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Abstract <p>We study the existence of a local classical solution to the Einstein-Scalar equations in higher dimensions. We reduce the problem to a single first-order integro-differential equation. Then, we employ the contraction mapping in the appropriate Banach space. Using the Banach fixed theorem, we show that there exists a unique fixed point, which is the solution to the main problem. Finally, for given initial data, we prove the existence of a local classical solution.</p>

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Existence of a Local Classical Solution to the Einstein-Scalar System in Higher Dimensions

  • 期刊论文

  • 发表日期：

    2025年3月2日

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  • Mirda Prisma Wijayanto,
  • Fiki Taufik Akbar,
  • Bobby Eka Gunara

摘要

Abstract

We study the existence of a local classical solution to the Einstein-Scalar equations in higher dimensions. We reduce the problem to a single first-order integro-differential equation. Then, we employ the contraction mapping in the appropriate Banach space. Using the Banach fixed theorem, we show that there exists a unique fixed point, which is the solution to the main problem. Finally, for given initial data, we prove the existence of a local classical solution.