Tag Archives: General Relativity

A brief history of space (4/4)

Sequel of the preceding post A Brief History of Space (3/4) : From Descartes to Schwarzschild

Cosmology developed rapidly after the completion of general relativity by Albert Einstein, in 1915. In this theory, the Universe does not reduce to a space and a time which are absolute and separate; it is made up of the union of space and time into a four dimensional geometry, which is curved by the presence of matter.

Albert Einstein (here in 1910) developed the theory of relativity and was awarded the 1921 Nobel prize for physics. Image by © Hulton-Deutsch, Collection/CORBIS

It is in fact the curvature of space-time as a whole which allows one to correctly model gravity, and not only the curvature of space, such as Clifford had hoped. The non-Euclidean character of the Universe appeared from then on not as a strangeness, but on the contrary as a physical necessity for taking account of gravitational effects. The curvature is connected to the density of matter. In 1917, Einstein presented the first relativistic model for the universe. Like Riemann, he wanted a closed universe (one whose volume and circumference were perfectly finite and measurable) without a boundary; he also chose the hypersphere to model the spatial part of the Universe.

Einstein static universe in a space-time diagram.

At any rate, Einstein’s model made the hypothesis of a static Universe, with the radius of the hypersphere remaining invariable over the course of time. In truth, the cosmological solutions of relativity allow complete freedom for one to imagine a space which expands or contracts over the course of time: this was demonstrated by the Russian theorist Alexander Friedmann, between 1922 and 1924.

At the same time, the installment of the large telescope at Mount Wilson, in the United States, allowed for a radical change in the cosmic landscape. In 1924, the observations of Edwin Hubble proved that the nebula NGC 6822 was situated far beyond our galaxy. Very rapidly, Hubble and his collaborators showed that this was the case for all of the spiral nebulae, including our famous neighbor, the Andromeda nebula: these are galaxies in their own right, and the Universe is made up of the ensemble of these galaxies. The “island-universes” already envisaged by Thomas Wright, Kant and Johann Heinrich Lambert were legitimized by experiment, and the physical Universe seemed suddenly to be immensely enlarged, passing from a few thousand to several dozen million light-years at the minimum. Beyond this spatial enlargement, the second major discovery concerned the time evolution of the Universe. In 1925, indications accumulated which tended to lead one to believe that other galaxies were systematically moving away from ours, with speeds which were proportional to their distance. Continue reading

The Warped Science of Interstellar (4/6) : Time dilation and Penrose process

Sequel of the preceding post The Warped Science of Interstellar (3/6)

In november  2014, the Hollywood blockbuster and science-fiction movie Interstellar was released on screens and  much mediatic excitation arose about it.
This is the fourth of a series of 6 posts devoted to the analysis of some of the scientific aspects of the film, adapted from a paper I published last spring in Inference : International Review of Science.


The elasticity of time is a major consequence of relativity theory, according to which time runs differently for two observers with a relative acceleration – or, from the Equivalence Principle, moving in gravitational fields of different intensities. This well-known phenomenon, checked experimentally to high accuracy, is called « time dilation ».

The celebrated "smooth watches" by Salvador Dali are a nice metaphor of time elasticity predicted by Einstein's relativity theory.
The celebrated “smooth watches” by Salvador Dali are a nice metaphor of time elasticity predicted by Einstein’s relativity theory.

Thus, close to the event horizon of a black hole, where the gravitational field is huge, time dilation is also huge, because the clocks will be strongly slowed down compared to farther clocks. This is one of the most stunning elements of the scenario of Interstellar : on the water planet so close to Gargantua, it is claimed that 1 hour in the planet’s reference frame corresponds to 7 years in an observer’s reference frame far from the black hole (for instance on Earth). This corresponds to a time dilation factor of 60,000. Although the time dilation tends to infinity when a clock tends to the event horizon (this is precisely why no signal can leave it to reach any external observer), at first sight a time dilation as large as 60,000 seems impossible for a planet orbiting the black hole on a stable orbit.

