Gravitational Radiation from Black Holes

University Of Pittsburgh, Pittsburgh PA

Investigators

Abstract

Waves, such as water, sound and electromagnetic waves, are a prominent feature of physical systems. A revolutionary prediction of Einstein's general theory of relativity is that accelerated bodies produce gravitational waves, analogous to the way electric charges produce electromagnetic waves. At present, gravitational waves have only been detected indirectly by the way they deplete energy from co-orbiting pulsars. A Laser Interferometric Gravity Wave Observatory (LIGO) has been constructed that is expected to open up a new form of astronomy by direct detection of these waves. The most powerful source of gravitational waves is the inspiral and merger of two co-orbiting black holes. Computer simulations provide the theoretical details necessary for LIGO to tune in the gravitational signal and monitor the dynamics of the merger. Einstein's equations describe the production of gravitational waves but their complexity makes a purely analytic approach inadequate. This has necessitated the introduction of computational methods into general relativity. The project's goal is to develop advanced methods to simulate the production of gravitational waves from black holes. The approach uses techniques for solving Einstein's equations which have been developed in collaboration with computational mathematicians, thoroughly calibrated on test problems and implemented as a community resource in the Einstein toolkit. The techniques will be further developed to measure the loss of energy and angular momentum carried off by gravitational waves, and other physical properties of binary black hole inspirals, such as the electromagnetic radiation counterpart. The approach utilizes characteristic evolution based upon the light cones on which the radiation propagates. Most computational work is based upon time evolution using the Cauchy initial value problem. The reformulation of the initial value problem for general relativity in terms of light cones by Bondi and by Penrose resulted in the first clear understanding of gravitational radiation. The global strategy proposed here combines Cauchy evolution in the interior region containing the black holes with characteristic evolution in the exterior region extending along the light cones to infinity. Characteristic evolution led to the first 3-dimensional code which could successfully locate, track, evolve and compute the waveform for a single distorted, spinning and moving black hole. However, in a binary problem, the focusing of the light cones leads to interior caustics which prevent a purely characteristic approach. On the other hand, present Cauchy codes require a finite artificial outer boundary which introduces inefficiency and errors in extracting the waveform. The proposed work integrates the complementary strengths of Cauchy and characteristic evolution to provide an accurate global treatment.