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Modified Gravity Theories From the Barrow Hypothesis: Quantum Gravityby@hypothesis

Modified Gravity Theories From the Barrow Hypothesis: Quantum Gravity

by HypothesisAugust 9th, 2024
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Ankit Anand, Ruben Campos Delgado, Ankit. Anand and Ruben. Delgado. Modified Einstein equations with the Jacobson’s approach. 3 Quantum gravitational corrections to the Schwarzschild metric. 4 Conclusions and References. The paper is available on arxiv.org/2413687.
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Authors:

(1) Ankit Anand, Department of Physics, Indian Institute of Technology Madras, Chennai 600 036, India;

(2) Ruben Campos Delgado, Bethe Center for Theoretical Physics, Physikalisches Institut der Universit¨at Bonn, Nussallee 12, 53115 Bonn, Germany.

Abstract and 1 Introduction

2 Modified Einstein equations with the Jacobson’s approach

3 Quantum gravitational corrections to the Schwarzschild metric

4 Conclusions and References

3 Quantum gravitational corrections to the Schwarzschild metric

In order to solve (2.9), we start with the Ansatz



where



The Ricci scalar has the structure



Case I


We compare our solutions with the ones of Xiao and Tian [32], which read



With all these terms the final expression for the metric is



which generalizes the result of [32]. Notice that the coefficients (3.14) are formally divergent, but the solutions (3.15)-(3.17) are finite.

Case II


We compare now our solutions with the ones of Calmet and Kuipers, [22], which read



With all these terms the final expression for the metric is



hich generalizes the result of [22]. Again, notice that the coefficients (3.23) are formally divergent, but the solutions (3.24)-(3.26) are finite.


This paper is available on arxiv under CC BY 4.0 Deed license.