As explained by Thorne in his popular book, such a large time dilation was a « non-negotiable » request of the film director, for the needs of the story. Intuitively, even an expert in general relativity would estimate impossible to reconcile an enormous time differential with a planet skimming up the event horizon and safely enduring the correspondingly enormous gravitational forces. However Thorne did a few hours of calculations and came to the conclusion that in fact it was marginally possible (although very unlikely). The key point is the black hole’s spin. A rotating black hole, described by the Kerr metric, behaves rather differently from a static one, described by the Schwarzschild metric. The time dilation equation derived from the Kerr metric takes the form:

1 – (dτ/dt)2 = 2GMr/c2rho2, where rho2 = r2 + (J/Mc)2cos2θ.

Continue reading

My books (1) : Black holes

Until now I published as an author 30 books in my native language (French), including 14 science essays, 7 historical novels  and 9 poetry collections (for the interested reader, visit my French blog  here.
Although my various books have been translated in 14 languages (including Chinese, Korean, Bengali…), only 4 of my essays have been translated in English.

The first one was :

Black Holes

312 pages – Cambridge University Press, 1992 – ISBN 0 521 40029 5 (hardback) – ISBN 0 521 40906 3 (paperback) – Foreword by Joseph Silk.

black-holesBlack holes are the most fascinating discovery of modern astronomy. They have already become legendary, and form the basis of many myths and fantasies. Are they really the monsters of science fiction which devour light and stars? Are they purely hypothetical objects from the theory of relativity or are they an observable reality?
In answering these questions, the author takes us on a fabulous voyage through space and time. He explains how stars are born, light up and die. He takes us into the strange world of supernovae, X-ray stars and quasars. We travel on a journey to the very edge of the universe and to the limits on contemporary physics.
The amount of information conveyed is impressive. The intended audience is readers with some understanding of physics who are seeking a coherent, accurate nonmathematical overview of black-hole physics and all the astronomical situations that the discipline seems to explain. Also, any student embarking on a serious technical study of general relativity or astrophysics will find the book a first-rate overview of an important part of the story. (…) This is an outstanding work of scientific exposition.” — John Barrow, Nature Continue reading

The Rise of Big Bang Models (2) : Static solutions

Sequel of previous post :  From Myth to Science

In this series of posts about the history of relativistic cosmology, I  provide an epistemological analysis of the developments of the field  from 1917 to 2006, based on the seminal articles by Einstein, de Sitter, Friedmann, Lemaître, Hubble, Gamow and other main historical figures of the field. It appears that most of the ingredients of the present-day standard cosmological model, including the accelation of the expansion due to a repulsive dark energy, the interpretation of the cosmological constant as vacuum energy or the possible non-trivial topology of space, had been anticipated by Lemaître, although his papers remain mostly  unquoted.

The History of Relativistic Cosmology can be divided into 6 periods :

– the initial one (1917-1927), during which the first relativistic universe models were derived in the absence of any cosmological clue.

– a period of development (1927-1945), during which the cosmological redshifts were discovered and interpreted in the framework of dynamical Friedmann-Lemaître solutions, whose geometrical and mathematical aspects were investigated in more details.

– a period of consolidation (1945-1965), during which primordial nucleosynthesis of light elements and fossil radiation were predicted.

– a period of acceptation (1965-1980), during which the big bang theory triumphed over the « rival » steady state theory.

– a period of enlargement (1980-1998), when high energy physics and quantum effects were introduced for describing the early universe.

– the present period of high precision experimental cosmology, where the fundamental cosmological parameters are now measured with a precision of a few %, and new problematics arise (nature of the dark energy, topology of the universe, new cosmologies in quantum gravity theories, etc.)

Let us follow chonologically the rather hectic evolution of the ideas in the field. Continue reading