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Black holes and bits: A simple path to Bekenstein-Hawking entropy

Jorge Pinochet

Abstract

In the early 1970s, Jacob Bekenstein discovered that black holes have entropy, which became one of the greatest scientific revolutions of the second half of the 20th century. The objective of this paper is to present a simple derivation -- partly heuristic and partly geometric -- of the equation for the entropy of a black hole, which we now know as the Bekenstein-Hawking entropy. We will also briefly explore the physical implications of this equation and its relationship to the work of Stephen Hawking.

Black holes and bits: A simple path to Bekenstein-Hawking entropy

Abstract

In the early 1970s, Jacob Bekenstein discovered that black holes have entropy, which became one of the greatest scientific revolutions of the second half of the 20th century. The objective of this paper is to present a simple derivation -- partly heuristic and partly geometric -- of the equation for the entropy of a black hole, which we now know as the Bekenstein-Hawking entropy. We will also briefly explore the physical implications of this equation and its relationship to the work of Stephen Hawking.
Paper Structure (4 sections, 8 equations, 3 figures)

This paper contains 4 sections, 8 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Bekenstein-Hawking Entropy
  3. Hawking Temperature and Bekenstein-Hawking Entropy
  4. Concluding remarks

Figures (3)

  • Figure 1: Internal structure of a Schwarzschild black hole.
  • Figure 2: The event horizon can be imagined as a spherical surface of total area $A$ composed of a large number of elementary cells of area $l_{P}^{2}$, each one of which stores a bit of information (0 or 1).
  • Figure 3: Hawking radiation causes the black hole to evaporate. A distant observer detects this radiation as thermal emission with a temperature $T_{H}$.