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Main Authors: Ha, Songmin, Rothkopf, Alexander
Format: Preprint
Published: 2026
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Online Access:https://arxiv.org/abs/2602.15469
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author Ha, Songmin
Rothkopf, Alexander
author_facet Ha, Songmin
Rothkopf, Alexander
contents A key tenet of general relativity is the dynamical nature of space-time, ideally represented as an initial value problem. Here we explore the variational formulation of classical Einstein-Hilbert gravity as initial value problem by constructing its Schwinger-Keldysh-Galley (SKG) action, including a careful treatment of boundary terms. The construction is based on a doubling of degrees of freedom and independent of a foliation. The action naturally decomposes into a bulk term furnishing Einstein's equations and a boundary term, which is related to conserved quantities, such as the Komar mass. We find that since only trivial connecting conditions must be specified on boundaries, the variational action principle for gravity as an initial value problem is rendered well-posed without the need to add additional boundary terms. The SKG approach to gravity offers a novel and complementary avenue to solve for the metric of spacetime directly from the action, bypassing the governing equations.
format Preprint
id arxiv_https___arxiv_org_abs_2602_15469
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle A fresh look at boundary terms in Einstein-Hilbert gravity via an initial value variational principle
Ha, Songmin
Rothkopf, Alexander
General Relativity and Quantum Cosmology
High Energy Physics - Phenomenology
High Energy Physics - Theory
A key tenet of general relativity is the dynamical nature of space-time, ideally represented as an initial value problem. Here we explore the variational formulation of classical Einstein-Hilbert gravity as initial value problem by constructing its Schwinger-Keldysh-Galley (SKG) action, including a careful treatment of boundary terms. The construction is based on a doubling of degrees of freedom and independent of a foliation. The action naturally decomposes into a bulk term furnishing Einstein's equations and a boundary term, which is related to conserved quantities, such as the Komar mass. We find that since only trivial connecting conditions must be specified on boundaries, the variational action principle for gravity as an initial value problem is rendered well-posed without the need to add additional boundary terms. The SKG approach to gravity offers a novel and complementary avenue to solve for the metric of spacetime directly from the action, bypassing the governing equations.
title A fresh look at boundary terms in Einstein-Hilbert gravity via an initial value variational principle
topic General Relativity and Quantum Cosmology
High Energy Physics - Phenomenology
High Energy Physics - Theory
url https://arxiv.org/abs/2602.15469