Reflections on a Life in Physics:
At the age of 20, Hawking arrived at Cambridge with the intention of studying cosmology under Fred Hoyle, but was assigned to Dennis Sharma due to Hoyle’s full capacity. His initial work focused on astrophysics, but Hawking pursued his passion for cosmology despite not initially connecting with the subject.

A Life-Changing Diagnosis:
Hawking experiences a decline in his physical abilities, leading to a diagnosis of a serious condition that was never explicitly revealed to him. Despite the uncertainty surrounding his health, Hawking remained determined to complete his PhD and found motivation in the support of his father and the love of Jane, whom he later married.

The Question of a Beginning:
In the 1960s, the field of cosmology grappled with the question of whether the universe had a beginning. Two alternative theories emerged: the steady-state theory, which proposed a continuously expanding universe with constant matter creation, and the bouncing universe theory, suggesting a cyclical pattern of contraction and expansion.

Background Microwave Radiation and a Bouncing Universe:
The discovery of a faint background of microwave radiation in 1964 provided evidence against the steady-state theory, supporting the idea of a hot and dense early state of the universe. Hawking’s research focused on the possibility of a bouncing universe, inspired by the work of Soviet scientists Lifshitz and Kaladnikov.

Penrose’s Approach and Proving Singularities:
Roger Penrose introduced a new approach to studying singularities in general relativity, emphasizing general properties instead of explicitly solving field equations. Using Penrose’s approach, Hawking demonstrated that singularities were inevitable in the expansion of the universe, contradicting Lifshitz and Kaladnikov’s claims. This led to the conclusion that general relativity predicted a beginning for the universe, a significant finding in cosmology.

Black Hole Surface and Event Horizon:
Hawking’s research centered around black hole singularities and event horizons. The event horizon obeys an area theorem, which increases when matter or radiation falls into a black hole. The black hole no-hair theorem states that, once settled, a black hole can be described by mass and angular momentum.

Gravitational Wave Observations:
LIGO’s detection of gravitational waves from black hole mergers allows testing the black hole no-hair theorem. Gravitational wave data can help determine the horizon areas and test the area and no-hair theorems.

Entropy Analogy:
Hawking proposed an analogy between black hole area and thermodynamic entropy. Entropy measures disorder or lack of knowledge about a system’s precise state. Initially, black holes were considered completely black and couldn’t be in thermal equilibrium.

Quantum Particles and Black Holes:
Hawking considered the behavior of quantum particles near black holes, including the possibility of atoms with a primordial black hole nucleus. His studies led to the discovery of black hole radiation, linking the horizon’s area to its entropy.

Imaginary Time and Euclidean Approach:
Combining general relativity with quantum theory involves replacing ordinary time with imaginary time. The Euclidean approach turns time into a fourth spatial dimension, creating a smooth spacetime without singularities. This solved the problem of predictability breakdown due to singularities.

Black Hole Evaporation and Information Paradox:
Hawking’s calculations showed that black holes emit thermal radiation, causing them to shrink and eventually evaporate. The paradox arises from the radiation carrying away information about the black hole, which contradicts quantum mechanics. Current research aims to explain how information is returned from a black hole using super rotation charges.

Hawking’s Renewed Interest in Cosmology:
Stephen Hawking’s focus shifted from black holes to cosmology in the 1970s due to the idea that the early universe underwent inflationary expansion, where its size grew rapidly.

Quantum Effects during Inflation:
In 1982, Hawking proposed that quantum effects during inflation could create the seeds for structures in our universe, similar to the radiation from a black hole horizon.

Nuffield Workshop and Established Picture of Inflation:
Through the Nuffield workshop in Cambridge, Hawking collaborated with other experts in the field and established the present picture of inflation, including density fluctuations that led to galaxy formation.

Precision Science and Satellite Observations:
Hawking’s theories were ahead of experimental evidence, with the discovery of fluctuations in the microwave sky by the Kirby satellite in 1993. Cosmology became a precision science in 2003 with results from the WMAP satellite.

Planck Satellite and Blueprint for Universe Structure:
The Planck satellite provided a detailed map of the cosmic microwave temperature, showing irregularities predicted by inflation. These variations indicate regions with higher density, leading to the formation of galaxies and stars. Hawking emphasized the significance of this map as a blueprint for the universe’s structure.

The Quest for a Singularity-Free Space-Time:
Hawking expressed dissatisfaction with the original inflationary scenario due to its reliance on an initial singularity. He sought a space-time without a singularity, akin to the Euclidean version of a black hole.

The Role of Imaginary Time:
Hawking collaborated with Jim Hartle to apply the Euclidean approach to cosmology. According to this approach, histories in imaginary time can be closed surfaces with no beginning or end.

The No-Boundary Proposal:
Hawking and Hartle introduced the no-boundary proposal, where the boundary condition of the universe is that it has no boundary. This sidestepped the difficulty of time having a beginning by turning it into a direction in space.

Predicting Our Universe:
With colleagues, Hawking set out to calculate the universe’s emergence from the Big Bang using the no-boundary proposal. The proposal predicted that our universe would arise from a burst of inflation, initially smooth with tiny departures leading to the structures we observe.

Verification through Microwave Background:
The irregularities in the observed microwave background align with the predictions of inflation and the no-boundary proposal. However, one crucial prediction remains unverified: a small part of the fluctuations in the microwave radiation should be attributable to gravitational waves generated during the rapid expansion phase.

Hope for Future Experiments:
Ongoing experiments with satellites like Planck and new cosmic microwave experiments offer the potential to provide firm evidence for this primordial signal and further validate the theory.

Stephen Hawking’s popular book, A Brief History of Time:
Written to explain cosmology to a general audience. Unexpectedly successful, conveying the idea of a rational, understandable universe.

Importance of scientific communication:
Stressed the significance of scientists explaining their work, particularly in cosmology.

Future experiments in cosmology:
Mapping the positions of billions of galaxies. Using supercomputers like Cosmos to better understand our place in the universe. Possibility of using gravitational waves to look back to the Big Bang.

Importance of space exploration:
Recent advances in cosmology have been made through space-based observations. Continued space exploration is essential for humanity’s future and survival.

Personal reflections on black holes and the universe:
Hawking expressed gratitude for living in a time of theoretical physics advancements. His contributions to the field, however small, brought him joy. He marveled at humans’ ability to comprehend the laws governing the universe.

Encouragement to look up and stay curious:
Urged the audience to observe the stars and contemplate the universe’s existence. Curiosity and perseverance are key to overcoming life’s difficulties.