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Modified Gravity Theories From the Barrow Hypothesis: Modified Einstein Equationsby@hypothesis

Modified Gravity Theories From the Barrow Hypothesis: Modified Einstein Equations

by HypothesisAugust 9th, 2024
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This paper is available on arxiv.org under CC BY 4.0 Deed license. The Barrow hypothesis suggests that the entropy has the form. The general solution of (2.5) is (https://cdn.hackernoon.com/images/fWZa4tUiBGemnqQfBGgCPf9594N2-az83y6g.png)
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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

2 Modified Einstein equations with the Jacobson’s approach

The Barrow hypothesis suggests that the entropy has the form



The general solution of (2.5) is



where Λ′ is the integration constant. This expression matches the result of [30]. Since our goal is to see what happens when ∆ is a radial function, thus we expand



where c is some constant. By doing a series expansion of (2.6), integrating by parts and collecting powers of ǫ, we find



The limit ǫ → 0 reduces to general relativity.


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