f(R,T)引力下的白矮星平衡构型探讨：超越传统重力理论

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本文主要探讨了在f(R, T)引力理论框架下的白矮星的恒星平衡构型。这种引力理论是对传统广义相对论（GR）的一种扩展，考虑了Ricci标量R和能量动量张量T的非线性耦合。具体来说，研究者采用了一个特定的形式f(R, T) = R + 2ΔT，其中Δ是一个常数，这使得他们能够推导出该理论下的静水力平衡方程。在研究过程中，作者计算并分析了白矮星的关键物理特性，如质量、半径、压力和能量密度，这些属性随参数Δ的变化而变化。值得注意的是，当Δ取负值时，模型预测了更大的白矮星质量上限，这个极限超过了钱德拉塞卡极限，这是GR中白矮星最大质量的经典界限。同时，与标准GR结果相比，f(R, T)理论中的白矮星半径会有所增大，而中心密度则降低，这表明其对星体结构的影响独特。相比于传统的GR，f(R, T)理论对白矮星形态的主要影响体现在半径的增大上，这可能暗示着在引力作用上存在额外的修正。通过将理论预测与实际观测到的大量白矮星数据进行比较，研究人员设定了一个参数α的下限，即α > -3×10^-4，这为理论与观测的一致性提供了约束。这篇文章发表于《欧洲物理杂志C》(Eur. Phys. J. C) 2017年，是一篇开放获取的研究，由来自巴西、意大利和秘鲁的多个研究机构的科学家共同完成。他们的工作不仅深化了对白矮星物理学的理解，也为引力理论的拓展提供了实验证据。整个研究过程包括理论建模、数值计算以及与现实观测数据的比较，展示了f(R, T)引力对天体物理学的重要贡献。

Eur. Phys. J. C (2017) 77:871

https://doi.org/10.1140/epjc/s10052-017-5413-5

Regular Article - Theoretical Physics

Stellar equilibrium conﬁgurations of white dwarfs in the f (R, T)

gravity

G. A. Carvalho

1,a

, R. V. Lobato

1,2,3

, P. H. R. S. Moraes

, José D. V. Arbañil

, E. Otoniel

R. M. Marinho Jr

, M. Malheiro

Departamento de Física, Instituto Tecnológico de Aeronáutica, São José dos Campos, SP 12228-900, Brazil

Dipartimento di Fisica, Sapienza Università di Roma, P.le Aldo Moro 5, 00185 Rome, Italy

ICRANet, P.zza della Repubblica 10, 65122 Pescara, Italy

Departamento de Ciencias, Universidad Privada del Norte, Avenida Alfredo Mendiola 6062 Urbanización Los Olivos, Lima, Peru

Instituto de Formação de Professores, Universidade Federal do Cariri, Brejo Santo, CE 63260-000, Brazil

Received: 9 October 2017 / Accepted: 23 November 2017 / Published online: 15 December 2017

Abstract In this work we investigate the equilibrium con-

ﬁgurations of white dwarfs in a modiﬁed gravity theory, na-

mely, f (R, T ) gravity, for which R and T stand for the Ricci

scalar and trace of the energy-momentum tensor, respec-

tively. Considering the functional form f (R, T ) = R +2λT ,

with λ being a constant, we obtain the hydrostatic equilibrium

equation for the theory. Some physical properties of white

dwarfs, such as: mass, radius, pressure and energy density,

as well as their dependence on the parameter λ are derived.

More massive and larger white dwarfs are found for negative

values of λ when it decreases. The equilibrium conﬁgurations

predict a maximum mass limit for white dwarfs slightly above

the Chandrasekhar limit, with larger radii and lower central

densities when compared to standard gravity outcomes. The

most important effect of f (R, T ) theory for massive white

dwarfs is the increase of the radius in comparison with GR

and also f (R) results. By comparing our results with some

observational data of massive white dwarfs we also ﬁnd a

lower limit for λ, namely, λ>−3 ×10

−4

1 Introduction

White dwarfs (WDs) are the ﬁnal evolution state of main

sequence stars with initial masses up to 8.5–10.6 M



.They

correspond to 95–97% of all observed stars in the Universe

[1]. The main sequence progenitors can reach sufﬁciently

high core temperatures (8–12×10

K), to proceed to carbon

burning and produce either oxygen-neon (ONe) core WDs or

undergo a core-collapse supernova (SNII) via electron cap-

ture on the products of carbon burning.

e-mail: araujogc@ita.br

Chandrasekhar has shown that a WD cannot sustain a mass

over 1.44M



, establishing the so-called Chandrasekhar mass

limit [2]. If a WD grows over this limit, as in binary systems

in which a WD is receiving mass from a nearby star, a type Ia

supernova (SNIa) explosion may occur. SNIa progenitors are

expectedto be similar, with nearly equal luminosity,therefore

being considered standard candles [3]. In fact, in the late

1990s, the use of SNIa led to the discovery that the expansion

of the Universe is accelerating [4,5].

Nevertheless, some super luminous SNIas were found

recently [6,7]. It has been suggested that their progenitors

are WDs that exceed the Chandrasekhar mass limit (2.1–2.8

)[6–11], being termed “super-Chandrasekhar WDs”.

WDs usually are not considered as a “laboratory” for

strong ﬁeld regimes. However, general relativistic effects

have shownto be non-negligible in the massive and very mag-

netic WD regime [12–16]. Particularly, it has been shown in

[13] and [17] that the inclusion of general relativistic effects

tends to reduce the maximum mass of WDs with strong mag-

netic ﬁelds. Chandrasekhar and Tooper showed that instabil-

ity criteria for WDs under radial oscillations in a general

relativistic framework has its consequences for critical cen-

tral density depending on the composition of the star [18,19].

Moreover, in [20–22] it was shown that this critical central

density yields a larger minimum radius in comparison with

Newtonian gravity outcomes.

On this regard,despite the detection of gravitational waves

[23] and innumerable other positive results, as one can check,

for instance, in [24], there are two cosmological phenomena,

namely dark energy and dark matter, not well understood

within the General Relativity (GR) framework. Such a dark

sector of the universe composition is a possible indication

123

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