From Gravitons to Gravity: Myths and Reality
T.Padmanabhan

TL;DR
This paper critically examines the common belief that Einstein's gravity can be derived solely from a self-coupled spin-2 field, demonstrating that such an approach is fundamentally flawed and does not reproduce Einstein's theory.
Contribution
The paper provides a rigorous analysis showing the impossibility of deriving Einstein-Hilbert action from linear graviton theory and clarifies the role of the coupling tensor in the formulation.
Findings
Proves linear theory cannot produce Einstein-Hilbert action.
Identifies the coupling tensor as not the conventional energy-momentum tensor.
Constructs Einstein's theory by coupling to a different tensor, not the standard energy-momentum tensor.
Abstract
There is a general belief, reinforced by statements in standard textbooks, that: (i) one can obtain the full non-linear Einstein's theory of gravity by coupling a massless, spin-2 field self-consistently to the total energy momentum tensor, including its own; (ii) this procedure is unique and leads to Einstein-Hilbert action and (iii) it only uses standard concepts in Lorentz invariant field theory and does not involve any geometrical assumptions. After providing several reasons why such beliefs are suspect -- and critically re-examining several previous attempts -- we provide a detailed analysis aimed at clarifying the situation. First, we prove that it is \textit{impossible} to obtain the Einstein-Hilbert (EH) action, starting from the standard action for gravitons in linear theory and iterating repeatedly. Second, we use the Taylor series expansion of the action for…
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