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Using thermodynamics to learn gravitational wave physics

Caio César Rodrigues Evangelista, Níckolas de Aguiar Alves

Abstract

Black holes are some of the most interesting objects in the universe. While they first arise in the complicated behavior of general relativity, the physical laws ruling their behavior are surprisingly simple. For example, one of the core facts about black holes is that their area never decreases, much alike the entropy in thermodynamics. In this note directed at introductory physics students and their instructors, we use this similarity to understand properties of black hole physics using standard techniques from an undergraduate course in thermal physics. We explore the never-decreasing nature of black hole area to obtain bounds on the energy emitted in a black hole merger (a calculation originally done by Hawking). We show how this allows us to think of black holes in manners very similar to heat engines, and how these ideas have been used in modern gravitational wave observatories to test general relativity. This allows a research-level topic to be discussed in introductory physics lectures.

Using thermodynamics to learn gravitational wave physics

Abstract

Black holes are some of the most interesting objects in the universe. While they first arise in the complicated behavior of general relativity, the physical laws ruling their behavior are surprisingly simple. For example, one of the core facts about black holes is that their area never decreases, much alike the entropy in thermodynamics. In this note directed at introductory physics students and their instructors, we use this similarity to understand properties of black hole physics using standard techniques from an undergraduate course in thermal physics. We explore the never-decreasing nature of black hole area to obtain bounds on the energy emitted in a black hole merger (a calculation originally done by Hawking). We show how this allows us to think of black holes in manners very similar to heat engines, and how these ideas have been used in modern gravitational wave observatories to test general relativity. This allows a research-level topic to be discussed in introductory physics lectures.
Paper Structure (9 sections, 20 equations, 3 figures)

This paper contains 9 sections, 20 equations, 3 figures.

Table of Contents

  1. Introduction
  2. What Is a Black Hole?
  3. Hawking's Area Theorem
  4. Merging Black Holes
  5. Limiting Cases
  6. Vanishing spins
  7. Equal aligned spins
  8. Equal antialigned spins
  9. Discussion

Figures (3)

  • Figure 1: Two black holes spinning around the line that connects them. Their spins can be aligned (as in the left panel) or antialigned (as in the right panel). In this setup, the black holes cannot orbit each other, and may only collide head-on. From a theoretical perspective, this is an interesting scenario because the gravitational waves will not carry away angular momentum, which will simplify our calculations.
  • Figure 2: Allowed efficiency $\eta$ for emission of gravitational waves for a merger of two spinless black holes into a new spinless black hole. The parameter $\delta$---see Eq. \ref{['eq: delta']}---measures the difference between the masses of the two black holes. Notice more energy can be emitted when the two black holes have similar masses.
  • Figure 3: Allowed efficiency $\eta$ for emission of gravitational waves for a merger of two Kerr black holes with equal masses and equal antialigned spins. $\chi$ is the magnitude of the dimensionless spin of either one of the black holes. Notice more energy can be emitted when the two black holes rapidly spin in opposite directions.