Bypassing stability conditions and curing logarithmic singularities
By Jörg Frauendiener and Jörg Hennig
Assume you want to model a general relativistic spacetime. Due to the annoying limitations of conventional computers, like finite memory and processing speed, it is tempting to focus on a finite portion of the spacetime. Then, without waiting endlessly, one can obtain an approximate description of this portion. One just has to choose a suitable numerical method and solve the field equations for the metric at some set of grid-points. While this approach is standard, it introduces unpleasant problems. Firstly, the set of equations needs to be complemented with boundary conditions at the outer edges of this finite portion, in order to obtain a complete mathematical problem. This, however, is quite unphysical as usually no information about the actual behaviour at such an artificial boundary is available. Consequently, spurious gravitational radiation enters the numerical domain. Secondly, if one is interested in accurately describing gravitational waves, one should recall that these are only well-defined at infinity. Hence it is desirable to extend the simulation up to infinity.
Jörg Frauendiener and Jörg Hennig trapped at infinity.
Hopefully yes: Measure their Berry phases.
By Blagoje Oblak
Some years ago, at a dinner party, I met a fellow physicist who asked me what I was working on. I told him I was studying asymptotic symmetries — symmetries of space-time seen by observers located far away from all sources of the gravitational field. Remarkably, I said, these symmetries often have a beautiful infinite-dimensional structure and may provide new insights in our understanding of gravity. Somewhat sceptical, he replied: `Well surely this must be in some toy model — some extra dimensions, or postulated particles and fields… There’s no way this is directly relevant to our actual, real world!’ While I could understand his perspective, I also felt a little hurt by his cynicism towards theoretical science, so I was happy to retort: No, asymptotic symmetries do not require anything beyond what has been firmly established by experiment; just take pure general relativity, and their magic reveals itself.
- Blagoje Oblak performing a gravitational experiment in the Mediterranean. Photo credit: Geoffrey Mullier.
By Steven Carlip and Samuel Loomis
Imagine you are given a bucket of points and asked to assemble them into a spacetime. What kind of “glue” would you need?
In causal set theory, the only added ingredient is the set of causal relations, the knowledge of which points are to the past and future of which. In particular, suppose your points were taken at random from a real spacetime, at some typical length scale ℓ. Then on scales large compared to ℓ, the causal diamonds – the sets formed by intersecting the past of one point with the future of another – determine the topology; the causal relations determine the metric up to a scale factor; and the remaining scale factor is just a local volume, which can be obtained by counting points. As the slogan of Rafael Sorkin, the founder of the field, goes, “Order + Number = Geometry.”
Samuel Loomis and Steven Carlip with their causal set.
I-Love-Q Probes of Modied Gravity
By Toral Gupta, Barun Majumder, Kent Yagi, and Nicolás Yunes
Although General Relativity has passed all tests carried out so far with flying colors, probes of the extreme gravity regime, where the gravitational interaction is simultaneously strong, non-linear and highly dynamical, have only recently began. This is timely because attempts to reconcile general relativity with quantum mechanics, be it in the form of string theory or loop quantum gravity, and attempts to explain cosmological observations, be it in the early or late universe, may require modifications to Einstein’s general theory. New electromagnetic telescopes, like the Neutron Star Interior Composition Explorer, and gravitational wave detectors, like advanced LIGO and Virgo, can now provide the first detailed observations of the extreme gravity regime. These new telescopes herald the era of extreme experimental relativity, allowing for new stringent constraints of deviations from Einstein’s theory, or perhaps, if we are lucky, pointing to signals of departures.
Toral Gupta is a graduate student at Indian Institute of Technology Gandhinagar.
Barun Majumder is a research assistant at Wilfrid Laurier University.
Kent Yagi is an assistant professor at University of Virginia.
Nicolás Yunes is an associate professor at Montana State University.
From quantum gravity to early universe cosmology using group field theory condensates
By Marco de Cesare, Daniele Oriti, Andreas Pithis, and Mairi Sakellariadou
“If you can look into the seeds of spacetime,
And say which grain will grow and which will not,
Speak then to me.”
