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Hamiltonian Reduction for Einstein’s Equations in the (2+2) Formalism
윤종혁 한국물리학회 2014 THE JOURNAL OF THE KOREAN PHYSICAL SOCIETY Vol.64 No.2
I apply the Hamiltonian reduction procedure to general spacetimes of 4 dimensions in the (2+2)formalism and find privileged spacetime coordinates in which the physical Hamiltonian is expressedin terms of the conformal two metric and its conjugate momentum. Physical time is the areaelement of the spatial cross-section of null hypersurfaces, and the physical radial coordinate isdefined by equipotential surfaces on a given spacelike hypersurface of constant physical time. Thephysical Hamiltonian is local and positive in the privileged coordinates. I present the complete setof Hamilton’s equations and find that they coincide with the Einstein’s equations written in theprivileged coordinates. This shows that the Hamiltonian reduction is self-consistent and respectsgeneral covariance.
Generating Functions in the (2+2)-Formalism of General Relativity
윤종혁 한국물리학회 2009 THE JOURNAL OF THE KOREAN PHYSICAL SOCIETY Vol.54 No.4
In the (2+2)-formalism, the vacuum Einstein equations can be decomposed into four divergence-type equations and the Hamilton's equations of motion that follow from a non-vanishing Hamiltonian. In this paper, we report that the quasi-local flux integrals associated with divergence-type equations are the generating functions of translations in the (1 + 1 )-dimensional manifold and of the diffeomorphisms of the compact two-surface, which enables us to interpret them as quasi-local flux integrals of energy, linear momentum and angular momentum, respectively. At the null infinity, these fluxes reduce to the Bondi flux of energy, linear momentum and angular momentum. This formalism may be regarded as a 4-dimensional Kaluza-Klein theory without isometries in the (2,2)-splitting of spacetimes.
Consistent Hamiltonian Reduction
윤종혁 한국물리학회 2014 THE JOURNAL OF THE KOREAN PHYSICAL SOCIETY Vol.64 No.5
I show that the recently proposed (2+2) Hamiltonian reduction of Einstein’s equations of 4-dimensional spacetimes is consistent with general covariance. The consistency proof is extrinsic, as itfollows from the fact that Hamilton’s equations derived from the non-zero gravitational Hamiltonianare identical to the Ricci-flat condition of 4-dimensional spacetimes in privileged coordinates.
허리 불안정성이 있는 허리통증 환자에게 실시한 자가-복합 운동프로그램이 통증과 기능, 심리사회적, 균형 능력 그리고 배가로근에 미치는 효과
윤종혁,정대근,박삼호 대한통합의학회 2022 대한통합의학회지 Vol.10 No.2
Purpose : Low back pain (LBP) is reported as a risk of experiencing musculoskeletal disorders due to muscle stiffness and hypokinetics. The lumbar spine in an unstable state causes imbalance and lumbar instability. Therefore, This study examined the effects of lumbar stabilization exercise and self-complex exercise program on pain, function, psychosocial level, static balance ability, and transverse abdominal muscle (TrA) thickness and contraction ratio in patients with lumbar instability. Methods : The design of this is a randomized controlled trial (RCT). Twenty-six LBP patients participated in this study. Screening tests were performed and assigned to the experimental group (n=13) and control group (n=13) using a random allocation program. Both groups underwent a lumbar stabilization exercise program. In addition, the experimental group implemented the self-complex exercise program. All interventions were applied three times per week for four weeks. The quadruple visual analog (QVAS), the Korean version of the Oswestry disability index (K-ODI), Korean version of fear-avoidance belief questionnaire (FABQ), static balance ability, TrA thickness, and contraction ratio were compared to evaluate the effect on intervention. Statistical significance was set at α=.05. Results : Both groups showed significant differences before and after the intervention in QVAS, K-ODI, FABQ, static balance ability, and TrA thickness in contraction (p<.05). In addition, significant differences in K-ODI and FABQ were observed between the experimental group and control group (p<.05). Conclusion : A lumbar stabilization exercise and self-complex exercise program resulted in reduced dysfunctions, psychosocial stability in patients with lumbar instability. Therefore, Lumbar stabilization exercise and self-complex exercise program for patients with lumbar instability are effective method with clinical significance in improving the function and psychosocial stability.