In this post, I want to focus on Roger Penrose, Emeritus Professor of Mathematical Physics at Oxford University, who was awarded half of the approximately $1.1 million prize for proving mathematically that black holes exist and they are fully consistent with Albert Einstein’s theory of gravity, known as general relativity.
The second half was split between Dr. Genzel and Dr. Ghez for their relentless and decades long investigation of monster black hole here in the center of our own galaxy, gathering evidence to convict it of being a supermassive black hole.
Black holes were one of the first and most extreme predictions of Einstein’s General Theory of Relativity, first announced in November 1915. The general theory explains the force we call gravity, as objects try to follow a straight line through a universe whose geometry is warped (curved) by matter and energy. See e.g.
Born in 1931 into an intellectual family, Emeritus Prof. Penrose is a talented mathematician, who also invented a new way of portraying space-time, called a Penrose diagram. This clever invention bypassed most of the mathematical complexities of general relativity, rendering it more accessible to the general reader. See, e.g. the Penrose diagram below for the Schwarzschild solution that yields the black hole:
His diagrams are now the literal lingua franca of cosmology, and ubiquitous in most textbooks. But Penrose's prime achievement - for which he received half the Nobel award in physics - was to prove that if too much mass accumulated in too small a place, collapse into a black hole was inevitable. At the boundary of a black hole, called the event horizon, one would have to go faster than the speed of light to escape. Inside the boundary, time and space would collapse and so all directions would lead downward, to the center or "singularity" where the density became infinite and the laws of physics, as we knew them, would break down.
But first things first. The stroke of genius that started it all appeared as a specific theorem in a January, 1965 paper in Physical Review Letters and entitled: Gravitational Collapse and Space and Time Singularities.
The key, critical component emerged as the Penrose Singularity Theorem:
If the space-time contains a non-compact
Cauchy hypersurface å and a closed, future-trapped surface, and if
the convergence condition holds for null
u u then there are future incomplete null
geodesics
Here a “Cauchy
surface” is basically an instantaneous snapshot that provides good initial
value conditions for the entire space-time. "Null geodesics" refer to paths through space time traversed by massless particles. See also:
http://brane-space.blogspot.com/2014/12/a-look-at-general-relativity-and_27.html
It is precisely the "incomplete geodesics" which pave the way for the existence of singularities and black holes. (A "singularity" in a Lorentzian manifold is actually an incomplete, endless curve). Also involved are ''trapped surfaces'', areas that inevitably shrink over time. These surfaces are formed by the explosion of a star at the end of its life, thus causing its collapse and the subsequent formation of a black hole. At that moment, a gravitational singularity is created where time ceases to exist. (See top graphic for a sketch of a singularity in relation to a black hole).
Shortly after Penrose made his breakthrough calculations, he collaborated with Hawking and used the same methods to prove that if general relativity was right, the universe must have its origin in an instantaneous singularity: the Big Bang.
One Caltech astrophysicist - John Preskill- quoted in a NY Times' piece, said:
“I’m thinking of how much Stephen Hawking would have enjoyed sharing a Prize for advances in General Relativity,”
Maybe. But many believe it was Hawking's emphasis on "quantum black holes" and their "evaporation" (which he claimed could be observed) that derailed that aspiration. Had Hawking instead worked with Penrose on stellar-collapsed cores (as black holes) he might have shared the Nobel. Many technical arguments between Penrose and Hawking on this and related issues can be found in the excellent monograph: 'The Nature Of Space And Time', Princeton University Press, 1996.
In general, black hole identification is predicated upon observing its effects as a member of a binary (double) star system. Thereby, the black hole presence is inferred from x-rays given off when the companion star’s gaseous layers are sucked into it. As those accreting gaseous layers are pulled through the hole's event horizon, they are condensed and the impacting plasma leads to intense heating and x-rays.
The most convincing recent find which puts the question of black holes existence to rest once and for all has been via the Laser Interferometer Gravitational Wave Observatory (LIGO). e.g.
https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.116.061102
The LIGO detection provides the first direct evidence for gravitational waves but also opens the door to using them to study the powerful cosmic events that create them, in this case two colliding black holes. Based on the paper cited in the above link, the two black holes are each roughly 30 times the mass of the Sun. They evidently merged some 1.3 billion light years from Earth. The gravitational waves themselves were generated in the final moments before the black holes merged. The signal was brief but definitive and we on Earth have now received it.
See Also:
http://brane-space.blogspot.com/2020/06/a-new-perspective-on-history-of.html
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