scholarly journals HOW TO BYPASS BIRKHOFF THROUGH EXTRA DIMENSIONS: A SIMPLE FRAMEWORK FOR INVESTIGATING THE GRAVITATIONAL COLLAPSE IN VACUUM

2006 ◽  
Vol 15 (12) ◽  
pp. 2217-2222 ◽  
Author(s):  
PIOTR BIZOŃ ◽  
BERND G. SCHMIDT
Keyword(s):  
Gravitational Collapse ◽  
Einstein Equations ◽  
Dimensional System ◽  
Spherically Symmetric ◽  
Asymptotically Flat ◽  
Spherical Collapse ◽  
Geometric Setting ◽  
Birkhoff's Theorem ◽  
Birkhoff’S Theorem ◽  
Odd Dimensions

It is fair to say that our current mathematical understanding of the dynamics of gravitational collapse to a black hole is limited to the spherically symmetric situation and, in fact, even in this case much remains to be learned. The reason is that Einstein's equations become tractable only if they are reduced to a (1 + 1)-dimensional system of partial differential equations. Owing to this technical obstacle, very little is known about the collapse of pure gravitational waves because by Birkhoff's theorem there is no spherical collapse in vacuum. In this essay, we describe a new cohomogeneity-two symmetry reduction of the vacuum Einstein equations in five and higher odd dimensions which evades Birkhoff's theorem and admits time-dependent asymptotically flat solutions. We argue that this model provides an attractive (1 + 1)-dimensional geometric setting for investigating the dynamics of gravitational collapse in vacuum.

scholarly journals Extreme black hole anabasis

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Shahar Hadar ◽  
Alexandru Lupsasca ◽  
Achilleas P. Porfyriadis
Keyword(s):  
Boundary Condition ◽  
Black Hole ◽  
Spherically Symmetric ◽  
Asymptotically Flat ◽  
Flat Region ◽  
Extreme Black Hole ◽  
Condition Change ◽  
Birkhoff's Theorem ◽  
Birkhoff’S Theorem

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.

SPHERICAL AND NON-SPHERICAL GRAVITATIONAL COLLAPSE IN MONOPOLE-ANTI-DE SITTER–VAIDYA SPACE–TIME

2006 ◽  
Vol 15 (11) ◽  
pp. 1977-1984 ◽  
Author(s):  
K. D. PATIL ◽  
U. S. THOOL
Keyword(s):  
Gravitational Collapse ◽  
Space Time ◽  
Spherically Symmetric ◽  
De Sitter ◽  
Spherical Collapse ◽  
Time Singularities

In the present work, we investigate the influence of the monopole field on the occurrence of the space–time singularities in the gravitational collapse of anti-de Sitter–Vaidya space–time. It has been found that the spherically symmetric monopole-anti-de Sitter–Vaidya space–time contradicts the CCH, whereas the non-spherical collapse respects it.

scholarly journals ON THE SOLUTION TO THE "FROZEN STAR" PARADOX, NATURE OF ASTROPHYSICAL BLACK HOLES, NON-EXISTENCE OF GRAVITATIONAL SINGULARITY IN THE PHYSICAL UNIVERSE AND APPLICABILITY OF THE BIRKHOFF'S THEOREM

2011 ◽  
Vol 20 (10) ◽  
pp. 1891-1899 ◽  
Author(s):  
SHUANG-NAN ZHANG
Keyword(s):  
Black Holes ◽  
Event Horizon ◽  
Gravitational Collapse ◽  
Finite Time ◽  
External Observer ◽  
Gravitational Radius ◽  
Physical Universe ◽  
Gravitational Singularity ◽  
Birkhoff's Theorem ◽  
Birkhoff’S Theorem

