Compact stars in f(T) = T + xi T beta gravity

arXiv:2308.00627 · gr-qc, astro-ph.HE · Submitted 2024-01-04 · Read on arXiv

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Introduction to the show: ident: Astrophysics Radio. Generated commentary on the latest astrophysics papers.

Vera: Next we'll be talking about the paper "Compact stars in f(T) = T + xi T beta gravity".

Jocelyn: The paper was written by J. C. N. de Araujo and H. G. M. Fortes from Instituto Nacional de Pesquisas Espaciais and Instituto Federal Fluminense.

Vera: Stay tuned as we take you through the paper and discuss its implications.

Title: Vera: We're starting things off today with a new paper titled "Compact stars in f(T) = T + xi T beta gravity" by J. C. N. de Araujo and H. G. M. Fortes.

Jocelyn: That title looks like it belongs in a heavy math textbook rather than a radio show, Vera.

Vera: It certainly does, Jocelyn, but the subject matter is something we can actually see in the sky.

Jocelyn: You're talking about those incredibly dense compact stars?

Vera: Exactly, specifically things like neutron stars that push the limits of physics.

Subrahmanyan: To understand why the title is so complex, you really have to look at that f(T) part. In General Relativity, we say gravity is caused by the curvature of spacetime. This paper uses Teleparallel gravity, which says gravity comes from torsion instead. It's a different mathematical framework for describing the same physical phenomenon.

Jocelyn: So instead of space bending, it's more like the fabric of the universe is twisting?

Subrahmanyan: That's a great way to put it.

Vera: And the xi and beta in that equation are just ways to tweak the strength of that twist?

Subrahmanyan: Precisely, they are constants that let us test how much extra torsion we might need to explain the universe.

Vera: The authors are coming from the Instituto Nacional de Pesquisas Espaciais in Brazil, which is a major center for this kind of work.

Jocelyn: I'm curious if these torsion models will actually match the pulsars we're finding in our latest surveys.

Subrahmanyan: They might actually explain some of the anomalies we see in high-mass objects.

Vera: Let's see if their specific math holds up when we look at the actual results.

Paper discussion segment 2: Vera: We've just established that this paper explores gravity through torsion, so let's look at what they actually found regarding those xi and beta parameters.

Jocelyn: Those symbols in the title seem to be the heart of the whole study.

Subrahmanyan: They really are, as they define the specific way the gravity is modified.

Vera: One interesting thing they found is that beta has to be a positive integer for the equations to stay well-behaved.

Jocelyn: Why is that such a strict requirement?

Subrahmanyan: If beta isn't a positive integer, the math becomes incredibly difficult to solve and the equations could even diverge.

Vera: And once they set beta, the value of xi determines how the star behaves.

Jocelyn: Does that mean the stars could end up being much heavier than what we're used to?

Subrahmanyan: It absolutely can, depending on whether beta is even or odd. If beta is an odd integer and xi is positive, the torsion becomes more negative, which makes the gravitational pull much stronger. This allows the star to become much more massive and compact than what General Relativity allows.

Vera: But if beta is an even number, the results are actually the opposite?

Jocelyn: So we might see stars that are less massive than the standard models predict?

Subrahmanyan: Yes, even values of beta tend to generate sequences that fall below the General Relativity line.

Vera: It's amazing how much a single exponent can change the entire structure of a star.

Jocelyn: But how did they actually calculate these things in the first place?

Paper discussion segment 3: Vera: We've seen how these different gravity models change the mass and size of stars, so let's talk about the methodology they used to get there.

Jocelyn: It sounds like a massive computational task.

Subrahmanyan: It really is, which is why they had to write a custom numerical solver in Python.

Vera: They're using these generalized Tolman-Oppenheimer-Volkoff equations to model the stars, right?

Subrahmanyan: That's right, they've adapted the standard TOV equations to account for the extra torsion terms.

Jocelyn: I noticed they had to be very careful with their boundary conditions at the center of the star.

Subrahmanyan: They did, because they had to ensure the pressure and the metric were regular at the very center.

Vera: There was also a lot of discussion in the paper about how to define the mass of the star.

Jocelyn: I heard that the usual way we do things in General Relativity doesn't work here?

