arxiv: 2605.05500 · v1 · submitted 2026-05-06 · 🌀 gr-qc

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Exact solution and Classical tests of New General Relativity

A. N. Semenova, V. A. Parkhomenko, V. P. Vandeev

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Pith reviewed 2026-05-08 15:46 UTC · model grok-4.3

classification 🌀 gr-qc

keywords New General Relativityexact solutionspherically symmetricvacuum solutionclassical testsperihelion precessionlight deflection

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The pith

New General Relativity admits an exact two-parameter static spherically symmetric vacuum solution whose extra parameter is constrained by classical tests.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper derives an exact static spherically symmetric vacuum solution to the field equations of New General Relativity. Unlike the one-parameter Schwarzschild solution in General Relativity, this solution depends on two parameters. The authors then apply the four classical tests of gravity—perihelion precession, light deflection, Shapiro time delay, and gravitational redshift—to obtain a stricter upper bound on the second parameter than earlier analyses.

Core claim

We present an exact static spherically symmetric vacuum solution of the New General Relativity field equations characterized by two parameters and use the classical tests of relativistic gravity to derive a more stringent constraint on the second parameter compared to prior work.

What carries the argument

The two-parameter exact static spherically symmetric vacuum metric that solves the NGR field equations.

If this is right

The second parameter must satisfy a narrower range of values to remain consistent with all four classical tests.
New General Relativity can reproduce observed weak-field gravity while allowing an extra degree of freedom in the vacuum solution.
The solution can be used to model isolated objects or black-hole candidates in NGR without immediate conflict with solar-system data.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

Strong-field observations such as black-hole shadows or gravitational-wave ringdown could further restrict or rule out the second parameter.
Similar two-parameter extensions might appear in rotating or time-dependent solutions within the same theory.

Load-bearing premise

The derived two-parameter metric is the physically relevant vacuum solution and the classical tests apply to it directly without extra assumptions about matter or higher-order behavior.

What would settle it

A high-precision measurement of Mercury's perihelion precession or light deflection by the Sun that falls outside the range allowed by the tighter bound on the second parameter would show the solution does not match observations.

Figures

Figures reproduced from arXiv: 2605.05500 by A. N. Semenova, V. A. Parkhomenko, V. P. Vandeev.

**Figure 1.** Figure 1: Precession of perihelion 4.1 Precession of planetary orbits For the motion of massive bodies δ = 1, so the linear order of the Eq. (33) is u ′′ + u = 3ME2 2L2c 2 k 2 k 2 − 1 + M k2 (13k 2 − 7)u 4(k 2 − 1)2 − Mc 2 2L2 k 2 + 2 k 2 − 1 + M(5k 4 + 5k 2 + 8)u 4(k 2 − 1)2 , (34) which is an ordinary harmonic oscillator equation with a constant external force u ′′ + (1 − β)u = α, where α = Mc 2 2L2(k 2 − 1) view at source ↗

**Figure 2.** Figure 2: Bending of light beam It turns out that to describe the effect of gravitational light deflection, the linear term in M on the right-hand side is sufficient. And equation u ′′ + (1 − β)u = α with parameters α = 3ME2 2L2c 2 · k 2 k 2 − 1 , β = 3M2E2 8L2c 2 · k 2 (13k 2 − 7) (k 2 − 1)2 , (39) 5 view at source ↗

**Figure 3.** Figure 3: Diagram of the arrangement of light source S, the receiver R, and the gravitating mass M. view at source ↗

read the original abstract

In this work, we present an exact static spherically symmetric vacuum solution of the New General Relativity (NGR) field equations. Unlike the Schwarzschild solution in General Relativity (GR), this solution is characterized by two parameters. Subsequently, using the four classical tests of relativistic gravity (perihelion precession, light bending, Shapiro time delay and gravitational redshift), a more stringent constraint on the value of the second parameter was derived compared to the original work [1].

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

They found a two-parameter exact vacuum solution in NGR and tightened the bound on the extra parameter using classical tests, but interior matching is the key open question.

read the letter

The paper presents an exact static spherically symmetric vacuum solution in New General Relativity with two free parameters, and then uses the four classical tests to derive a tighter constraint on the second one than in the cited prior work. They solve the field equations for the chosen ansatz rather than assuming the form outright, and the post-Newtonian expansions for perihelion precession, light deflection, Shapiro delay, and redshift are carried through in the usual way for this theory.

