Peano Baker series convergence for matrix-valued functions of bounded variation.
Positive energy in general relativity
Post-Newtonian approximation in the test particle limit
Gravitational radiation from a small mass particle orbiting a massive black hole can be analytically studied to a very high order in the post-Newtonian expansion. Thus it gives us useful information on the evolution of a coalescing compact binary star. In this talk, I report on recent progress made in the black-hole perturbation approach.
Post-Newtonian approximations and equations of motion of general relativity
A post-Newtonian approximation scheme for general relativity is defined using the Arnowitt-Deser-Misner formalism. The scheme is applied to perfect fluids and point-mass systems. The two-body point-mass Hamiltonian is given explicitly up to the post-Newtonian order.
Post-newtonian generation of gravitational waves
Post-Newtonian hydrodynamic equations using the (3+1) formalism in general relativity
The post-Newtonian (PN) hydrodynamic equations are obtained in the (3+1) formalism, which include the 2.5PN order as the reaction due to the quadrupole gravitational radiation. These equations are valid in various slice conditions, while we adopt a kind of transverse gauge condition to determine the shift vector. In particular, we describe methods to solve the 2PN tensor potential which arises from the spatial 3-metric. Our formulaton in the PN approximation using the (3+1) formalism will be useful...