Authors: Atman Bharadwaj
This paper presents a comprehensive framework that integrates quantum gravitational corrections derived from string theory, loop quantum gravity (LQG), and non-commutative geometry into the Einstein-Hilbert action. By combining these three approaches, we derive modified field equations that encapsulate quantum effects in spacetime curvature. The unified corrections are formulated as higher-order curvature terms and modifications arising from the discrete structure of spacetime and non-commutative coordinates. Our results demonstrate that these corrections can resolve classical singularities, leading to a finite Ricci scalar even at small radii, thus providing a non-singular description of black hole interiors. Additionally, the framework predicts alterations in the effective potential near black holes, which could manifest as observable deviations in gravitational wave signals and other astrophysical phenomena. This work not only bridges the gap between general relativity and quantum mechanics but also opens new avenues for both theoretical exploration and observational verification of quantum gravitational effects.
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[v1] 2024-05-18 18:41:17
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