Subrahmanyan: That's a crucial point because the vacuum around the star isn't a simple Schwarzschild metric in this theory. Since the space outside the star is affected by the torsion, they had to calculate the mass as seen by an observer far away, which they call M infinity.

Vera: So they're looking at the mass measured at infinity rather than just integrating the density?

Jocelyn: That seems like a much more consistent way to handle a modified theory.

Subrahmanyan: It's the only way to make sure the mass is actually what an observer would feel.

Vera: So, what does this all mean for the actual stars we see through our telescopes?

Conclusion: Vera: We're coming to the end of our discussion on "Compact stars in f(T) = T + xi T beta gravity," and it's clear this paper has some big implications.

Jocelyn: I'm thinking specifically about those high-mass objects like the one found in the GW190814 event.

Subrahmanyan: This model could be a perfect candidate to explain why some objects seem too heavy to be neutron stars under General Relativity.

Vera: It really provides a new way to look at the limits of how massive a star can actually get.

Jocelyn: I'll be keeping a close eye on the next batch of pulsar data for any hints of this torsion effect.

Subrahmanyan: This work shows that even small tweaks to the torsion can change the entire landscape of stellar evolution.

Vera: It's a fascinating look at how different mathematical foundations can change our view of the sky.

Jocelyn: Thanks for joining us, Subrahmanyan, and thanks to everyone for listening.

Subrahmanyan: It was a pleasure to discuss it with you both.

Vera: We'll see you next time with another paper.

Jocelyn: Goodbye!

Subrahmanyan: Goodbye!

J. C. N. de Araujo, H. G. M. Fortes

Instituto Nacional de Pesquisas Espaciais · Instituto Federal Fluminense

gr-qc, astro-ph.HE

Submitted: 2024-01-04

Updated: 2026-08-21

Journal ref: The European Physical Journal C, Volume 83, article number 1168, (2023)

DOI: 10.1140/epjc/s10052-023-12342-9

License: http://creativecommons.org/licenses/by/4.0/

Importance score: 68/100

The gist: This paper investigates "Compact stars in f(T) = T + xi T beta gravity," aiming to "generalise such extension considering compact stars in f(T) = T + xi T beta gravity, where xi and beta are real

Key concepts

Teleparallel Gravity: This framework describes gravity as coming from torsion, which is a different mathematical approach than General Relativity's description of gravity via spacetime curvature. It suggests that the fabric of the universe might be twisting rather than just bending.
$f(T) = T + \xi T^\beta$ gravity: This is the specific mathematical model used in the paper. The parameters $\xi$ and $\beta$ are constants that allow researchers to 'tweak the strength of that twist' (torsion), enabling tests of how much extra torsion might be needed to explain physical phenomena.
Compact Stars: These are incredibly dense objects, such as neutron stars, which represent extreme limits in physics. The study uses these stars to test how different gravity models predict their structure and maximum possible mass.
Mass at Infinity ($M_\infty$): Because the space outside the star is affected by torsion in this theory, the standard method of calculating mass does not work. Therefore, researchers must calculate the mass as observed by an observer far away from the star, which is denoted as $M_\infty$.

Terminology

General Relativity — 17× in this paper
Equation of State (EoS) — 1× in this paper · explained in 4 episodes

Summary

This paper investigates Compact stars in f(T) = T + xi T beta gravity, aiming to "generalise such extension considering compact stars in f(T) = T + xi T beta gravity, where xi and beta are real constants and looking out for the implications in their maximum masses and compactness in comparison to the General Relativity. While the Teleparallel Theory is equivalent to General Relativity, the authors note that whereas in the latter gravity has to do with curvature, in the former gravity is described by torsion." The study extends previous research that focused on the quadratic case, f(T) = T + xi T squared, to a more general power-law model.

The theoretical framework utilizes a spherically symmetric metric and a specific nondiagonal (rotated) tetrad to recover spherically symmetric solutions in vacuum. The model is defined by the functional form f(T) = T + xi T beta. The authors derive a non-trivial system of equations involving A', B, B', xi, beta, P and rho, which are used to model the structure of a spherically symmetrical object that is in hydrostatic equilibrium.

