Kruskal Coordinates and Mass of Schwarzschild Black Holes: No Finite Mass Black Hole at All

Mitra, Abhas

doi:10.4236/ijaa.2012.24031

Cited by 10 publications

(10 citation statements)

References 52 publications

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“…In any case, BH solutions implicitly correspond to M = 0 implying that entire mass-energy must be radiated away asymptotically during continued collapse. 8,9,[11][12][13][14][15][16]19,20 And naturally, one can easily explain the origin of cosmic Gamma Ray Bursts whose duration could be as large as an hour and which can be rejuvenated by magneto-radiative eruptions of the nascent MECO.…”

Section: Discussionmentioning

confidence: 99%

“…This conclusion that the work of OS demands r 0 = 0 could have obtained in a much more direct fashion simply from the definition of y in Eq. (9). To this effect, we rewrite this equation as…”

Section: Critical Analysis Of Os Collapse In Schwarzschild Framementioning

confidence: 99%

“…7 Similarly, the vacuum Schwarzschild/Hilbert solution too becomes vacuous when the gravitating object is assumed to shrink to a geometrical point or "spacetime singularity." 8,9,[13][14][15][16] …”

Section: Physical Interpretationsmentioning

confidence: 99%

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The Mass of the Oppenheimer–snyder-Black Hole: Only Finite Mass Quasi-Black Holes

Mitra

Singh

2013

Int. J. Mod. Phys. D

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Oppenheimer and Snyder (OS) in their paper apparently showed the formation of an event horizon [see Eq. (37) in Phys. Rev. 56 (1939) 455] for a collapsing homogeneous dust ball of mass M as the circumference radius of the outermost surface, r b → r 0 = 2GM/c 2 in a proper time τ 0 ∝ r −1/2 0 in the limit of large Schwarzschild time t → ∞. But Eq. (37) was approximated from Eq. (36) whose essential character is (t ∼ r 0 ln √ y+1where, at the boundary of the star y = r b /r 0 = r b c 2 /2GM . And since the argument of a logarithmic function cannot be negative, one must have y ≥ 1 or 2GM/r b c 2 ≤ 1. This shows that, at least, in this case (i) trapped surfaces are not formed, (ii) if the collapse indeed proceeds upto r = 0, we must have M = 0, and (iii) proper time taken for collapse τ → ∞. Thus, the gravitational mass of OS-black holes (OS-BHs), is unique and equal to zero. In fact, by invoking Birkhoff's theorem, it has been found that the OS collapse is only a fictitious mathematical artifact because it corresponds to a matter density ρ = 0 [Mitra, Astrophys. Space Sci. 332 (2011) 43, arXiv:1101]. Further, this is also in agreement with the proof that Schwarzschild BHs have the unique gravitational mass M = 0 [Mitra, J. Math. Phys. 50 (2009), arXiv:0904.4754], and they represent asymptotic final state of physical collapse for which entire mass-energy is radiated out Glendenning, Mon. Not. R. Astron. Soc. Lett. 404 (2010) L50, arXiv:1003.3518]. Finally this is in agreement with the conclusion that "the discussion of physical behavior of black holes, classical or quantum, is only of academic interestwe wonder whether nature allows gravitational collapse to continue inside the EH at all"

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Section: Discussionmentioning

confidence: 99%

Section: Critical Analysis Of Os Collapse In Schwarzschild Framementioning

confidence: 99%

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The Mass of the Oppenheimer–snyder-Black Hole: Only Finite Mass Quasi-Black Holes

Mitra

Singh

2013

Int. J. Mod. Phys. D

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“…It is used to represent the infinities (timelike infinities vertically in two regions representing spacetime past and future, and spacelike infinities representing the evolution of the mass of a chunk of matter on the surface of a black hole). Figure 2 extends t'Hooft's model, using the horizontal axis to represent the masses of soft matter (Parzygnat, 2014;Mitra 1999a;Mitra 1999b). The relationship between chunks of matter and a black hole in the neighborhood of surrounding ones, represented by the Penrose diagram in Figure 2, says to us that, as well as it is feasible to achieve antipodal points with matching features on a black hole horizon, we are allowed to hypothesize the simultaneous presence on the horizon of particles with positive and negative mass.…”

Section: Antipodal Masses: An Hypothesismentioning

confidence: 99%

Topological Assessment of Entangled Particles on Black Hole Horizons

Tozzi¹,

Peters²

2018

Preprint

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The entangled antipodal points on black hole surfaces, recently described by t’Hooft, display an unnoticed relationship with the Borsuk-Ulam theorem.  Taking into account this observation and other recent claims, suggesting that quantum entanglement takes place on the antipodal points of a S3 hypersphere, a novel framework can be developed, based on algebraic topological issues: a feature encompassed in an S2 unentangled state gives rise, when projected one dimension higher, to two entangled particles.  This allows us to achieve a mathematical description of the holographic principle occurring in S2.  Furthermore, our observations let us to hypothesize that a) quantum entanglement might occur in a four-dimensional spacetime, while disentanglement might be achieved on a motionless, three-dimensional manifold; b) a negative mass might exist on the surface of a black hole.

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“…It is used to represent the infinities (timelike infinities vertically in two regions representing spacetime past and future, and spacelike infinities representing the evolution of the mass of a chunk of matter on the surface of a black hole). Figure 3 extends 't Hooft's model, using the horizontal axis to represent the masses of soft matter [23][24][25]. The relationship between chunks of matter and a black hole in the neighborhood of surrounding ones, represented by the Penrose diagram in Figure 3, says to us that, as well as it is feasible to achieve antipodal points with matching features on a black hole horizon, we are allowed to hypothesize the simultaneous presence on the horizon of particles with positive and negative mass.…”

Section: -Antipodal Masses: a Hypothesismentioning

confidence: 99%

Topology of Black Holes’ Horizons

Tozzi

Peters

2019

Emerg Sci J

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The Möbius strip spacetime topology and the entangled antipodal points on black hole surfaces, recently described by ‘t Hooft, display an unnoticed relationship with the Borsuk-Ulam theorem from algebraic topology. Considering this observation and other recent claims which suggest that quantum entanglement takes place on the antipodal points of a S3 hypersphere, a novel topological framework can be developed: a feature encompassed in an S2 unentangled state gives rise, when projected one dimension higher, to two entangled particles. This allows us to achieve a mathematical description of the holographic principle occurring in S2. Furthermore, our observations let us to hypothesize that a) quantum entanglement might occur in a four-dimensional spacetime, while disentanglement might be achieved on a motionless, three-dimensional manifold; b) a negative mass might exist on the surface of a black hole.

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Kruskal Coordinates and Mass of Schwarzschild Black Holes: No Finite Mass Black Hole at All

Abstract: When one presumes that the gravitational mass of a neutral massenpunkt M is finite, the Schwarzschild coordinates appear to fail to describe the region within the event horizon (EH),   , r t

Cited by 10 publications

References 52 publications

The Mass of the Oppenheimer–snyder-Black Hole: Only Finite Mass Quasi-Black Holes

The Mass of the Oppenheimer–snyder-Black Hole: Only Finite Mass Quasi-Black Holes

Topological Assessment of Entangled Particles on Black Hole Horizons

Topology of Black Holes’ Horizons

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