2016/07/08 by Seung Hun Oh, Oh, Seung Hun, Kyoungtae Kimm +5
Physics and Astronomy · #Astrophysical Phenomena and Observations #Experimental and Theoretical Physics Studies #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Mathematical Physics (math-ph) #Pulsars and Gravitational Waves Research
paper · pdf · doi:10.48550/arxiv.1607.02254
openalex publication_date 2016/07/08 · openalex created_date 2022/10/06 · openalex updated_date 2026/07/28
The purpose of this paper is to demonstrate a new method of generating exact\nsolutions to the Einstein's equations obtained by the Hamiltonian reduction.\nThe key element to the successful Hamiltonian reduction is finding the\nprivileged spacetime coordinates in which physical degrees of freedom\nmanifestly reside in the conformal two-metric, and all the other metric\ncomponents are determined by the conformal two-metric. In the privileged\ncoordinates the Einstein's constraint equations become trivial; the Hamiltonian\nand momentum constraints are simply the defining equations of a non-vanishing\ngravitational Hamiltonian and momentum densities in terms of conformal\ntwo-metric and its conjugate momentum, respectively. Thus, given any conformal\ntwo-metric, which is a constraint-free data, one can construct the whole\n4-dimensional spacetime by integrating the first-order superpotential\nequations. As the first examples of using Hamiltonian reduction in solving the\nEinstein's equations, we found two exact solutions to the Einstein's equations\nin the privileged coordinates. Suitable coordinate transformations from the\nprivileged to the standard coordinates show that they are just the\nEinstein-Rosen wave and the Schwarzschild solution. The local gravitational\nHamiltonian and momentum densities of these spacetimes are also presented in\nthe privileged coordinates.\n