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arxiv: 2510.17066 · v2 · submitted 2025-10-20 · 🌀 gr-qc

Compact Stars in Symmetric Teleparallel Scalar-Tensor Gravity

Grigorios Panotopoulos , Andr\'es Lueiza-Colip\'i , Nikolaos Dimakis , Andronikos Paliathanasis This is my paper

Pith reviewed 2026-05-18 06:46 UTC · model grok-4.3

classification 🌀 gr-qc
keywords symmetric teleparallel gravityscalar-tensor theorycompact objectsblack hole solutionsminisuperspacevariational symmetriesReissner-Nordström exterior
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The pith

Symmetric teleparallel scalar-tensor gravity supports viable compact stars through interior solutions matched to extremal Reissner-Nordström exteriors.

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

The paper investigates static spherically symmetric compact objects in symmetric teleparallel scalar-tensor gravity, an extension of Brans-Dicke models. The authors select a nontrivial connection so the theory remains different from general relativity yet admits exact solutions. They reduce the equations via a minisuperspace description and use variational symmetries to obtain conservation laws that reconstruct analytic black-hole solutions. Matching interior compact-object solutions to an extremal Reissner-Nordström exterior then shows the theory permits realistic astrophysical objects. A sympathetic reader would care because this indicates the framework can describe actual stars and black holes.

Core claim

The symmetric teleparallel scalar-tensor theory supports the existence of viable astrophysical objects. The field equations admit a minisuperspace description, and variational symmetries produce conservation laws in vacuum that allow reconstruction of analytic black-hole solutions. Interior solutions for compact objects are constructed and matched to an extremal Reissner-Nordström exterior.

What carries the argument

Minisuperspace reduction of the field equations together with variational symmetries that generate conservation laws for reconstructing analytic solutions.

If this is right

  • Analytic black-hole solutions exist because the conservation laws permit their reconstruction.
  • Interior structures of compact objects can be matched to extremal charged black-hole exteriors.
  • The theory admits viable astrophysical objects with static spherical symmetry.
  • The minisuperspace method yields exact solutions in this modified gravity setting.

Where Pith is reading between the lines

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

  • The same symmetry-based reconstruction might apply to rotating configurations or other geometries.
  • Mass-radius relations derived from these interiors could be compared with neutron-star observations.
  • Similar variational techniques could be tested in other teleparallel scalar-tensor models.

Load-bearing premise

A nontrivial connection can be chosen that makes the theory a genuinely nontrivial extension of general relativity while still allowing analytic solutions through minisuperspace reduction and variational symmetries.

What would settle it

Failure to construct any regular interior solution that matches the extremal Reissner-Nordström exterior while satisfying the field equations and physical requirements would show the theory does not support such objects.

Figures

Figures reproduced from arXiv: 2510.17066 by Andr\'es Lueiza-Colip\'i, Andronikos Paliathanasis, Grigorios Panotopoulos, Nikolaos Dimakis.

Figure 1
Figure 1. Figure 1: FIG. 1: Factor of compactness, [PITH_FULL_IMAGE:figures/full_fig_p009_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: Stellar mass as a function of the central energy density. [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: Gravitational redshift, [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: Mass-to-radius relationships for the 3 models considered here, see text. The black dashed line corresponds [PITH_FULL_IMAGE:figures/full_fig_p011_4.png] view at source ↗
read the original abstract

We investigate the existence of static, spherically symmetric compact objects within the framework of symmetric teleparallel scalar-tensor gravity. This theory extends the Brans-Dicke and scalar-tensor models within the symmetric teleparallel formalism. We consider a nontrivial connection that allows for genuinely nontrivial solutions in the limit of General Relativity. The field equations admit a minisuperspace description and by applying the method of variational symmetries we construct the corresponding conservation laws in vacuum. The application of these conservation laws enables the reconstruction of analytic black-hole solutions. Finally, we study the interior structure of compact objects matched to an extremal Reissner-Nordstr\"{o}m exterior and show that the symmetric teleparallel scalar-tensor theory supports the existence of viable astrophysical objects.

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.

Referee Report

2 major / 2 minor

Summary. The manuscript investigates static spherically symmetric compact objects in symmetric teleparallel scalar-tensor gravity. It adopts a nontrivial connection permitting a nontrivial general-relativity limit, reduces the field equations to a minisuperspace description, applies variational symmetries to obtain conservation laws in the vacuum sector, reconstructs analytic black-hole solutions from those laws, and constructs interior solutions that are matched to an extremal Reissner-Nordström exterior, concluding that the theory admits viable astrophysical objects.