– adapted quote from William Shakespeare’s, Macbeth
When we try to describe the earliest stages of the expansion of our Universe, the current picture of spacetime and its geometry as given by Einstein’s theory of General Relativity (GR) breaks down due to the extreme physical conditions faced at the Big Bang. More specifically, theorems by Hawking and Penrose imply that the cosmos emerged from a spacetime singularity. The existence of a cosmological singularity represents a main obstacle in obtaining a complete and consistent picture of cosmic evolution. However, there are reasons to believe that quantum gravitational effects taking place at the smallest scale could lead to a resolution of such singularities. This would have a huge impact for our understanding of gravity at a microscopic level, and for Cosmology of the very early Universe.
Marco de Cesare is a PhD student at King’s College London, working under the supervision of Mairi Sakellariadou on the cosmological consequences of quantum gravity.
Andreas Pithis is a PhD student at King’s College London, UK. He is a frequent visitor of the MPI for Gravitational Physics and held a visiting graduate fellowship at Perimeter Institute for Theoretical Physics, Canada.
Mairi Sakellariadou is a professor of theoretical physics at King’s College London and a member of the LIGO Scientific Collaboration. She is also Chair of the Gravitational Physics Division of the European Physical Society.
Daniele Oriti is a senior researcher and group leader at the Max Planck Institute for Gravitational Physics (Albert Einstein Institute) in Potsdam.
The road from Dunsink to the exceptional symmetries of M-theory
By Leron Borsten and Alessio Marrani
Our journey starts in the fall of 1843 at the Dunsink Observatory, presiding from its hill-top vantage over the westerly reaches of Dublin City, seat to the then Astronomer Royal Sir William Rowan Hamilton. In the preceding months Hamilton had become preoccupied by the observation that multiplication by a complex phase induces a rotation in the Argand plane, revealing an intimate link between two-dimensional Euclidean geometry and the complex numbers ℂ. Fascinated by this unification of geometry and algebra, Hamilton set about the task of constructing a new number system that would do for three dimensions what the complexes did for two. After a series of trying failures, on October 16th 1843, while walking from the Dunsink Observatory to a meeting of the Royal Irish Academy on Dawson Street, Hamilton surmounted his apparent impasse in a moment of inspired clarity: rotations in three dimensions require a four-dimensional algebra with one real and three imaginary units satisfying the fundamental relations i2 = j2 = k2 = ijk = -1. The quaternions ℍ were thus born. Taken in that instant of epiphany, Hamilton etched his now famous equations onto the underside of Broome bridge, a cave painting illuminated not by campfire, but mathematical insight and imagination. Like all great mathematical expressions, once seen they hang elegant and timeless, eternal patterns in the fixed stars merely chanced upon by our ancestral explorers.
Leron Borsten (left) and Alessio Marrani (right) stood before Hamilton’s fundamental relations, Broome bridge Dublin. Leron is currently a Schrödinger Fellow in the School of Theoretical Physics, Dublin Institute for Advanced Studies. Alessio is currently a Senior Grantee at the Enrico Fermi Research Centre, Roma.
By Javier Olmedo, Sahil Saini and Parampreet Singh
Black holes are perhaps the most exotic objects in our Universe with very intriguing properties. The event horizon does not allow light and matter to escape, and hides the central singularity. As in the case of the big bang singularity, the central singularity is a strong curvature singularity where all in-falling objects are annihilated irrespective of their strength. Since singularities point out pathologies of general relativity, a more fundamental description obtained from quantum gravity must resolve the problem of singularities. Singularity resolution is also important for resolving many of the paradoxes and conundrums that plague the classical theory such as the cosmic censorship conjecture, black hole evaporation, black hole information loss paradox, etc.
