Time evolution of the inside of the black hole’s horizon

Abstract

We consider the Wheeler–DeWitt equation near the horizon of the black hole where the entangled vacuum state is chosen as the static universe state. Then, using the entangled property of the vacuum state, we investigate the dynamical evolution of the subsystems, namely inside and outside of the horizon

Quantum time in near-horizon zone of black hole

“…In this section, we consider the near horizon of black hole and frozen vacuum of it and then apply the PaW mechanism through the von Neumann prescription for near horizon vicinity. We review our previous paper [27] which is a straightforward modification of PaW mechanism of previous section in a particular region. It is important to note that in PaW approach one can consider time quantum degree of freedom as an abstract purification space without any physical relevance.…”

“…to obtain the time evolution of the inside of black hole. For more details and timeless picture of wheeler-DeWitt equation refer to [27].…”

“…In other words whatever happen near horizon, the vacuum there is a frozen vacuum (10). For more information about this behavior refer to [27,28].…”

“…In this investigation the review of PaW approach is done for near-horizon zone of black hole which is a straightforward modification of PaW mechanism for near-horizon zone which has been done by authors [27]. In addition some of the criticisms of this mechanism are reconsidered in this particular vicinity of black hole.…”

“…Now suppose Alice an in-falling observer is falling into the black hole. If she knows the Hawking radiation states R B and without meeting Bob she is aware of the interior states A by ER = EP R correspondence which asserts that the interior states A are a map of early Hawking radiation R B (A = R B donkey map)[27,29]. On the other hand, Alice is aware of exterior states B by her knowledge of black hole which claims that the exterior states B are purified by interior A.…”