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numerical relativity

Subdiscipline of physics devoted to the use of computer simulations for exploring the structure and consequences of Einstein’s theories, special and general relativity.

Notably, the centerpiece of general relativity are Einstein’s equations, which relate certain properties of the matter contained in a spacetime to that spacetime’s geometry. A model universe in which matter distorts the geometry – and is in turn influenced by those distortions – in exactly the way prescribed by Einstein’s equations is called a solution of these equations. Some simple solutions can simply be written down on a piece of paper (“exact solutions”). More complicated situations can only be described by simulating space, time and matter in a computer (“numerical solution”), and this is one of the main tasks of numerical relativity.

Numerical relativity has led to interesting results about black holes and gravitational waves, for instance about the gravitational wave produced when two black holes collide and merge. They have also shed light on what general relativity predicts for the properties of spacetime close to a black hole’s central singularity (further information about this can be found in the spotlight text Of singularities and breadmaking). The branch of numerical relativity that is of interest for the study of phenomena such as supernovae, jets, and merging or collapsing neutron stars is relativistic (magneto-)hydrodynamics, more about which can be found in the spotlight text The realm of relativistic hydrodynamics.

Definitioner

time

It is a fact of life that not all events in our universe happen concurrently - instead, there is a certain order. Defining a time coordinate or defining time, the way physicists do it, is to define a prescription to associate with each event a number so as to reflect that order - if event B happens after event A, then the number associated with B should be larger than that associated with A. The first step of this definition is to construct a clock: Choose a simple process that repeats regularly. (What is "regular"? Luckily, in our universe, all elementary processes such as a swinging pendulum, the oscillations of atoms or of electronic circuits lead to the same concept of regularity.) As a second step, install a counter: A mechanism that, with every repetition of the chosen process, raises the count by one. With this definition, one can at least assign a time (the numerical value of the counter) to events happening at location of the clock. For events at different locations, an additional definition is necessary: One needs to define simultaneity. After all, the statement that some far-away event A happens at 12 o'clock is the same as saying that event A and "our clock counter shows 12:00:00" are simultaneous. The how and why of defining simultaneity - a centre-piece of Einstein's special theory of relativity - are described in the spotlight topic Defining "now". With all these preparations, physicists can, in principle, assign a time coordinate value ("a time") to any possible events, and describes how fast or how slow processes happen, compared to that time coordinate.

space

In a strict sense: Space as we know it from everyday life: the totality of all locations in which objects can sit, with three dimensions. In a more general sense used by mathematicians, all kinds of sets of points are spaces - a line for instance, which has but a single dimension, or a two-dimensional surface, but also higher-dimensional spaces. Also, in such more general spaces, geometry can be different from the standard Euclidean geometry taught in high schools - such spaces can be curved.

solution

In the context of general relativity: a solution or, more precisely, a solution of the Einstein equations is a model universe that follows the law of gravity as prescribed by general relativity. See also exact solution.

numerical relativity

Subdiscipline of physics devoted to the use of computer simulations for exploring the structure and consequences of Einstein's theories, special and general relativity. Notably, the centerpiece of general relativity are Einstein's equations, which relate certain properties of the matter contained in a spacetime to that spacetime's geometry. A model universe in which matter distorts the geometry - and is in turn influenced by those distortions - in exactly the way prescribed by Einstein's equations is called a solution of these equations. Some simple solutions can simply be written down on a piece of paper ("exact solutions"). More complicated situations can only be described by simulating space, time and matter in a computer ("numerical solution"), and this is one of the main tasks of numerical relativity. Numerical relativity has led to interesting results about black holes and gravitational waves, for instance about the gravitational wave produced when two black holes collide and merge. They have also shed light on what general relativity predicts for the properties of spacetime close to a black hole's central singularity (further information about this can be found in the spotlight text Of singularities and breadmaking). The branch of numerical relativity that is of interest for the study of phenomena such as supernovae, jets, and merging or collapsing neutron stars is relativistic (magneto-)hydrodynamics, more about which can be found in the spotlight text The realm of relativistic hydrodynamics.

matter

In general relativity: All contents of spacetime that contribute to its curvature: particles, dust, gases, fluids, electromagnetic and other fields. In particle physics: All elementary particles with half-integer spin, such as electrons and quarks, as well as their composites such as protons and neutrons, in contrast with force particles.

geometry

That part of mathematics concerning itself with surfaces or more general spaces as well as objects defined on such spaces, such as points or lines as well as the objects constructable from points and lines, such as triangles.

general relativity (general theory of relativity)

Albert Einstein's theory of gravity; a generalization of his special theory of relativity. For information about the concepts and applications of this theory, we recommend the chapter general relativity of our introductory section Elementary Einstein. Further information about many different aspects of general relativity and its applications can be found in our section Spotlights on relativity.

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numerical relativity

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