#### Stephen Hawking (University of Cambridge Professor) – Quantum Black Holes | Oxford Mathematics (Jul 2020)

#### Chapters

#### Abstract

Unraveling the Mysteries of Black Holes: A Journey Through Gravitational Waves, Entropy, and the Information Paradox

The revolutionary detection of gravitational waves by LIGO heralded a new era in astrophysics, offering profound insights into the enigmatic world of black holes. This discovery not only substantiates Einstein’s theories of strong field gravity but also opens a gateway to testing fundamental black hole properties, such as mass, spin, and horizon area. Intriguingly, it intertwines black hole entropy with the laws of thermodynamics, notably the second law which postulates the inexorable increase of entropy. This intersection of black hole properties and thermodynamics culminates in a paradox that challenges our understanding of information loss and quantum mechanics, a paradox that Stephen Hawking’s groundbreaking theories on black hole radiation and information retention seek to resolve.

I. LIGO’s Breakthrough and Einstein’s Validation

The first detection of gravitational waves by LIGO marks an epochal moment in gravitational wave astronomy. This groundbreaking observation is not only a testament to Einstein’s gravitational theories but also a milestone that allows for the empirical testing of black hole characteristics. The analysis of these waves provides unprecedented data on black holes, particularly regarding their mass, spin, and event horizon properties. Furthermore, these detections open up the possibility of testing the Kerr solution and the no-hair theorem by analyzing the final stages of black hole formation.

II. The Thermodynamics of Black Holes

The discovery that black hole entropy is analogous to thermodynamic entropy represents a significant conceptual leap. Stephen Hawking and Brandon Carter’s work, showing a relationship between a black hole’s mass change and the area change of its event horizon, draws parallels to basic thermodynamic principles. Jacob Bekenstein’s suggestion that a black hole’s event horizon area is akin to its entropy further cements this analogy, contributing to our understanding of black hole properties, including their eventual state of information loss. Analogy to thermodynamics is more striking when one considers that the surface gravity of a black hole, a measure of its gravitational field strength, is analogous to temperature and uniform across the event horizon, just like temperature in thermal equilibrium.

III. The Information Loss Paradox

The paradox of information loss in black holes arises from the concept that they possess finite entropy proportional to their event horizon area, suggesting a finite temperature and the possibility of equilibrium with thermal radiation. This idea, seemingly contradicting the classical view that black holes cannot emit anything, presents a significant challenge to the established laws of physics. It is also connected to the concept of entropy and the second law of thermodynamics. According to the second law, entropy always increases. However, black hole formation seems to contradict this law, as information about the matter that collapsed to form the black hole appears to be lost. This raises questions about whether information is truly lost or whether there is a mechanism by which it can be recovered.

IV. Hawking’s Pioneering Discovery

Stephen Hawking’s seminal discovery that black holes emit radiation, known as Hawking radiation, was a turning point. It suggested that black holes, contrary to previous beliefs, could emit particles, thus preserving the laws of thermodynamics. This finding, initially met with skepticism, has been corroborated through various approaches, reinforcing our understanding of black hole radiation as a physical reality. Hawking’s discovery implies a finite black hole temperature, contradicting classical concepts that prohibit the emission of thermal radiation from a black hole.

V. Quantum Mechanics and Black Hole Radiation

The concept of virtual particle pairs in quantum mechanics, and how they interact with black holes, plays a crucial role in understanding Hawking radiation. When one particle of a pair is captured by a black hole, the other can escape, manifesting as radiation. This phenomenon offers insight into how black holes might lose mass over time and eventually evaporate.

VI. The Challenge to Scientific Determinism

Stephen Hawking’s exploration of information loss in black holes presents a fundamental challenge to the principle of scientific determinism. The apparent randomness of particles emitted from black holes raises questions about the predictability of the universe and the deterministic nature of quantum mechanics. Hawking and his colleagues developed a theory based on super rotation charges to explain how information is regained from black holes. They suggest that the quantum state of the negative energy particle falling into the black hole can be known, enabling the determination of the full quantum state and the outgoing radiation’s pure state.

VII. Resolving the Information Paradox

Hawking’s later work proposes that information is not lost in black holes but is instead encoded on the horizon. This concept of supertranslations and superrotations on the horizon challenges traditional notions about black holes and opens up new theoretical pathways in physics. Furthermore, Hawking’s research on the emission of gravitational radiation from black holes and the possible existence of naked singularities when black holes disappear further complicates the picture. In addition, Penrose’s strong cosmic censorship conjecture suggests that spacetime is causally convex, although its applicability in these situations remains unclear.

VIII. Rethinking Black Holes

Hawking concludes that black holes, once thought to be inescapable and information-destroying entities, might hold the keys to understanding the universe’s deepest secrets. His theories suggest that not only is information retained in black holes, but there may also be mechanisms to escape them, potentially leading to other universes. In the context of scientific determinism, Hawking explores how the apparent randomness of particles emitted from black holes challenges the principle of causality and questions the predictability of the universe’s evolution.

In summary, the journey from LIGO’s initial detection to Hawking’s theories on black hole radiation and information retention paints a captivating picture of modern astrophysics. It intertwines the rigors of empirical observation with the elegance of theoretical physics, continually challenging and expanding our understanding of the cosmos.

Notes by: Alkaid