Author(s):
(1) Gopal Yadav, Department of Physics, Indian Institute of Technology & Chennai Mathematical Institute. Table of Links Abstract & Introduction Brief Review of Wedge Holography Emerging Multiverse from Wedge Holography Application to Information Paradox Application to Grandfather Paradox Conclusion Acknowledgements and References 6 Conclusion In this work, we propose the existence of a multiverse in the Karch-Randall braneworld using the idea of wedge holography. Multiverse is described in the sense that if we talk about 2n universes, then those will be represented by Karch-Randall branes embedded in the bulk. These branes will contain black holes or not that can be controlled by gravitational action. We studied three cases: • We constructed mutiverse from d-dimensional Karch-Randall branes embedded in AdSd+1 in section 3.1. The geometry of these branes is AdSd. In this case, the multiverse consists of 2n anti de-Sitter branes and all are connected to each other at the defect via transparent boundary conditions. Multiverse consists of AdS branes exists forever once created. • We constructed multiverse from d-dimensional de-Sitter spaces on Karch-Randall branes embedded in (d + 1)-dimensional bulk AdSd+1 in 3.2. Multiverse made up of 2n de-Sitter branes has a short lifetime. All the de-Sitter branes in this setup should be created and annihilated at the same time. Defect CFT is a non-unitary conformal field theory becauseof dS/CFT correspondence. • We also discussed why it is not possible to describe multiverse as a mixture of d-dimensional de-Sitter and anti de-Sitter spacetimes in the same bulk in section 3.3. We can have the multiverse with anti de-Sitter branes (M1) or de-Sitter branes (M2) but not the mixture of the two. Because AdS branes intersect at “time-like” boundary and de-Sitter branes intersect at “space-like” boundary of the bulk AdSd+1. Universes in M1 can communicate with each other, similarly, M2 consists of communicating de-Sitter branes but M1 can’t communicate with M2 As a consistency check of the proposal, we calculated the Page curves of two black holes for n = 2 multiverse. We assumed that black hole and bath systems between −2ρ ≤ r ≤ 2ρ and −ρ ≤ r ≤ ρ. In this case, we found that entanglement entropy contribution from the Hartman-Maldacena surfaces has a linear dependence on time for the AdS and Schwarzschild black holes and it is zero for the de-Sitter black hole, whereas island surfaces contributions are constant. Therefore this reproduces the Page curve. Using this idea, we obtain the Page curve of Schwarzschild de-Sitter black hole and one can also do the same for Reissner-Nordström deSitter black hole. This proposal is helpful in the computation of the Page curve of black holes with multiple horizons from wedge holography. We also discussed the possibility of getting a Page curve of these black holes using two Karch-Randall branes, one as a black hole and the other as a bath. In this case, there will be an issue in defining the island surface and identifying what kind of radiation we are getting. For example, when a Karch-Randall brane consists of black hole and cosmological event horizons, i.e., Schwarzschild de-Sitter black hole on the brane, the observer collecting the radiation will not be able to identify clearly whether it is Hawking radiation or Gibbons-Hawking radiation. We checked our proposal for very simple examples without DGP term on the Karch-Randall branes, but one can also talk about massless gravity by adding the DGP term on the KarchRandall branes [35]. In this case, tensions of the branes will recieve correction from the extra term in (11). Further, we argued that one could resolve the “grandfather paradox” using this setup where all universes communicate via transparent boundary conditions at the interface point. To avoid the paradox, one can travel to another universe where his grandfather is not living, so he can’t kill his grandfather. We have given a qualitative idea to resolve the “grandfather paradox” but detailed analysis requires more research in this direction using wedge holography. This paper is available on arxiv under CC 4.0 license. Author(s): (1) Gopal Yadav, Department of Physics, Indian Institute of Technology & Chennai Mathematical Institute. Author(s): Author(s): (1) Gopal Yadav, Department of Physics, Indian Institute of Technology & Chennai Mathematical Institute. Table of Links Abstract & Introduction Abstract & Introduction