A significant portion of the paper addresses the problem of mass definition in theories with torsion. The authors state that unlike the GR where the mass is unambiguously given, in f(T) models this is considered an open question. Because the vacuum space-time is not given by the Schwarzschild metric in this theory, the authors argue that the most appropriated way to calculate mass in f(T) gravity seems to consider the mass measured by an observer at infinity: M infinity = r to infinity r over 2 B(r). Additionally, they consider the total rest mass M 0, defined by dM 0 = 4 pi rho 0 e B/2 r squared dr.

For numerical modeling, the authors adopt a polytropic EOS given by P = k rho 0 gamma, specifically setting n = 1 (which corresponds to gamma = 2) and using dimensionless forms where k = G = c = 1. The authors conclude that beta must be a positive integer to solve the differential equations, noting that we are led to constrain the beta parameter to positive integers which is a restriction not imposed by cosmology.

The numerical results reveal that even and odd values of beta have very different behaviours. For the case where xi = 0.05:

Even beta ’s generate sequences bellow the GR sequence and present maximum masses.
Odd beta ’s generate sequences above that of GR and do not have maximum masses.

This occurs because "for xi > 0 the torsion is more negative for odd beta ’s, making the gravitational interaction... more intense, which allows the objects [to] be much more compact than those predicted by GR."

When xi = -0.05, the roles of odd and even beta ’s are reversed. The study further demonstrates that the models are highly sensitive to the parameters, noting that the calculations are even more sensitive to xi as beta increases.

In summary, the authors find that the functional form of f(T) in power-law of T can change significantly the limits of mass and compactness of the star. Specifically, "if xi T beta < 0, there is no maximum mass and the stars are increasingly compact. Conversely, models for xi T beta > 0 generate sequences bellow those of General Relativity and present maximum masses, although lower than that of General Relativity."

Improvements for AI systems

(Warning: The following improvements involve developing entirely new modules for a General AI system, requiring massive computational resources and novel mathematical frameworks.)

Based on the advanced theoretical physics presented in these references (especially concerning f(T) gravity, compact object structure, and numerical relativity), the current AI architecture must be upgraded from a general pattern-matching system to a Constraint-Driven Theoretical Physics Simulator (CDTPS).

The AI requires a specialized module capable of solving coupled, non-linear Partial Differential Equations (PDEs) derived from modified field theories, specifically those involving the f(T) Lagrangian density. This moves beyond standard numerical solvers by incorporating geometric constraints inherent to modified gravity.

What the Improved AI System Can Do:

Predict Compact Object Structure: The system can solve the generalized Tolman-Oppenheimer-Volkoff (TOV) equations for exotic matter (like quark or boson stars) under arbitrary f(T) modifications. It can output precise, stable mass-radius relationships (M(R) curves) for neutron stars and quark stars, allowing direct comparison with observational limits (e.g., maximum observed masses).
Determine Stability Boundaries: It can calculate the onset of gravitational collapse or phase transitions within these objects by analyzing the stability of solutions to the governing PDEs.
Handle Heterogeneous Equations of State (EoS): The AI can integrate multiple, complex EoS inputs (e.g., polytropic vs. realistic nuclear matter models) into a single, self-consistent simulation framework, drastically reducing the iterative time required by human research groups.

The AI must be upgraded with a high-dimensional Bayesian inference module that treats multiple, disparate physical observations as simultaneous constraints on a single theoretical model parameter space (e.g., the coefficients alpha, beta in f(T) = T + alpha T squared + beta O(T)).

This module combines symbolic computation with graph theory to systematically explore the landscape of possible gravitational theories, moving beyond simply analyzing known f(T) forms.

Abstract

The Teleparallel Theory is equivalent to General Relativity, but whereas in the latter gravity has to do with curvature, in the former gravity is described by torsion. As is well known, there is in the literature a host of alternative theories of gravity, among them the so called extended theories, in which additional terms are added to the action, such as for example in the f(R) and f(T) gravities, where R is the Ricci scalar and T is the scalar torsion, respectively. One of the ways to probe alternative gravity is via compact objects. In fact, there is in the literature a series of papers on compact objects in f(R) and f(T) gravity. In particular, there are several papers that consider f(T) = T + ξT squared, where ξ is a real constant. In this paper, we generalise such extension considering compact stars in f (T) = T + ξT β gravity, where ξ and β are real constants and looking out for the implications in their maximum masses and compactness in comparison to the General Relativity. Also, we are led to constrain the β parameter to positive integers which is a restriction not imposed by cosmology.