Dr. Javier Olmedo is a postdoctoral researcher at Pennsylvania State University
Sahil Saini is a graduate student at Louisiana State University
Dr. Parampreet Singh is an associate professor at Louisiana Stare University
Black holes have mirror versions too. Known as white holes, these are solutions of general relativity with the same spacetime metric. If the black holes do not allow even the light to escape once it enters the horizon, thus nothing can enter the white hole horizon. Light and matter can only escape from the white hole. It has sometimes been speculated that black hole and white hole solutions can be connected, providing gateways between different universes or travelling within the same universe, but details have been sparse. The reason is due to the presence of the central singularity which does not allow a bridge between the black and white holes. Continue reading
by Jocelyn Read, California State University Fullerton
With several binary black hole mergers observed in the past two years, astronomers and relativists have become familiar with their general features: a quick chirp signal lasting seconds or less, a familiar inspiral-merger-ringdown pattern of waves, and a dark event in a distant galaxy, billions of light-years away.
GW170817 is a little bit different.
We’ve already seen systems like its presumed antecedent in our galaxy, where pulsars with neutron-star companions precisely map out their hours-long orbits with radio blips. We can imagine, then, the last 80 million or so years of GW170817’s source. Two neutron stars, in a galaxy only 40 Mpc away, driven through a slow but steady inspiral by gravitational radiation. For us distant observers, things become more interesting when the increasing orbital frequency sends the emitted gravitational waves into the sensitive range of our ground-based detectors.
Dr. Jocelyn Read explains gravitational waves to undergraduate students Isabella Molina and Erick Leon.
I wanted to take this opportunity to give a sense of scale, so consider this a tour of some interesting way-points along the signal’s path through that sensitive range of frequencies. Many thanks to my colleagues in the LIGO and Virgo collaborations who’ve helped lay out these markers over the last weeks – and of course, any remaining errors are my own. Continue reading
by Luc Blanchet and Alexandre Le Tiec
The first law of binary black hole mechanics can be extended to include non local tail effects.
Ever since Kepler’s discovery of the laws of planetary motion, the “two-body problem” has always played a central role in gravitational physics. In Einstein’s general theory of relativity, the simplest and most “universal,” purely gravitational, two-body problem is that of a binary system of black holes. The inspiral and merger of two compact objects (i.e. bodies whose radius is comparable to their mass, in “geometric” units where G = c = 1) produces copious amounts of gravitational radiation, as was recently discovered by LIGO’s multiple detections of gravitational waves from black hole binary systems.
Alexandre Le Tiec (left) celebrates the detection of gravitational waves and Luc Blanchet (right) thinks about gravitational waves in Quy Nhon, Vietnam
In general relativity, the inspiral and onset of the merger of two compact objects is indeed universal, as it does not depend on the nature of the bodies, be they black holes or neutron stars, or possibly more exotic objects like boson stars or even naked singularities. However, the gravitational waves generated during the post-merger phase depend on the internal structure of the compact objects, and in the case of neutron stars should reveal many details about the scenario for the formation of the final black hole after merger, and the equation of state of nuclear matter deep inside the neutron stars
by Adriana V. Araujo, Diego F. López and José G. Pereira
The Quest for Consistency in Spacetime Kinematics
Newton’s inception of the theory for the gravitational interaction in 1687 was a landmark for modern physics. In addition to explaining all known gravitational phenomena of that time, Newton’s gravitational theory was consistent with the kinematic rules of the Galilei group, known as Galilei relativity. Such consistency provided an atmosphere of intellectual comfort, which lasted for more than two centuries.
From left to right, José, Adriana and Diego. Click here to see the authors taking advantage of all dimensions of a space section of the universe.
By the mid nineteenth century, most secrets of the electric and magnetic fields were already unveiled. Those advancements culminated with the publication by Maxwell of a comprehensive treatise on the unification of electricity and magnetism, which became known as Maxwell’s theory. This theory brought to the scene the first inconsistency of our tale. In fact, it became immediately clear that the electromagnetic theory was inconsistent with the Galilei relativity: electromagnetism was claiming for a new relativity. In response to this claim, and with contributions from Lorentz and Poincaré, Einstein published in 1905 the basics of what is know today as Einstein special relativity. According to this theory, for velocities near the velocity of light, spacetime kinematics would no longer be ruled by Galilei, but by the Poincaré group. Most importantly, electromagnetism was consistent with Einstein special relativity! Mission accomplished? Not quite! Continue reading