Referee Report

1 major / 2 minor

Summary. The manuscript claims to derive an exact static spherically symmetric vacuum solution of the New General Relativity (NGR) field equations, which depends on two parameters unlike the Schwarzschild solution in GR. It then applies the four classical tests (perihelion precession, light bending, Shapiro time delay, and gravitational redshift) to this solution to derive a more stringent constraint on the second parameter than in the referenced prior work.

Significance. If the two-parameter vacuum solution is the general one and can be matched to interior matter solutions without fixing the extra parameter, the work would supply a new exact solution in a teleparallel gravity theory and updated solar-system bounds from multiple tests. The explicit construction of an exact solution from the field equations is a clear strength.

major comments (1)

The derivation of the two-parameter static spherically symmetric vacuum solution is presented, but the manuscript does not examine whether this exterior solution admits consistent matching to a non-vacuum interior (e.g., a perfect-fluid star) while leaving the second parameter free. In NGR the field equations involve both the metric and the tetrad; junction conditions on the torsion and tetrad at the boundary may force the second parameter to a specific value (commonly zero). This matching question is load-bearing for the claim that the classical tests can be used to constrain the parameter, because those tests describe the exterior geometry around bodies with matter interiors.

minor comments (2)

The introduction should explicitly state the precise Lagrangian of NGR employed and its relation to the teleparallel equivalent of GR (TEGR) to avoid ambiguity in the field equations used.
A direct comparison table or quoted values showing the previous bound from reference [1] versus the new bound obtained here would improve clarity in the discussion of the constraints.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments on our manuscript. Below we address the major comment point by point and indicate the changes we will make to the revised version.

read point-by-point responses

Referee: The derivation of the two-parameter static spherically symmetric vacuum solution is presented, but the manuscript does not examine whether this exterior solution admits consistent matching to a non-vacuum interior (e.g., a perfect-fluid star) while leaving the second parameter free. In NGR the field equations involve both the metric and the tetrad; junction conditions on the torsion and tetrad at the boundary may force the second parameter to a specific value (commonly zero). This matching question is load-bearing for the claim that the classical tests can be used to constrain the parameter, because those tests describe the exterior geometry around bodies with matter interiors.

Authors: We agree that the consistency of the exterior vacuum solution with interior matter distributions via appropriate junction conditions is an important aspect not addressed in the original manuscript. Our work derives the exact static spherically symmetric vacuum solution of the NGR field equations and applies the classical tests to the resulting exterior geometry and tetrad. In the revised version we will add a new subsection that examines the junction conditions in NGR, which require continuity of the tetrad and suitable matching of the torsion tensor at the boundary. We will show that, for a static perfect-fluid interior with a compatible tetrad choice, the second parameter is not necessarily fixed by the matching conditions and can remain free, thereby preserving the applicability of the exterior solution to the classical tests. If the analysis indicates otherwise for generic interiors, we will update the conclusions and the derived constraints accordingly. revision: yes

Circularity Check

0 steps flagged

No significant circularity in derivation of vacuum solution or parameter bounds

full rationale

The paper derives an exact static spherically symmetric vacuum solution directly from the NGR field equations, yielding a two-parameter family as a first-principles result independent of the classical tests. The subsequent application of perihelion precession, light deflection, Shapiro delay, and redshift to obtain a tighter bound on the second parameter is a standard observational constraint on a free parameter, not a fitted input renamed as a prediction or a self-referential loop. No self-citation is load-bearing for the existence of the solution itself, no ansatz is smuggled via prior work, and no uniqueness theorem from the same authors is invoked to force the form. The chain from field equations to exterior solution to bounds remains self-contained without reducing any claimed result to its own inputs by construction.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on the field equations of New General Relativity (assumed known from prior literature) and the assumption that a static spherically symmetric ansatz yields an exact vacuum solution with exactly two free parameters. No new entities are introduced.

free parameters (1)

second parameter
The solution is stated to depend on two parameters; the second one is constrained by the classical tests and is therefore fitted to data.

axioms (1)

domain assumption The field equations of New General Relativity admit a static spherically symmetric vacuum solution.
Invoked in the first sentence of the abstract as the starting point for deriving the exact solution.

pith-pipeline@v0.9.0 · 5375 in / 1363 out tokens · 41908 ms · 2026-05-08T15:46:55.105123+00:00 · methodology

discussion (0)

Reference graph

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