article · The European Physical Journal C
Testing modifications to general relativity requires observing extreme environments, such as massive neutron stars, that cannot be recreated in terrestrial laboratories. Using a linear modified gravity framework where geometry couples directly with matter, an exact analytical solution has been derived for anisotropic fluid spheres in hydrostatic equilibrium without relying on assumptions regarding the equation of state. Observational data for the massive pulsar PSR J0740+6620 from space telescopes establish an upper bound on the theory's dimensional coupling parameter. Because the coupling between matter and geometry introduces an additional force that partially counteracts gravity, the model predicts that stars of a given mass are slightly larger than general relativity predicts. Under this theory, the maximum permissible compactness reaches 0.757, approximately three percent higher than standard relativistic limits, allowing a theoretical maximum stellar mass of around 4.26 solar masses.
Neutron stars represent some of the most extreme physical environments in the observable universe, offering conditions impossible to reproduce on Earth. Investigating how these dense objects behave helps scientists test the boundaries of Einstein's general relativity. Refining such gravitational theories improves fundamental understanding of how matter and spacetime interact under extreme densities, shaping broader models of the cosmos and astrophysical phenomena.
The abstract does not indicate an application pathway, as this research focuses exclusively on fundamental theoretical astrophysics and gravitational physics.
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Abstract Many physically inspired general relativity (GR) modifications predict significant deviations in the properties of spacetime surrounding massive neutron stars. Among these modifications is $$f({\mathcal {R}}, {\mathbb {T}})$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>f</mml:mi> <mml:mo>(</mml:mo> <mml:mi>R</mml:mi> <mml:mo>,</mml:mo> <mml:mi>T</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> , where $${\mathcal {R}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>R</mml:mi> </mml:math> is the Ricci scalar, $$ {\mathbb {T}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>T</mml:mi> </mml:math> is the trace of the energy–momentum tensor, the gravitational theory that is thought to be a neutral extension of GR. Neutron stars with masses above 1.8 $$M_{\odot }$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>M</mml:mi> <mml:mo>⊙</mml:mo> </mml:msub> </mml:math> expressed as radio pulsars are precious tests of fundamental physics in extreme conditions unique in the observable universe and unavailable to terrestrial experiments. We obtained an exact analytical solution for anisotropic perfect-fluid spheres in hydrostatic equilibrium using the frame of the linear form of $$f({\mathcal {R}},{\mathbb {T}})={\mathcal {R}}+\beta {\mathbb {T}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>f</mml:mi> <mml:mo>(</mml:mo> <mml:mi>R</mml:mi> <mml:mo>,</mml:mo> <mml:mi>T</mml:mi> <mml:mo>)</mml:mo> <mml:mo>=</mml:mo> <mml:mi>R</mml:mi> <mml:mo>+</mml:mo> <mml:mi>β</mml:mi> <mml:mi>T</mml:mi> </mml:mrow> </mml:math> where $$\beta $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>β</mml:mi> </mml:math> is a dimensional parameter. We show that the dimensional parameter $$\beta $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>β</mml:mi> </mml:math> and the compactness, $$C=\frac{2GM}{Rc^2}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>C</mml:mi> <mml:mo>=</mml:mo> <mml:mfrac> <mml:mrow> <mml:mn>2</mml:mn> <mml:mi>G</mml:mi> <mml:mi>M</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>R</mml:mi> <mml:msup> <mml:mi>c</mml:mi> <mml:mn>2</mml:mn> </mml:msup> </mml:mrow> </mml:mfrac> </mml:mrow> </mml:math> can be used to express all physical quantities within the star. We fix the dimensional parameter $$\beta $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>β</mml:mi> </mml:math> to be at most $$\beta _1=\frac{\beta }{\kappa ^2}= 0.1$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>β</mml:mi> <mml:mn>1</mml:mn> </mml:msub> <mml:mo>=</mml:mo> <mml:mfrac> <mml:mi>β</mml:mi> <mml:msup> <mml:mi>κ</mml:mi> <mml:mn>2</mml:mn> </mml:msup> </mml:mfrac> <mml:mo>=</mml:mo> <mml:mn>0.1</mml:mn> </mml:mrow> </mml:math> in positive values through the use of observational data from NICER and X-ray Multi-Mirror telescopes on the pulsar $${\textit{PSR J0740+6620}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>PSR J</mml:mi> <mml:mn>0740</mml:mn> <mml:mo>+</mml:mo> <mml:mn>6620</mml:mn> </mml:mrow> </mml:math> , which provide information on its mass and radius. The mass and radius of the pulsar $${\textit{PSR J0740+6620}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>PSR J</mml:mi> <mml:mn>0740</mml:mn> <mml:mo>+</mml:mo> <mml:mn>6620</mml:mn> </mml:mrow> </mml:math> were determined by analyzing data obtained from NICER and X-ray Multi-Mirror telescopes. It is important to mention that no assumptions about equations of state were made in this research. Nevertheless, the model demonstrates a good fit with linear patterns involving bag constants. Generally, when the dimensional parameter $$\beta $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>β</mml:mi> </mml:math> is positive, the theory predicts that a star of the same mass will have a slightly larger size than what is predicted by GR. It has been explained that the hydrodynamic equilibrium equation includes an additional force resulting from the coupling between matter and geometry. This force partially reduces the effect of gravitational force. As a result, we compute the maximum compactness allowed by the strong energy condition for $$f({\mathcal {R}}, {\mathbb {T}})={\mathcal {R}}+\beta {\mathbb {T}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>f</mml:mi> <mml:mo>(</mml:mo> <mml:mi>R</mml:mi> <mml:mo>,</mml:mo> <mml:mi>T</mml:mi> <mml:mo>)</mml:mo> <mml:mo>=</mml:mo> <mml:mi>R</mml:mi> <mml:mo>+</mml:mo> <mml:mi>β</mml:mi> <mml:mi>T</mml:mi> </mml:mrow> </mml:math> and for GR, which are $$C = 0.757$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>C</mml:mi> <mml:mo>=</mml:mo> <mml:mn>0.757</mml:mn> </mml:mrow> </mml:math> and 0.725, respectively. These values are approximately 3% higher than the prediction made by GR.. Furthermore, we estimate the maximum mass $$M\approx 4.26 M_{\odot }$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>M</mml:mi> <mml:mo>≈</mml:mo> <mml:mn>4.26</mml:mn> <mml:msub> <mml:mi>M</mml:mi> <mml:mo>⊙</mml:mo> </mml:msub> </mml:mrow> </mml:math> at a radius of $$R\approx 15.9$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>R</mml:mi> <mml:mo>≈</mml:mo> <mml:mn>15.9</mml:mn> </mml:mrow> </mml:math> km for the surface density at saturation nuclear density <jats:alternati
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DOI: 10.1140/epjc/s10052-023-11882-4
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