Abstract
Flat-space cosmologies (FSC) are solutions to three dimensional theories of gravity without cosmological constant that have cosmological horizons. A detector located near the time-like singularity of the spacetime can absorb Hawking modes that are created near the horizon. Continuation of this process will eventually cause the entropy of the radiation to be larger than the entropy of the FSC, which leads to the information paradox. In this paper, we resolve this paradox for the FSC using the island proposal. To do this, we couple an auxiliary flat bath system to this spacetime in timelike singularity so that Hawking modes are allowed to enter the bath and the entropy of radiation can be measured in its asymptotic region where gravity is also weak. We show that adding island regions that receive the partners of Hawking modes cause the entropy of radiation to follow a Page curve which leads to resolving the information paradox. Moreover, we design a quantum teleportation protocol by which one can extract the information residing in islands.
Highlights
Einstein gravity without cosmological constants in three dimensions has been considered with more interest
The event horizons for these asymptotically flat spacetimes are cosmological horizons, they are called flat-space cosmologies (FSCs). These spacetimes can be locally converted to Minkowski spacetime, and their relationship to Minkowski spacetime is similar to what Banados-Teitelboim-Zanelli (BTZ) black holes have to the anti–de Sitter (AdS) spacetimes
The FSCs can be obtained from the BTZ black hole by taking the flat-space limit, which makes a large number of its properties proven from the asymptomatic AdS case using the flat-space limit
Summary
Einstein gravity without cosmological constants in three dimensions has been considered with more interest. By this addition, the state of Hawking mode and its partner is purified to a Bell state, the increasing of entanglement entropy of radiation is stopped and information paradox is resolved The boundary of these new regions are located either inside or outside the horizon and are called quantum extremal surfaces (QES) since they are minimum of the following generalized entropy functional for the radiation [13,14], SRad 1⁄4 Min. The Area refers to the area of codimension 2 boundary surface of island, ∂I, and SvN1⁄2R ∪ I is the von Neumann entropy of the quantum state of combined radiation and island systems computed in the effective semiclassical theory. The last section, IV, is devoted to the conclusion and future directions
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