The process of gravitational collapse excites the fields propagating in the background geometry and gives rise to thermal radiation. We demonstrate by explicit calculations that the density matrix corresponding to such radiation actually describes a pure state. While Hawking's leading order density matrix contains only the diagonal terms, we calculate the off-diagonal correlation terms. These correlations start very small, but then grow in time. The cumulative effect is that the correlations become comparable to the leading order terms and significantly modify the density matrix. While the trace of the Hawking's density matrix squared decreases during the evolution, the trace of the total density matrix squared remains unity at all times and all frequencies. This implies that the process of radiation from a collapsing object is unitary.Introduction. One of the most pressing problems in modern physics is the information loss paradox in black hole physics. Since Hawking radiation is purely thermal [1], it is possible to convert a pure state into a mixed state, which is forbidden in unitary quantum mechanics [2]. It was often argued that subtle correlations between the emitted Hawking quanta which are usually neglected could be enough to recover information about the initial state and convert an apparently maximally mixed thermal state into a pure state [3,4]. This point of view was also often criticized by noticing that small corrections to the leading order Hawking terms are not enough to recover unitarity [5]. Most of this discussion is given for the case of radiation from the pre-existing black hole, or in the limit when the horizon is already formed in infinite future. The purpose of this paper is to address this problem from a point of view of an asymptotic observer who is observing a time-dependent gravitational collapse. We find indeed that the process of gravitational collapse and subsequent evaporation is manifestly unitary as described in the foliation of an asymptotic observer.
We study time-dependant Hawking-like radiation as seen by an infalling observer during gravitational collapse of a thin shell. We calculate the occupation number of particles whose frequencies are measured in the proper time of an infalling observer in Eddington-Finkelstein coordinates. We solve the equations for the whole process from the beginning of the collapse till the moment when the collapsing shell reaches zero radius. The radiation distribution is not thermal in the whole frequency regime, but it is approximately thermal for the wavelengths of the order of the Schwarzschild radius of the collapsing shell. After the Schwarzschild radius is crossed, the temperature increases without limits as the singularity is approached. We also calculate the density matrix associated with this radiation. It turns out that the off-diagonal correlation terms to the diagonal Hawking's leading order terms are very important. While the trace of the diagonal (Hawking's) density matrix squared decreases during the evolution, the trace of the total density matrix squared remains unity at all times and all frequencies.
We study the end stages of gravitational collapse of the thin shell of matter in ingoing Eddington-Finkelstein coordinates. We use the functional Schrodinger formalism to capture quantum effects in the near singularity limit. We find that that the equations of motion which govern the behavior of the collapsing shell near the classical singularity become strongly non-local. This reinforces previous arguments that quantum gravity in the strong field regime might be non-local. We managed to solve the non-local equation of motion for the dust shell case, and found an explicit form of the wavefunction describing the collapsing shell. This wavefunction and the corresponding probability density are non-singular at the origin, thus indicating that quantization should be able to rid gravity of singularities, just as it was the case with the singular Coulomb potential.
In this paper, we study the collapse of a massive shell in 2 þ 1 and 3 þ 1 dimensional gravity with antide Sitter asymptotics. Using the Gauss-Codazzi method, we derive gravitational equations of motion of the shell. We then use the functional Schrödinger formalism to calculate the spectrum of particles produced during the collapse. At the late time, radiation agrees very well with the standard Hawking results. In 3 þ 1 dimensions, we reproduce the Hawking-Page transition. We then construct the density matrix of this collapsing system and analyze the information content in the emitted radiation. We find that the offdiagonal elements of the density matrix are very important in preserving the unitarity of the system.
Drug resistance is a significant obstacle to successful and durable anti-cancer therapy. Targeted therapy is often effective during early phases of treatment; however, eventually cancer cells adapt and transition to drug-resistant cells states rendering the treatment ineffective. It is proposed that cell state can be a determinant of drug efficacy and manipulated to affect the development of anticancer drug resistance. In this work, we developed two stochastic cell state models and an integrated stochastic-deterministic model referenced to brain tumors. The stochastic cell state models included transcriptionally-permissive and -restrictive states based on the underlying hypothesis that epigenetic instability mitigates lock-in of drug-resistant states. When moderate epigenetic instability was implemented the drug-resistant cell populations were reduced, on average, by 60%, whereas a high level of epigenetic disruption reduced them by about 90%. The stochastic-deterministic model utilized the stochastic cell state model to drive the dynamics of the DNA repair enzyme, methylguanine-methyltransferase (MGMT), that repairs temozolomide (TMZ)-induced O6-methylguanine (O6mG) adducts. In the presence of epigenetic instability, the production of MGMT decreased that coincided with an increase of O6mG adducts following a multiple-dose regimen of TMZ. Generation of epigenetic instability via epigenetic modifier therapy could be a viable strategy to mitigate anticancer drug resistance.
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