A new cubic theory of gravity in five dimensions: black hole, Birkhoff's theorem and
                    C
                    -function

Abstract We study the SL(2) transformation properties of spherically symmetric perturbations of the Bertotti-Robinson universe and identify an invariant μ that characterizes the backreaction of these linear solutions. The only backreaction allowed by Birkhoff’s theorem is one that destroys the AdS2× S2 boundary and builds the exterior of an asymptotically flat Reissner-Nordström black hole with $$ Q=M\sqrt{1-\mu /4} $$ Q = M 1 − μ / 4 . We call such backreaction with boundary condition change an anabasis. We show that the addition of linear anabasis perturbations to Bertotti-Robinson may be thought of as a boundary condition that defines a connected AdS2×S2. The connected AdS2 is a nearly-AdS2 with its SL(2) broken appropriately for it to maintain connection to the asymptotically flat region of Reissner-Nordström. We perform a backreaction calculation with matter in the connected AdS2× S2 and show that it correctly captures the dynamics of the asymptotically flat black hole.

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Birkhoff’S Theorem In The Einstein–Cartan–Kalb–Ramond Theory Of Gravity

Astrophysics and Space Science ◽

10.1007/s10509-005-8191-8 ◽

2005 ◽

Vol 299 (3) ◽

pp. 239-243

Author(s):

F. Rahaman ◽

R. Mukherji ◽

R. Mondal

Keyword(s):

Theory Of Gravity ◽

Birkhoff's Theorem ◽

Birkhoff’S Theorem

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Birkhoff’s theorem in f(R) theory of gravity

The European Physical Journal Plus ◽

10.1140/epjp/i2018-12241-5 ◽

2018 ◽

Vol 133 (9) ◽

Cited By ~ 1

Author(s):

P. J. Ravindranath ◽

Y. Aditya ◽

D. R. K. Reddy ◽

M. V. Subba Rao

Keyword(s):

Theory Of Gravity ◽

Birkhoff's Theorem ◽

Birkhoff’S Theorem

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A short note on extreme points of certain polytopes

Special Matrices ◽

10.1515/spma-2020-0005 ◽

2020 ◽

Vol 8 (1) ◽

pp. 36-39

Author(s):

Lei Cao ◽

Ariana Hall ◽

Selcuk Koyuncu

Keyword(s):

Short Proof ◽

Convex Polytopes ◽

Short Note ◽

Convex Polytope ◽

Extreme Points ◽

Alternative Proof ◽

Stochastic Matrices ◽

Doubly Stochastic ◽

Birkhoff's Theorem ◽

Birkhoff’S Theorem

AbstractWe give a short proof of Mirsky’s result regarding the extreme points of the convex polytope of doubly substochastic matrices via Birkhoff’s Theorem and the doubly stochastic completion of doubly sub-stochastic matrices. In addition, we give an alternative proof of the extreme points of the convex polytopes of symmetric doubly substochastic matrices via its corresponding loopy graphs.

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