Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Entanglement Entropy for the Black 0-Brane

Angshuman Choudhury, Davide Laurenzano

TL;DR

This work investigates entanglement between a BFSS Black Hole (a bound state of $N$ D0-branes) and its Hawking radiation within the Matrix Theory dual. By constructing a Hilbert-space framework that factorizes into partially evaporated Black Hole and radiation sectors, it derives the radiation density matrix and the von Neumann entropy $S(t)$, showing it follows a Page curve and that information is recovered after complete evaporation. The analysis combines a microscopic Hilbert-space decomposition with a quantitative emission-time model based on the radial coordinate distribution, introducing a geometric parameter $a$ that modulates the entropy profile. The results support a unitary evaporation picture in the BFSS/Matrix Theory context and link BH geometry to the entanglement dynamics, offering a concrete gauge/gravity realization of information recovery in quantum gravity.

Abstract

We analyse the entanglement entropy between the Black 0-Brane solution to supergravity and its Hawking radiation. The Black 0-Brane admits a dual Gauge theory description in terms of the Matrix model for M-Theory, named BFSS theory, which is the theory of open strings on a collection of N D0-branes. Recent studies of the model have highlighted a mechanism of Black Hole evaporation for this system, based on the chaotic nature of the theory and the existence of flat directions. This paper further explores this idea, through the computation of the von Neumann entropy of Hawking radiation. In particular, we show that the expected Page curve is indeed reproduced, consistently with a complete recovery of information after the Black Hole has fully evaporated. A pivotal step in the computation is the definition of a Hilbert space which allows for a quantum mechanical description of partially evaporated Black Holes. We find that the entanglement entropy depends on the choice of a parameter, which can be interpreted as summarizing the geometric features of the Black Hole, such as the size of the resolved singularity and the size of the horizon.

Entanglement Entropy for the Black 0-Brane

TL;DR

This work investigates entanglement between a BFSS Black Hole (a bound state of D0-branes) and its Hawking radiation within the Matrix Theory dual. By constructing a Hilbert-space framework that factorizes into partially evaporated Black Hole and radiation sectors, it derives the radiation density matrix and the von Neumann entropy , showing it follows a Page curve and that information is recovered after complete evaporation. The analysis combines a microscopic Hilbert-space decomposition with a quantitative emission-time model based on the radial coordinate distribution, introducing a geometric parameter that modulates the entropy profile. The results support a unitary evaporation picture in the BFSS/Matrix Theory context and link BH geometry to the entanglement dynamics, offering a concrete gauge/gravity realization of information recovery in quantum gravity.

Abstract

We analyse the entanglement entropy between the Black 0-Brane solution to supergravity and its Hawking radiation. The Black 0-Brane admits a dual Gauge theory description in terms of the Matrix model for M-Theory, named BFSS theory, which is the theory of open strings on a collection of N D0-branes. Recent studies of the model have highlighted a mechanism of Black Hole evaporation for this system, based on the chaotic nature of the theory and the existence of flat directions. This paper further explores this idea, through the computation of the von Neumann entropy of Hawking radiation. In particular, we show that the expected Page curve is indeed reproduced, consistently with a complete recovery of information after the Black Hole has fully evaporated. A pivotal step in the computation is the definition of a Hilbert space which allows for a quantum mechanical description of partially evaporated Black Holes. We find that the entanglement entropy depends on the choice of a parameter, which can be interpreted as summarizing the geometric features of the Black Hole, such as the size of the resolved singularity and the size of the horizon.
Paper Structure (9 sections, 54 equations, 4 figures)

This paper contains 9 sections, 54 equations, 4 figures.

Table of Contents

  1. Introduction
  2. A Mechanism for BFSS Black Hole Evaporation
  3. Black Hole Formation
  4. Black Hole Evaporation
  5. Quantized System Description
  6. Page Curve for the BFSS Black Hole
  7. A Quantitative Estimate of the Emission Time
  8. Conclusion and Outlook
  9. Normalization factor for Probabilities

Figures (4)

  • Figure 1: Entanglement entropy for the radiation as a function of time.
  • Figure 2: Purity of the radiation density matrix as a function of time.
  • Figure 3: Refined entropy vs time graph for a 4 D0-brane BH. Equation (\ref{['eq:EmissionTime2']}) is the mean emission time with $a=1, 1.5, 2, 2.5$ and is compared with the curve when considering equation (\ref{['eq:EmissionTime1']}) as the mean emission time.
  • Figure 4: Refined entropy vs time graph. The plot shows entropy graphs obtained by considering equation (\ref{['eq:EmissionTime2']}) as the mean emission time equation with $a=2$ and $N=2, 4, 6$.