2017/04/30 by Shan-Ming Ruan, Run-Qiu Yang
Mathematics · Physics and Astronomy · #Action (physics) #Black Holes and Theoretical Physics #Boundary (topology) #Boundary value problem #Classical mechanics #Cosmology and Gravitation Theories #Dirichlet boundary condition #General relativity #Gravitation #Joint (building) #Limit (mathematics) #Mathematical analysis #Mathematics #Metric (unit) #Noncommutative and Quantum Gravity Theories #Physics #Principle of least action #Quantum mechanics #Term (time) #Theoretical physics #Transformation (genetics) #Variational principle #gr-qc #hep-th
paper · pdf · doi:10.1088/1361-6382/aa8053
published as Class. Quantum Grav. 34 (2017) 175017 (18pp) · Published version with little modifications compared with previous one
openalex publication_date 2017/07/18 · openalex created_date 2017/07/31 · arxiv created 2017/08/16 · arxiv updated 2017/08/17 · openalex updated_date 2026/08/05
Abstract This paper compares three different methods of computing joint terms in the on-shell action of gravity, which are identifying the joint term by the variational principle in the Dirichlet boundary condition, treating the joint term as the limit contribution of a smooth boundary and finding the joint term by local SO( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mstyle displaystyle="false"> <mml:mn>1</mml:mn> <mml:mo>,</mml:mo> <mml:mi>d</mml:mi> <mml:mo>−</mml:mo> <mml:mn>1</mml:mn> </mml:mstyle> </mml:math> ) transformation. In general metric gravitational theory, we show that the differences between these joint terms are variational invariants under a fixed boundary condition. We also give an explicit condition to judge the existence of a joint term determined by the variational principle and apply it to general relativity as an example.