Scalar field entanglement entropy of a Schwarzschild black hole from the Schmidt decomposition viewpoint

Abstract

Scalar field entropy generated with the black hole horizon is considered in the light of the Schmidt decomposition to internal and external states of the field. Within the frame of this approach, the unitary character of the black hole evolution appears to be natural. We estimated the ratio of radiation field entropy to the Bekenstein–Hawking entropy, which has appeared to be small; in the zeroth order the ratio is constant. The obtained corrections to the massive radiation component are found to have both negative and positive values, hence witnessing the possibility of the information outflow from the black holes.

Scalar field entanglement entropy for a small Schwarzschild black hole

“…This paper complements [15] where the case M > 1 was considered. It is based on the similar principles.…”

“…The situation is complicated with the exact entropy dependence on N. In [15] the dependence on N had been neglected because of the large BH mass, but here we can not do the same trick.…”

Relativistic quantum information and time machines

“…It is the correlations between the two which reveal the secret information. It is in this way that information lost in the form of Hawking radiation may be recovered in the entanglement which exists in the field [51,60,61]. However others argue that not all the information can be accounted for by the correlations [52].…”

Towards experimentally testing the paradox of black hole information loss

“…In this scenario, information is lost as a black hole evaporates, inconsistent with the unitarity of quantum mechanics, which thus presents a serious obstacle for developing theories of quantum gravity. Many solutions aimed at reconciling a thermal Hawking radiation spectrum with unitarity were discussed [8][9][10][11][12][13], none is capable of successfully ending the dispute. As was pointed out by Wilczek and his collaborators [14,15], the thermal spectrum is due to the neglect of back reaction from emitted radiation in Hawking's original treatment.…”