Information retrieval from black holes

Abstract

It is generally believed that, when matter collapses to form a black hole, the complete information about the initial state of the matter cannot be retrieved by future asymptotic observers, through local measurements. This is contrary to the expectation from a unitary evolution in quantum theory and leads to (a version of) the black hole information paradox. Classically, nothing else, apart from mass, charge and angular momentum is expected to be revealed to such asymptotic observers after the formation of a black hole. Semi-classically, black holes evaporate after their formation through the Hawking radiation. The dominant part of the radiation is expected to be thermal and hence one cannot know anything about the initial data from the resultant radiation. However, there can be sources of distortions which make the radiation non-thermal. Although the distortions are not strong enough to make the evolution unitary, these distortions carry some part of information regarding the in-state. In this work, we show how one can decipher the information about the in-state of the field from these distortions. We show that the distortions of a particular kind -which we call non-vacuum distortions -can be used to fully reconstruct the initial data. The asymptotic observer can do this operationally by measuring certain well-defined observables of the quantum field at late times. We demonstrate that a general class of in-states encode all their information content in the correlation of late time out-going modes. Further, using a 1 + 1 dimensional CGHS model to accommodate back-reaction self-consistently, we show that observers can also infer and track the information content about the initial data, during the course of evaporation, unambiguously. Implications of such information extraction are discussed.

Gravitational collapse and Hawking-like radiation of a shell in AdS spacetime

“…Although Hawking's original calculations were based on a ray-tracing method in the vicinity of the black hole horizon [1,2], the Planckian spectrum of emitted radiation has been derived using other methods as well [3][4][5]. The thermal nature of Hawking radiation gives rise to the so-called information loss paradox and this has led to extensive research on the origin of Hawking radiation [6][7][8].…”

Unruh effect for inertial observers through vacuum correlations

“…We can further choose the boundary conditions for the set of initial states judiciously such that the contribution due to conformal anomaly exactly cancels out in the region of interest leading to a flat spacetime semi-classically, see for instance [29][30][31]. For this judicious choice of family of quantum states [32], the spacetime region x + < x + i remains unaffected by the conformal anomaly term. Therefore the results discussed in this work, use stability of the solution under these class of states.…”

“…A more detailed analysis of conformal anomaly modified evaporating black holes can be found in [5]. Our scheme to deal with such terms will be reported in details elsewhere [33].…”

Dynamic Realization of the Unruh Effect for a Geodesic Observer

“…This is important because as we discussed, in two-dimensional spacetime, the expectation value of the stress energy tensor has a conformal anomaly term which can violate this criterion in general, if this term is not accounted for in the source terms in the RHS. However, there exists a family of such states [27] which take care of the conformal anomaly terms and ensure that the geometry remains flat when the state is a vacuum from this family. Therefore the results discussed in this work, use stability of the solution under these class of states.…”