Multiverse in Karch-Randall Braneworld

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

Abstract

In this paper, we propose a model based on wedge holography that can describe the multiverse. In wedge holography, we consider two gravitating baths, one of which has strong gravity and the other one has weak gravity. To describe a multiverse, we consider 2n Karch-Randall branes, and we propose that various d-dimensional universes are localized on these branes. These branes are embedded in (d + 1)-dimensional spacetime. The model is useful in obtaining the Page curve of black holes with multiple horizons and in the resolution of the “grandfather paradox”. We explicitly obtain the Page curves of eternal AdS black holes for n = 2 multiverse and Schwarzschild de-Sitter black hole with two horizons.

1 Introduction

Recently doubly holographic setup has drawn the attention of many researchers to study the information paradox [1]. A version of the resolution of information paradox is to get the Page curve [2]. AdS/CFT conjecture states that bulk gravity is dual to quantum field theory on the AdS boundary [3]. Doubly holographic setup is the extended version where one considers two copies of AdS/BCFT-like systems [4–25]. The idea was started from the Karch-Randall model, where one chop off the AdS boundary by a Karch-Randall brane [26, 27]. Let us discuss three equivalent descriptions of the doubly holographic setup which is being used to obtain the Page curve.

• BCFT is living on d-dimensional boundary of AdS spacetime. BCFT has a (d − 1)-dimensional boundary, known as a defect.

• Gravity on d-dimensional Karch-Randall brane is coupled to BCFT at the defect via transparent boundary condition.

• d-dimensional BCFT has gravity dual which is Einstein gravity on AdSd+1

In this setup, the Karch-Randall brane contains a black hole whose Hawking radiation is collected by BCFT bath. One can define the radiation region on the BCFT bath, and the entanglement entropy of Hawking radiation can be obtained using the semiclassical formula in the second description [28]. The advantage of a doubly holographic setup is that we can compute entanglement entropy very easily using the classical Ryu-Takayanagi formula [29] in the third description. In this kind of setup, there exist two types of extremal surfaces: Hartman-Maldacena surface [30], which starts at the defect, crosses the black hole horizon, and goes to its thermofield double partner; in this process volume of Einstein-Rosen bridge grows. Another extremal surface is the island surface, which starts at BCFT and lands on the Karch-Randall brane. It turns out that initially, the entanglement entropy of the Hartman-Maldacena surface dominates, and after the Page time island surface takes over, and hence one gets the Page curve. The problem with this setup is that gravity becomes massive on the Karch-Randall brane, which is not physical [31–34]. See [5, 23, 35, 36] for computation of Page curve with massless gravity on Karch-Randall brane. Massless gravity on Karch-Randall brane in [35] arises due to the inclusion of the Dvali-Gabadadze-Porrati term [37] on the same. In [23], we explicitly showed that normalizable graviton wave function requires massless graviton. Another reason is that we implemented the Dirichlet boundary condition on the graviton wave function at the black hole horizon that quantized the graviton mass and allowed a massless graviton. Further, the tension of the Karch-Randall brane (in our case it was a fluxed hyper-surface) is inversely proportional to the black hole horizon and we obtained “volcano”-like potential hence one can localize massless gravity on the Karch-Randall brane. Despite massless gravity on the Karch-Randall brane, we had comparable entanglement entropies coming from Hartman-Maldacena and island surfaces. Therefore we obtained the Page curve of an eternal neutral black hole from a top-down approach. In [36], authors imposed Dirichlet boundary conditions on gravitating branes in wedge holography where they obtained the Page curve even in the presence of massless gravity. The existence of islands with massless gravity was present in [5] because of the geometrical construction of the critical Randall-Sundrum II model. Information paradox of flat space black holes was discussed in [38–40] [1] where one defines the subregions on the holographic screen to compute holographic entanglement entropy. The setup in which the bath is also gravitating is known as “wedge holography” [41, 42, 48]. See [43–46] for work on quantum entanglement, complexity, and entanglement negativity in de-Sitter space [2]

In wedge holography, we consider two Karch-Randall branes, Q1 and Q2, of tensions T1 and T2 such that T1 < T2. In this setup, Q2 contains a black hole whose Hawking radiation is collected by Q1. Literature on wedge holography can be found in [47–50].

It is easy to obtain the Page curve for black holes with a single horizon. In this paper, we address the following issues: we construct a multiverse using the idea of wedge holography and use this setup to get the Page curve of black holes with multiple horizons from wedge holography. Multiverse in this paper will be constructed by localizing Einstein’s gravity on various KarchRandall branes. These branes will be embedded into one higher dimension. Further, we propose that it is possible to travel between different universes because all are communicating with each other. We suspect that the “grandfather paradox” can be resolved in this setup.

The paper is organized as follows. In section 2, we briefly review wedge holography. In section 3, we discuss the existence of multiverse in the Karch-Randall braneworld with geometry anti de-Sitter, de-Sitter, and the issues when we mix de-Sitter and anti de-Sitter spacetimes in subsections 3.1, 3.2 and 3.3. In sections 4, we discuss application of the multiverse to information paradox where we have obtained the Page curve of eternal AdS black holes for n = 2 multiverse in 4.1 and Page curve of Schwarzschild de-Sitter black hole in 4.2 via 4.2.1 and 4.2.2. Section 5 is on the application of this model to grandfather paradox. Finally, we discuss our results in section 6.

[1] We thank C. Krishnan for pointing out these interesting papers to us.

[2] We thank S. Choudhury to bring his works to our attention.