A critical appraisal of the singularity theorems

Senovilla, José M. M.

doi:10.48550/arxiv.2108.07296

Cited by 3 publications

(5 citation statements)

References 51 publications

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“…For such a discussion we refer to [2,21,22]. A short but very compact and beautiful discussion regarding this theorem and the underlying assumptions has been reported recently by Senovilla [113]. Our main focus is on the subject of the convergence condition (equation (1.21), and more generally on the Focusing Condition (FC) (equation (1.22)) for the timelike case.…”

Section: Singularities and The Raychaudhuri Equationmentioning

confidence: 98%

Application of the Raychaudhuri Equation in Gravitational Systems

Choudhury¹

2023

Preprint

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hereby declare that this thesis is my own work and, to the best of my knowledge, it neither contains materials previously published or written by any other person, nor has it been submitted for any degree/diploma or any other academic award anywhere before. I have used the originality checking service to prevent inappropriate copying.I also declare that all copyrighted material incorporated into this thesis is in compliance with the Indian Copyright Act, 1957Act, (amended in 2012 and that I have received written permission from the copyright owners for my use of their work. I hereby grant permission to IISER Kolkata to store the thesis in a database which can be accessed by others.

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Section: Singularities and The Raychaudhuri Equationmentioning

confidence: 98%

Application of the Raychaudhuri Equation in Gravitational Systems

Choudhury¹

2023

Preprint

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“…43 It is the basis of various singularity theorems. 58,60,74,78,248 The theorems themselves do not establish the existence of physically relevant curvature singularites. 39,43 Moreover, a curvature singularity does not imply geodesic incompleteness.…”

Section: Acknowledgmentsmentioning

confidence: 99%

“…43,58,78 The singularity theorems follow a generic pattern. 58,248 It is assumed that a spacetime of sufficient differentiability satisfies (i) a condition on the curvature; (ii) a causality condition; (iii) an appropriate initial and/or boundary condition. Then there are null or timelike inextensible incomplete geodesics.…”

Section: Acknowledgmentsmentioning

confidence: 99%

Black holes and their horizons in semiclassical and modified theories of gravity

Mann,

Murk,

Terno

2021

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For distant observers black holes are trapped spacetime domains bounded by apparent horizons. We review properties of the near-horizon geometry emphasizing the consequences of two common implicit assumptions of semiclassical physics. The first is a consequence of the cosmic censorship conjecture, namely that curvature scalars are finite at apparent horizons. The second is that horizons form in finite asymptotic time (i.e. according to distant observers), a property implicitly assumed in conventional descriptions of black hole formation and evaporation. Taking these as the only requirements within the semiclassical framework, we find that in spherical symmetry only two classes of dynamic solutions are admissible, both describing evaporating black holes and expanding white holes. We review their properties and present the implications. The null energy condition is violated in the vicinity of the outer and satisfied in the vicinity of the inner apparent/anti-trapping horizon. Apparent and anti-trapping horizons are timelike surfaces of intermediately singular behavior, which is demonstrated in negative energy density firewalls. These and other properties are also present in axially symmetric solutions. Different generalizations of surface gravity to dynamic spacetimes are discordant and do not match the semiclassical results. We conclude by discussing signatures of these models and implications for the identification of observed ultra-compact objects.

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“…To establish singularity theorems that demonstrate the geodesic incompleteness of spacetime, one requires concepts such as Cauchy and trapped surfaces or energy conditions [45,46] (see also the self-contained review [47]). An example of such theorems is:…”

Section: Mathematical Black Holesmentioning

confidence: 99%

“…In a most compelling and convincing manner, Senovilla recently asserts in [45]: Sometimes the Penrose theorem is interpreted as definite proof that black holes form in gravitational collapse. This is incorrect and the actual fact is much more subtle.…”

Section: Mathematical Black Holesmentioning

confidence: 99%

How Much Cosmic Time Does It Take for a Star to Collapse Forming a Black Hole?

Haro

2024

Preprint

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The concept of a black hole is examined through a historical lens, emphasizing the distinctions between its mathematical definition and the observed phenomena in the cosmos. An essential point of contention is highlighted, the challenge of reconciling the ultimate state of gravitational collapse, conceptualized as a black hole with its associated future event horizon, with the vast age of the universe as measured in cosmic time. The work delves into the evolution of black hole theories, tracing their development from the early mathematical solutions, such as the Schwarzschild solution, to the contemporary understanding shaped by contributions from Hawking and Penrose. The complex interplay between mathematical descriptions and observational realities is explored, shedding light on the difficulties inherent in merging theoretical concepts with astrophysical observations. A particular focus is placed on the discrepancy between the theoretical formation of a black hole and the seemingly infinite cosmic time required for the collapse process according to the seminal work of Oppenheimer and Snyder. This apparent incongruity raises questions about the nature of objects labeled as black holes in astrophysics and prompts a critical examination of how observational data align with theoretical predictions. In essence, this exploration underscores the need for a nuanced and critical analysis of the concept of black holes, considering the intricate interplay between theoretical constructs and empirical observations within the framework of General Relativity.

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A critical appraisal of the singularity theorems

Cited by 3 publications

References 51 publications

Application of the Raychaudhuri Equation in Gravitational Systems

Application of the Raychaudhuri Equation in Gravitational Systems

Black holes and their horizons in semiclassical and modified theories of gravity

How Much Cosmic Time Does It Take for a Star to Collapse Forming a Black Hole?

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