to Quadratic Gravity, extending considerably our previous Rapid Communication [Phys. Rev. D 98, 021502(R) (2018)] on this topic. Using a conformal-to-Kundt metric ansatz, we arrive at…

General Relativity and Quantum Cosmology · Physics 2020-01-15 Jiri Podolsky , Robert Svarc , Vojtech Pravda , Alena Pravdova

We continue the study of the non-metric theory of gravity introduced in hep-th/0611182 and gr-qc/0703002 and obtain its general spherically symmetric vacuum solution. It respects the analog of the Birkhoff theorem, i.e., the vacuum…

General Relativity and Quantum Cosmology · Physics 2008-11-26 Kirill Krasnov , Yuri Shtanov

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…

General Relativity and Quantum Cosmology · Physics 2018-07-24 Xin-zhou Li , Xiang-hua Zhai , Ping Li

As a consequence of Birkhoff's theorem, the exterior gravitational field of a spherically symmetric star or black hole is always given by the Schwarzschild metric. In contrast, the exterior gravitational field of a rotating (axisymmetric)…

General Relativity and Quantum Cosmology · Physics 2022-09-22 R. Meinel

Contents: 1) Introduction and a few excursions [A word on the role of explicit solutions in other parts of physics and astrophysics. Einstein's field equations. "Just so" notes on the simplest solutions: The Minkowski, de Sitter and anti-de…

General Relativity and Quantum Cosmology · Physics 2007-05-23 Jiri Bicak

It is well-known that Birkhoff's theorem is no longer valid in theories with more than four dimensions. Thus, in these theories the effective 4-dimensional picture allows the existence of different possible, non-Schwarzschild, scenarios for…

General Relativity and Quantum Cosmology · Physics 2008-11-26 J. Ponce de Leon

We study non-linear massive gravity in the spherically symmetric context. Our main motivation is to investigate the effect of helicity-0 mode which remains elusive after analysis of cosmological perturbation around an open…

High Energy Physics - Theory · Physics 2012-12-19 Chien-I Chiang , Keisuke Izumi , Pisin Chen

We present a local seed-to--Kerr--Schild route to Birkhoff rigidity in four-dimensional spherical vacuum gravity. On the two-dimensional orbit space, the areal radius \(r\) determines a scalar \(F:=-(\nabla r)^2\), and the reduced vacuum…

General Relativity and Quantum Cosmology · Physics 2026-04-14 D. A. Easson

We discuss the validity, or lack thereof, of the Jebsen-Birkhoff theorem in scalar-tensor theories by generalizing it and regarding the Brans-Dicke-like scalar as effective matter. Both the Jordan and Einstein frames are discussed and an…

General Relativity and Quantum Cosmology · Physics 2010-04-06 Valerio Faraoni

In this paper, we systematically study spherically symmetric static spacetimes in the framework of Einstein-aether theory, and pay particular attention to the existence of black holes (BHs). In the present studies we first clarify several…

General Relativity and Quantum Cosmology · Physics 2020-09-18 Chao Zhang , Xiang Zhao , Kai Lin , Shaojun Zhang , Wen Zhao , Anzhong Wang

We present a new cubic theory of gravity in five dimensions which has second order traced field equations, analogous to BHT new massive gravity in three dimensions. Moreover, for static spherically symmetric spacetimes all the field…

General Relativity and Quantum Cosmology · Physics 2011-01-27 Julio Oliva , Sourya Ray

We study static spherically symmetric solutions of Einstein gravity plus an action polynomial in the Ricci scalar, $R$, of arbitrary degree, $n$, in arbitrary dimension, $D$. The global properties of all such solutions are derived by…

High Energy Physics - Theory · Physics 2010-11-19 S. Mignemi , D. L. Wiltshire

In this paper attention is focused on gravitational sector of the Born--Infeld theory, suggested in quant-ph/9608014. Vacuum equations for gravitational field are derived. The asymptotic for modified Schwarzschild solution is obtained, as a…

Quantum Physics · Physics 2010-11-19 Dmitriy Palatnik

A nonsymmetric gravitational theory (NGT) is presented which is free of ghost poles, tachyons and higher-order poles and there are no problems with asymptotic boundary conditions. An extended Birkhoff theorem is shown to hold for the…

General Relativity and Quantum Cosmology · Physics 2008-02-03 J. W. Moffat

For field equations of 4th order, following from a Lagrangian `Ricci scalar plus Weyl scalar', it is shown (using methods of non-standard analysis) that in a neighbourhood of Minkowski space there do not exist regular static spherically…

General Relativity and Quantum Cosmology · Physics 2007-05-23 H. -J. Schmidt

Global properties of static, spherically symmetric configurations of scalar fields of sigma-model type with arbitrary potentials are studied in $D$ dimensions, including space-times containing multiple internal factor spaces. The latter are…

General Relativity and Quantum Cosmology · Physics 2015-06-25 K. A. Bronnikov , S. B. Fadeev , A. V. Michtchenko