[Paper Review] Distinguishing causal time from Minkowski time and a model for the black hole quantum eigenstates

Gerard ’t Hooft|ArXiv.org|Nov 18, 1997

Black Holes and Theoretical Physics2 references3 citations

TL;DR

This paper proposes a distinction between causal time—defined by causal structure in spacetime—and Minkowski time, arguing that black hole complementarity may require a multibranch time structure. It introduces a model for black hole quantum eigenstates using a non-Lorentz-invariant stress-energy tensor, suggesting a dynamical description of black hole states that could resolve information paradox issues.

ABSTRACT

A discussion is presented of the principle of black hole com- plementarity. It is argued that this principle could be viewed as a breakdown of general relativity, or alternatively, as the introduction of a time variable with multiple `sheets' or `branches' A consequence of the theory is that the stress-energy tensor as viewed by an outside observer is not simply the Lorentz-transform of the tensor viewed by an ingoing observer. This can serve as a justification of a new model for the black hole atmosphere, recently re-introduced. It is discussed how such a model may lead to a dynamical description of the black hole quantum states.

Motivation & Objective

• To clarify the conceptual distinction between causal time (based on causal structure) and Minkowski time (flat spacetime time) in quantum gravity.
• To address the black hole information paradox by reinterpreting black hole complementarity as a breakdown of general relativity or a multibranch time structure.
• To develop a dynamical model for black hole quantum eigenstates that avoids standard Lorentz invariance in the stress-energy tensor.
• To provide a theoretical foundation for a non-traditional description of black hole quantum states using causal time.
• To explore how such a model could lead to a consistent quantum description of black hole dynamics and entropy.

Proposed method

• Introduces a time variable with multiple 'sheets' or 'branches' to model causal evolution in black hole spacetimes.
• Analyzes the stress-energy tensor as seen by external versus infalling observers, showing it is not simply Lorentz-transformed.
• Proposes a modified stress-energy tensor that breaks Lorentz invariance in the black hole atmosphere, consistent with complementarity.
• Uses a framework where quantum states are defined on a causal time lattice, not a Minkowski time background.
• Applies the model to the black hole atmosphere, suggesting a discrete, quantum structure for the near-horizon region.
• Relies on principles of black hole complementarity and the idea that information is preserved via non-local correlations across horizons.

Experimental results

Research questions

• RQ1 How can causal time be distinguished from Minkowski time in a quantum gravitational context?
• RQ2 What are the implications of a multibranch time structure for black hole complementarity and information preservation?
• RQ3 How does the stress-energy tensor transform between external and infalling observers in a quantum black hole model?
• RQ4 Can a non-Lorentz-invariant stress-energy tensor provide a consistent description of black hole quantum states?
• RQ5 What dynamical model for black hole eigenstates emerges from this causal time framework?

Key findings

• Causal time, derived from causal structure, is fundamentally different from Minkowski time, especially near black hole horizons.
• The stress-energy tensor as seen by an outside observer is not the Lorentz transform of the one seen by an infalling observer, indicating a breakdown of standard covariance.
• A multibranch time structure can resolve issues in black hole complementarity by allowing non-local quantum correlations across the horizon.
• The model introduces a new description of the black hole atmosphere where quantum states are defined on causal time sheets.
• The framework supports a dynamical, discrete quantum description of black hole states that may preserve information.
• The approach provides a potential resolution to the black hole information paradox by redefining time and observer dependence in quantum gravity.