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 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.

2. Navigating through spacetime

2015 ◽  
Author(s):  
Katherine Blundell
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Event Horizon ◽  
Light Cone ◽  
Mathematical Language ◽  
Theory Of Relativity ◽  
Left Behind ◽  
Physical Universe

Mathematics is the perfect language needed for describing how the theory of relativity applies to the physical Universe and all of spacetime, and that description includes the strange behaviour that occurs near black holes. ‘Navigating through spacetime’ explains some of the complicated mathematical language using spacetime diagrams. It describes world-lines—the path left behind as an object journeys through spacetime—and light cones. Black holes profoundly affect the orientations of the light cones. As a particle approaches a black hole, its future light cone tilts more and more towards the black hole. When the particle crosses the event horizon, all of its possible future trajectories end inside the black hole.

scholarly journals TESTING THE KERR BLACK HOLE HYPOTHESIS

2011 ◽  
Vol 26 (33) ◽  
pp. 2453-2468 ◽  
Author(s):  
COSIMO BAMBI
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Event Horizon ◽  
Gravitational Collapse ◽  
State Of The Art ◽  
Kerr Black Hole ◽  
The State ◽  
Kerr Geometry

It is thought that the final product of the gravitational collapse is a Kerr black hole and astronomers have discovered several good astrophysical candidates. While there are some indirect evidences suggesting that the latter have an event horizon, and therefore that they are black holes, a proof that the spacetime around these objects is described by the Kerr geometry is still lacking. Recently, there has been an increasing interest in the possibility of testing the Kerr black hole hypothesis with present and future experiments. In this paper, I briefly review the state-of-the-art of the field, focusing on some recent results and works in progress.

scholarly journals A quantum bound on the compactness

2022 ◽  
Vol 82 (1) ◽  
Author(s):  
Roberto Casadio
Keyword(s):  
Black Holes ◽  
Gravitational Collapse ◽  
Gravitational Radius ◽  
Matter Source ◽  
Quantum Description ◽  
Simple Quantum

AbstractWe present a simple quantum description of the gravitational collapse of a ball of dust which excludes those states whose width is arbitrarily smaller than the gravitational radius of the matter source and supports the conclusion that black holes are macroscopic extended objects. We also comment briefly on the relevance of this result for the ultraviolet self-completion of gravity and the connection with the corpuscular picture of black holes.

Black holes

2021 ◽  
pp. 274-300
Author(s):  
Andrew M. Steane
Keyword(s):  
Black Holes ◽  
Event Horizon ◽  
Gravitational Collapse ◽  
Symmetric Spaces ◽  
Proper Time ◽  
Cosmic Censorship ◽  
General Nature ◽  
Spherically Symmetric ◽  
Event Horizons ◽  
Killing Horizon

We discuss event horizons and black holes. First Birkhoff’s theorem is derived, and we consider the general nature of spherically symmetric spaces. Then the concepts of null surface, Killing horizon and event horizon are defined and related to one another. Cosmic censorship is briefly discussed. The Schwarzshild horizon is discussed in detail. The divergence or otherwise of redshift, acceleration, speed and proper time is obtained for infalling observers and for Schwarzschild observers. Eddington-Finkelstein coordinates are introduced and used to discuss gravitational collapse. The growth of the horizon is noted, and the causality structure is briefly considered via an introduction to the conformal (Penrose-Carter) diagram. The maximal extension is then presented, with the Kruskal-Szekeres coordinates and associated diagram. Wormholes are briefly discussed. The chapter finishes with a survey of astronomical evidence for black holes.

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.

scholarly journals Event Horizon Telescope observations of the jet launching and collimation in Centaurus A

2021 ◽  
Author(s):  
Michael Janssen ◽  
Heino Falcke ◽  
Matthias Kadler ◽  
Eduardo Ros ◽  
Maciek Wielgus ◽  
...  
Keyword(s):  
Black Holes ◽  
Event Horizon ◽  
Galactic Nuclei ◽  
Galactic Centre ◽  
Radio Jets ◽  
Long Baseline ◽  
Wide Range ◽  
Terahertz Frequencies ◽  
Source Structure ◽  
Centaurus A

AbstractVery-long-baseline interferometry (VLBI) observations of active galactic nuclei at millimetre wavelengths have the power to reveal the launching and initial collimation region of extragalactic radio jets, down to 10–100 gravitational radii (rg ≡ GM/c2) scales in nearby sources1. Centaurus A is the closest radio-loud source to Earth2. It bridges the gap in mass and accretion rate between the supermassive black holes (SMBHs) in Messier 87 and our Galactic Centre. A large southern declination of −43° has, however, prevented VLBI imaging of Centaurus A below a wavelength of 1 cm thus far. Here we show the millimetre VLBI image of the source, which we obtained with the Event Horizon Telescope at 228 GHz. Compared with previous observations3, we image the jet of Centaurus A at a tenfold higher frequency and sixteen times sharper resolution and thereby probe sub-lightday structures. We reveal a highly collimated, asymmetrically edge-brightened jet as well as the fainter counterjet. We find that the source structure of Centaurus A resembles the jet in Messier 87 on ~500 rg scales remarkably well. Furthermore, we identify the location of Centaurus A’s SMBH with respect to its resolved jet core at a wavelength of 1.3 mm and conclude that the source’s event horizon shadow4 should be visible at terahertz frequencies. This location further supports the universal scale invariance of black holes over a wide range of masses5,6.

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.

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