Topological origin of holographic principle: Application to wormholes

Ahmed, Nasr; Rafat, H.

doi:10.1142/s0219887818501311

Cited by 13 publications

(14 citation statements)

References 25 publications

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“…The theory suggests that the entire universe can be seen as twodimensional information on the cosmological horizon. In HP, information (albeit quantum states evolving in spacetime) can be represented as a hologram, explainable via the theory of topological deformation retracts [15]. A deformation retract is a mapping of the boundary of a shape (surface) to its skeleton [16].…”

Section: -Holographic Principle and Topological Mappingsmentioning

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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Section: -Holographic Principle and Topological Mappingsmentioning

confidence: 99%

Topology of Black Holes’ Horizons

Tozzi

Peters

2019

Emerg Sci J

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“…In the current work, our aim is to provide a solid topological base to the space-time expansion through utilizing the extension theorem in topology. While all previous studies related to the theory of retracts have been pure mathematical studies, Ahmed and Rafat have started a series of publications [41,42,43,44] in which some applications of this topological theory in mathematical physics have been suggested for the first time. In [16], it has been suggested that the retraction theory in algebraic topology can provide a topological description of the gravitational collapse process which leads to the formation of space-time singularities.…”

Section: Introductionmentioning

confidence: 99%

A new topological perspective of expanding space-times with applications to cosmology

Ahmed,

Pradhan,

Salama

2021

Preprint

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We discuss the possible role of the Tietze extension theorem in providing a rigorous topological base to the expanding space-time in cosmology. A simple toy model has been introduced to show the analogy between the topological extension from a circle S to the whole space M and the cosmic expansion from a non-zero volume to the whole space-time in nonsingular cosmological models. A topological analogy to the cosmic scale factor function has been suggested, the paper refers to the possible applications of the topological extension in mathematical physics.

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“…Based on the holographic principle in quantum gravity [35], the holographic dark energy model has been constructed in [36]. This model links the dark energy density to the cosmic horizon [37,38] and has been tested through observations [39].…”

Section: Introductionmentioning

confidence: 99%

Ricci–Gauss–Bonnet holographic dark energy in Chern–Simons modified gravity: A flat FLRW quintessence-dominated universe

Ahmed

2019

Mod. Phys. Lett. A

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We discuss the recently suggested Ricci-Gauss-Bonnet holographic dark energy in Chern-Simons modified gravity. We have tested some general forms of the scale factor a(t), and used two physically reasonable forms which have been proved to be consistent with observations. Both solutions predict a sign flipping in the evolution of cosmic pressure which is positive during the early-time deceleration and negative during the late-time acceleration. This sign flipping in the evolution of cosmic pressure helps in explaining the cosmic deceleration-acceleration transition, and it has appeared in other cosmological models in different contexts. However, the current work shows a pressure singularity which needs to be explained. The evolution of the equation of state parameter ω(t) shows the same asymptotic behavior for both solutions indicating a quintessence-dominated universe in the far future. We also note that ω(t) goes to negative values (leaving the decelerating dust-dominated era at ω = 0) at exactly the same time the pressure becomes negative. Again, there is another singularity in the behavior of ω(t) which happens at the same cosmic time of the pressure singularity.

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Topological origin of holographic principle: Application to wormholes

Cited by 13 publications

References 25 publications

Topology of Black Holes’ Horizons

Topology of Black Holes’ Horizons

A new topological perspective of expanding space-times with applications to cosmology

Ricci–Gauss–Bonnet holographic dark energy in Chern–Simons modified gravity: A flat FLRW quintessence-dominated universe

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