Oppenheimer and Snyder found in 1939 that gravitational collapse in vacuum produces a "frozen star", i.e. the collapsing matter only asymptotically approaches the gravitational radius (event horizon) of the mass, but never cross it within a finite time for an external observer. Based upon our recent publication on the problem of gravitational collapse in the physical universe for an external observer, the following results are reported here: (1) Matter can indeed fall across the event horizon within a finite time and thus black holes (BHs), rather than "frozen stars", are formed in gravitational collapse in the physical universe. (2) Matter fallen into an astrophysical BH can never arrive at the exact center; the exact interior distribution of matter depends upon the history of the collapse process. Therefore gravitational singularity does not exist in the physical universe. (3) The metric at any radius is determined by the global distribution of matter, i.e. not only by the matter inside the given radius, even in a spherically symmetric and pressureless gravitational system. This is qualitatively different from the Newtonian gravity and the common (mis)understanding of the Birkhoff's Theorem. This result does not contract the "Lemaitre–Tolman–Bondi" solution for an external observer.

scholarly journals Gravitational collapse with rotating thin shells and cosmic censorship

2015 ◽  
Vol 24 (09) ◽  
pp. 1542002 ◽  
Author(s):  
Jorge V. Rocha
Keyword(s):  
Gravitational Collapse ◽  
Negative Pressure ◽  
Cosmic Censorship ◽  
Thin Shells ◽  
Five Dimensions ◽  
Asymptotically Flat ◽  
Angular Momenta ◽  
Flat Spacetimes ◽  
Odd Dimensions

Gravitational collapse of matter in the presence of rotation is a mostly unexplored topic but it might have important implications for cosmic censorship. Recently a convenient setup was identified to address this problem, by considering thin matter shells at the interface between two equal angular momenta Myers–Perry spacetimes in five dimensions. This note provides more details about the matching of such cohomogeneity-1 spacetimes and extends the results obtained therein to arbitrary higher odd dimensions. It is also pointed out that oscillatory orbits for shells in asymptotically flat spacetimes can be naturally obtained if the matter has a negative pressure component.

scholarly journals FORMATION OF TRAPPED SURFACES FOR THE SPHERICALLY SYMMETRIC EINSTEIN–VLASOV SYSTEM

2010 ◽  
Vol 07 (04) ◽  
pp. 707-731 ◽  
Author(s):  
HÅKAN ANDRÉASSON ◽  
GERHARD REIN
Keyword(s):  
Initial Data ◽  
Event Horizon ◽  
Apparent Horizon ◽  
Cosmic Censorship ◽  
Einstein Equations ◽  
Spherically Symmetric ◽  
Asymptotically Flat ◽  
Trapped Surfaces ◽  
Matter Model ◽  
Trapped Surface

We consider the spherically symmetric, asymptotically flat, non-vacuum Einstein equations, using as matter model a collisionless gas as described by the Vlasov equation. We find explicit conditions on the initial data which guarantee the formation of a trapped surface in the evolution which in particular implies that weak cosmic censorship holds for these data. We also analyze the evolution of solutions after a trapped surface has formed and we show that the event horizon is future complete. Furthermore we find that the apparent horizon and the event horizon do not coincide. This behavior is analogous to what is found in certain Vaidya spacetimes. The analysis is carried out in Eddington–Finkelstein coordinates.

Information paradox for a collapsing string cloud in rainbow gravity

2021 ◽  
pp. 2150084
Author(s):  
Umber Sheikh ◽  
Sufyan Liaqut ◽  
Zeeshan Yousaf ◽  
Muhammad Zaeem Ul Haq Bhatti
Keyword(s):  
Black Hole ◽  
Early Universe ◽  
Gravitational Collapse ◽  
Spherically Symmetric ◽  
Information Paradox ◽  
Spherical Collapse ◽  
Symmetric Spacetime ◽  
Spherically Symmetric Spacetime

This work is devoted to study the gravitational collapse of a string cloud in Rainbow gravity. The results are obtained for spherically symmetric spacetime. The radius and time to reach the horizon for a particle are calculated. This helps to understand the famous information paradox in the Early Universe and the intersteller gas clouds. Our study strengthens the view that the information can be carried out of the black hole as a result of the spherical collapse.

scholarly journals A short note on extreme points of certain polytopes

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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