Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 2004.10525

The Field-Theoretic Approach in General Relativity and Other Metric Theories. A Review

A. N. Petrov·J. Brian Pitts
View original source ↗Read source document ↗Export metadata ↓

Abstract

GR and other metric theories of gravity are formulated with an arbitrary auxiliary curved background in a Lagrangian formalism. A new sketch of how to include spinor fields is included. Conserved quantities are obtained using Noether's theorem and expressed as divergences of antisymmetric densities, connecting local perturbations with quasi-local conserved quantities. The background's arbitrariness matches the so-called non-localizability of gravitational energy (infinity of localizations). The formalism has two partly overlapping uses: practical applications of pure GR (with fictitious background) and foundational considerations in which background causality facilitates quantization. The Schwarzschild solution is a primary application. Various possibilities for calculating the mass using surface integration are given. A field-theoretic curved spacetime is given from spatial infinity to the horizon and even to the true singularity. Trajectories of test particles in the Schwarzschild geometry are gauge-dependent in that even breakdowns at the horizon can be suppressed (or generated) by naive gauge transformations. This fact illustrates the auxiliary nature of the background metric and the need for some notion of maximal extension---much as with coordinate transformations in geometric GR. A continuous collapse to a point mass in the field-theoretic framework is given. The field-theoretic method is generalized to arbitrary metric theories in $D$ dimensions. The results are developed in the framework of Lovelock gravity and applied to calculate masses of Schwarzschild-like black holes. The bimetric formalism makes it natural to consider a graviton mass. Babak and Grishchuk's numerical and hence nonperturbative work sheds light on questions of a (dis)continuous massless limit for massive pure spin-2 and the classical (in)stability of spin-2/spin-0 theory.

Explore related subjects

gr-qchep-thphysics.hist-ph

Keep this discovery

BibTeXRIS

A. N. Petrov, J. Brian Pitts. 2020-04-20. The Field-Theoretic Approach in General Relativity and Other Metric Theories. A Review. https://arxiv.org/abs/2004.10525

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Electrovacuum Black Hole Uniqueness

We prove the black hole uniqueness conjecture in the axially symmetric, stationary, electrovacuum setting, subject to the refined asymptotic analysis of the associated singular harmonic maps, which includes an analyticity hypothesis at the axes. More precisely, it is shown that any asymptotically flat solution of the Einstein--Maxwell equations in this class, with more than one black hole horizon component is either: Majumdar--Papapetrou, up to a duality rotation, in which case all logarithmic angle defects vanish, or every finite axis rod logarithmic angle defect is strictly negative and hence every interaction force is strictly attractive. The proof extends the singular harmonic map method used for vacuum Kerr uniqueness in [18].

gr-qc↗
arXiv2026

Constraining Modified Mass-to-Horizon Cosmology Through Primordial Inflationary Observables

We investigate slow-roll inflation in a modified cosmological framework inspired by a generalized mass-to-horizon relation (MHR), $M=\gamma {c^2 L^n}/{G}$, where $n$ is a real parameter and $\gamma$ a dimensional constant. Using Padmanabhan's emergence paradigm, we derive the modified Friedmann equations for a flat FRW universe and analyze the dynamics of a canonical scalar field (inflaton) under the slow-roll approximation. We study the resulting inflationary phenomenology for power-law and Starobinsky potentials. For power-law potentials, the MHR modification fails to reconcile these models with current CMB constraints on $r$ and $n_s$. In contrast, Starobinsky inflation exhibits significant sensitivity to deviations from $n=1$. A perturbative analysis ($n=1+\Delta$) yields corrections to inflationary observables. We observe that the scalar power-spectrum normalization, under a fixed-Starobinsky prescription, imposes the stringent constraint $0.960 \lesssim n \lesssim 1.040$ for $N=60$ efolds. This is considerably tighter than spectral-index bounds. Our results establish inflation, particularly Starobinsky-like models, as a sensitive probe of generalized horizon thermodynamics and departures from standard MHR scaling.

gr-qc↗
arXiv2026

Improving the Sensitivity of Gravitational Wave Detection with Weighted Conformal Prediction

In the last decade, kilometre-scale interferometric gravitational-wave detectors have observed hundreds of compact binary mergers, the majority of which are binary black holes. However, the data are noise-dominated, and multiple independent search algorithms (pipelines) are used to enhance sensitivity and improve robustness. Rather than the standard approach of selecting the most significant pipeline output, we combine the outputs from all pipelines using a conformal prediction-based framework to provide statistically rigorous confidence estimates for candidate events. While combining pipelines improves sensitivity and ranking robustness, it requires a principled statistical framework that remains valid as data properties evolve across observing runs. A key challenge is distribution shifts between simulated datasets used for training and calibration and the real, unlabelled, observations used for testing, which can invalidate coverage guarantees and bias confidence estimates. In this work, we address this challenge by incorporating likelihood-ratio reweighting into our conformal prediction framework to account for covariate shift. Using mock datasets containing simulated signals, we demonstrate that weighted conformal prediction restores well-calibrated coverage under covariate shift and increases the confidence of events near the detection threshold, recovering true signals that would otherwise be missed.

gr-qc↗