Work

A methodological framework for solving Einstein’s equations in axially symmetric spacetimes

Year: 2025

Type: article

Abstract: This work presents a novel methodology for deriving stationary and axially symmetric solutions to Einstein’s field equations using the $$1+3$$ 1 + 3 tetrad formalism. This approach reformulates the Einstein equations into first-order scalar equations, enabling systematic resolution in vacuum scenarios. We derive two distinct solutions in polar and hyperbolic geometries by assuming the separability of a key metric function. Our method reproduces well-known solutions such as Schwarzschild and Kerr metrics and extends the case of rotating spacetimes to hyperbolic configurations. Additionally, we explore the role of Killing tensors in enabling separable metric components, simplifying analyses of geodesic motion and physical phenomena. This framework demonstrates robustness and adaptability for addressing the complexities of axially symmetric spacetimes, paving the way for further applications to Kerr-like solutions in General Relativity.

Source: The European Physical Journal Plus

DOI: 10.1140/epjp/s13360-025-06240-0

Authors: J. Ospino, J. L. Hernández-Pastora, A. V. Araujo-Salcedo, L. A. Núñez

Institutions: Universidad de Salamanca, Universidad Industrial de Santander, Universidad de Los Andes

Language: English

Topic: Relativity and Gravitational Theory

Subfield: Astronomy and Astrophysics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,890