Significance. If the interior-exterior matching satisfies the full set of junction conditions required by the independent connection and the solutions obey regularity, energy conditions, and stability criteria, the work would supply explicit analytic examples of compact stars in an extension of scalar-tensor theories. The use of variational symmetries to derive conservation laws and reconstruct exact solutions is a methodological strength that provides analytic control uncommon in modified-gravity stellar models.

major comments (2)
  1. [§4 (Interior solutions and matching)] §4 (Interior solutions and matching): The central claim that the constructed interior solutions yield viable astrophysical objects rests on successful matching to the extremal Reissner-Nordström exterior. In symmetric teleparallel scalar-tensor gravity the independent connection generates additional boundary terms and continuity requirements on the connection coefficients and scalar field at a timelike hypersurface. The manuscript does not appear to verify these extra junction conditions explicitly beyond metric continuity, which is load-bearing for the claim that the composite spacetime solves the field equations.
  2. [§3.2 (Vacuum solutions via variational symmetries)] §3.2 (Vacuum solutions via variational symmetries): The reconstruction of analytic black-hole solutions relies on conservation laws obtained from variational symmetries in the minisuperspace. It is unclear whether these symmetries and the resulting first integrals remain valid when the same interior metric is extended across the matching surface with a nonzero scalar-field gradient; if the symmetries are broken by the matching, the analytic form used for the interior may not satisfy the full field equations.
minor comments (2)
  1. [Introduction] The definition of the nontrivial connection and its relation to the GR limit could be stated more explicitly in the introduction, including the explicit form of the connection coefficients chosen.
  2. Figure captions for the density and pressure profiles should include the specific parameter values used and note whether the plotted quantities satisfy the weak energy condition throughout the interior.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their thorough review and valuable comments on our manuscript. We address the major comments point by point below. Where appropriate, we have revised the manuscript to incorporate the suggestions and provide additional clarifications.

read point-by-point responses

  1. Referee: §4 (Interior solutions and matching): The central claim that the constructed interior solutions yield viable astrophysical objects rests on successful matching to the extremal Reissner-Nordström exterior. In symmetric teleparallel scalar-tensor gravity the independent connection generates additional boundary terms and continuity requirements on the connection coefficients and scalar field at a timelike hypersurface. The manuscript does not appear to verify these extra junction conditions explicitly beyond metric continuity, which is load-bearing for the claim that the composite spacetime solves the field equations.

    Authors: We appreciate the referee highlighting the importance of the full set of junction conditions in the presence of an independent connection. Upon careful review, our interior solutions were constructed such that the metric, the scalar field, and the connection coefficients are all continuous at the matching surface by appropriate choice of constants in the analytic expressions. However, to address this explicitly, we have added a detailed verification of the junction conditions, including the continuity of the connection and the absence of surface terms in the action, in a revised subsection of §4. This confirms that the matched spacetime satisfies the field equations throughout. revision: yes

  2. Referee: §3.2 (Vacuum solutions via variational symmetries): The reconstruction of analytic black-hole solutions relies on conservation laws obtained from variational symmetries in the minisuperspace. It is unclear whether these symmetries and the resulting first integrals remain valid when the same interior metric is extended across the matching surface with a nonzero scalar-field gradient; if the symmetries are broken by the matching, the analytic form used for the interior may not satisfy the full field equations.

    Authors: The variational symmetries and associated conservation laws are derived and applied exclusively in the vacuum sector to reconstruct the exterior black-hole solutions, including the extremal Reissner-Nordström case. The interior solutions are derived independently by solving the reduced field equations with a matter source in the minisuperspace, using a different ansatz that incorporates the nonzero scalar-field gradient. The matching conditions ensure continuity of the metric functions, scalar field, and its derivative at the boundary, but the vacuum symmetries do not extend into the interior region. We have clarified this separation of the vacuum and interior analyses in the revised manuscript to avoid any ambiguity. revision: yes

Circularity Check

0 steps flagged

No significant circularity; standard methods applied to new geometric setup

full rationale

The derivation begins with the choice of a nontrivial connection (an explicit modeling assumption to recover a nontrivial GR limit), then invokes the established minisuperspace reduction and variational symmetries to obtain conservation laws in the vacuum sector. These laws are used to reconstruct analytic solutions, which are subsequently matched to an extremal RN exterior. None of these steps reduces the final result to a fitted parameter, a self-defined quantity, or a load-bearing self-citation; the techniques are independent of the target solutions and the paper remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on the existence of a minisuperspace reduction and the applicability of variational symmetries to generate conservation laws that integrate the vacuum equations; these steps presuppose that the chosen nontrivial connection preserves the necessary symmetries and that the interior solution can be matched smoothly to the extremal Reissner-Nordström exterior without additional constraints.

axioms (2)
  • domain assumption The field equations of symmetric teleparallel scalar-tensor gravity admit a minisuperspace description for static spherically symmetric configurations.
    Invoked when the abstract states that the field equations admit a minisuperspace description and that variational symmetries yield conservation laws.
  • ad hoc to paper A nontrivial connection exists that allows genuinely nontrivial solutions in the general-relativity limit.
    Stated explicitly in the abstract as the choice that enables the constructions.

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