Numerical relativity for Horndeski gravity

Numerical Relativity

Solutions to Einstein’s equations of general relativity describe, among other things, the generation and propagation of gravitational waves. Interest in numerical relativity has been bolstered by the recent construction of gravitational wave observatories such as LIGO (the Laser Interferometric Gravitational-wave Observatory). This NSF-supported project consists of two observatories (near Hanfo...

Spectral Methods for Numerical Relativity

Equations arising in general relativity are usually too complicated to be solved analytically and one must rely on numerical methods to solve sets of coupled partial differential equations. Among the possible choices, this paper focuses on a class called spectral methods in which, typically, the various functions are expanded in sets of orthogonal polynomials or functions. First, a theoretical ...

Initial Data for Numerical Relativity

Initial data are the starting point for any numerical simulation. In the case of numerical relativity, Einstein's equations constrain our choices of these initial data. We will examine several of the formalisms used for specifying Cauchy initial data in the 3 + 1 decomposition of Einstein's equations. We will then explore how these formalisms have been used in constructing initial data for spac...

USING openGR FOR NUMERICAL RELATIVITY

Quantum Gravity without General Relativity

The quantum field theory of gravitation is constructed in terms of Lagrangian density of Dirac fields which couple to the electromagnetic field Aμ as well as the gravitational field G. The gravity appears in the mass term as m(1+gG)ψ̄ψ with the coupling constant of g. In addition to the gravitational force between fermions, the electromagnetic field Aμ interacts with the gravity as the fourth or...