Brief Review of Wedge Holography Brief Review of Wedge Holography Emerging Multiverse from Wedge Holography Emerging Multiverse from Wedge Holography Application to Information Paradox Application to Information Paradox Application to Grandfather Paradox Application to Grandfather Paradox Conclusion Conclusion Acknowledgements and References Acknowledgements and References 6 Conclusion In this work, we propose the existence of a multiverse in the Karch-Randall braneworld using the idea of wedge holography. Multiverse is described in the sense that if we talk about 2n universes, then those will be represented by Karch-Randall branes embedded in the bulk. These branes will contain black holes or not that can be controlled by gravitational action. We studied three cases: • We constructed mutiverse from d-dimensional Karch-Randall branes embedded in AdSd+1 in section 3.1. The geometry of these branes is AdSd. In this case, the multiverse consists of 2n anti de-Sitter branes and all are connected to each other at the defect via transparent boundary conditions. Multiverse consists of AdS branes exists forever once created. • We constructed multiverse from d-dimensional de-Sitter spaces on Karch-Randall branes embedded in (d + 1)-dimensional bulk AdSd+1 in 3.2. Multiverse made up of 2n de-Sitter branes has a short lifetime. All the de-Sitter branes in this setup should be created and annihilated at the same time. Defect CFT is a non-unitary conformal field theory becauseof dS/CFT correspondence. • We also discussed why it is not possible to describe multiverse as a mixture of d-dimensional de-Sitter and anti de-Sitter spacetimes in the same bulk in section 3.3. We can have the multiverse with anti de-Sitter branes (M1) or de-Sitter branes (M2) but not the mixture of the two. Because AdS branes intersect at “time-like” boundary and de-Sitter branes intersect at “space-like” boundary of the bulk AdSd+1. Universes in M1 can communicate with each other, similarly, M2 consists of communicating de-Sitter branes but M1 can’t communicate with M2 As a consistency check of the proposal, we calculated the Page curves of two black holes for n = 2 multiverse. We assumed that black hole and bath systems between −2ρ ≤ r ≤ 2ρ and −ρ ≤ r ≤ ρ. In this case, we found that entanglement entropy contribution from the Hartman-Maldacena surfaces has a linear dependence on time for the AdS and Schwarzschild black holes and it is zero for the de-Sitter black hole, whereas island surfaces contributions are constant. Therefore this reproduces the Page curve. Using this idea, we obtain the Page curve of Schwarzschild de-Sitter black hole and one can also do the same for Reissner-Nordström deSitter black hole. This proposal is helpful in the computation of the Page curve of black holes with multiple horizons from wedge holography. We also discussed the possibility of getting a Page curve of these black holes using two Karch-Randall branes, one as a black hole and the other as a bath. In this case, there will be an issue in defining the island surface and identifying what kind of radiation we are getting. For example, when a Karch-Randall brane consists of black hole and cosmological event horizons, i.e., Schwarzschild de-Sitter black hole on the brane, the observer collecting the radiation will not be able to identify clearly whether it is Hawking radiation or Gibbons-Hawking radiation. We checked our proposal for very simple examples without DGP term on the Karch-Randall branes, but one can also talk about massless gravity by adding the DGP term on the KarchRandall branes [35]. In this case, tensions of the branes will recieve correction from the extra term in (11). Further, we argued that one could resolve the “grandfather paradox” using this setup where all universes communicate via transparent boundary conditions at the interface point. To avoid the paradox, one can travel to another universe where his grandfather is not living, so he can’t kill his grandfather. We have given a qualitative idea to resolve the “grandfather paradox” but detailed analysis requires more research in this direction using wedge holography. This paper is available on arxiv under CC 4.0 license. This paper is available on arxiv under CC 4.0 license. available on arxiv

Multiverse in Karch-Randall Braneworld: Acknowledgements and References

Multiverse in Karch-Randall Braneworld: Application to Grandfather Paradox

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