Related papers: On the relation between mathematical and numerical…
Arithmetic operations can be defined in various ways, even if one assumes commutativity and associativity of addition and multiplication, and distributivity of multiplication with respect to addition. In consequence, whenever one encounters…
We report on the first numerical-relativity simulations of black-hole binaries that deviate from General Relativity due to quadratic-curvature corrections. Said theory of Quadratic Gravity propagates additional massive modes and admits both…
An approximate solution to Einstein's equations representing two widely-separated non-rotating black holes in a circular orbit is constructed by matching a post-Newtonian metric to two perturbed Schwarzschild metrics. The spacetime metric…
A benchmark problem for numerical relativity has been the head-on collision of two black holes starting from the ``Misner initial data,'' a closed form momentarily stationary solution to the constraint equations with an adjustable closeness…
With the goal of taking a step toward the construction of astrophysically realistic initial data for numerical simulations of black holes, we for the first time derive a family of fully general relativistic initial data based on…
Quantum aspects of black holes represent an important testing ground for a theory of quantum gravity. The recent success of string theory in reproducing the Bekenstein-Hawking black hole entropy formula provides a link between general…
The possible existence of black holes has fascinated scientists at least since Michell and Laplace's proposal that a gravitating object could exist from which light could not escape. In the 20th century, in light of the general theory of…
Tremendous progress has been made towards the solution of the binary-black-hole problem in numerical relativity. The waveforms produced by numerical relativity will play a role in gravitational wave detection as either test-beds for…
The nature of binary black hole coalescence is the final, uncharted frontier of the relativistic Kepler problem. In the United States, binary black hole coalescence has been identified as a computational ``Grand Challenge'' whose solution…
This paper is a small step towards the goal of constructing a coherent theory of physic and mathematics together. It is based on two ideas, the localization of mathematical systems in space or space time, and the separation of the concepts…
This a particularly exciting time for gravitational wave physics. Ground-based gravitational wave detectors are now operating at a sensitivity such that gravitational radiation may soon be directly detected, and recently several groups have…
General relativity's successes and limitations are compared to those of special relativity.
The extreme-gravity collisions of binaries with one black hole and one neutron star provide for excellent tests of general relativity. We here study how well one can constrain theories beyond general relativity with additional scalar fields…
We discuss black hole spacetimes with a geometrically defined quasi-local horizon on which the curvature tensor is algebraically special relative to the alignment classification. Based on many examples and analytical results, we conjecture…
We present the first results in a new program intended to make the best use of all available technologies to provide an effective understanding of waves from inspiralling black hole binaries in time for imminent observations. In particular,…
We discuss various universality aspects of numerical computations using standard algorithms. These aspects include empirical observations and rigorous results. We also make various speculations about computation in a broader sense.
Numerical relativity describes a discrete initial value problem for general relativity. A choice of gauge involves slicing space-time into space-like hypersurfaces. This introduces past and future gauge relative to the hypersurface of…
The most compelling evidences for the existence of stellar-mass black holes have been obtained through observations of X-ray binary systems. The application of classical methods and the development of new techniques have allowed us to…
The search for solutions of Einstein's equations representing relativistic cosmological models with a discrete matter content has been remarkably fruitful in the last decade. In this review we discuss the progress made in the study of a…
This article begins with a brief introduction to numerical relativity aimed at readers who have a background in applied mathematics but not necessarily in general relativity. I then introduce and summarise my work on the problem of treating…