Buchdahl limit of compact stars in presence of Weyl anomaly

We have derived the Buchdahl's limit for a relativistic star in presence of the Kalb-Ramond field in four as well as in higher dimensions. It turns out that the Buchdahl's limit gets severely affected by the inclusion of the Kalb-Ramond field. In particular, the Kalb-Ramond field in four spacetime dimensions enables one to pack extra mass in any compact stellar structure of a given radius. On the other hand, a completely opposite picture emerges if the Kalb-Ramond field exists in higher dimensions, where the mass content of a compact star is smaller compared to that in general relativity. Implications are discussed.

A breakthrough has been achieved in solving the Einstein field equations for a specific class of charged compact objects existing in higher dimensions with inhomogeneous matter distribution. The geometry of space-time is believed to be spheroid, encapsulated in [Formula: see text] dimensions of Euclidean space where [Formula: see text], [Formula: see text] be the space-time dimension. The internal physical [Formula: see text] space is elucidated by the Vaidya–Tikekar metric ansatz, which is defined by spheroidal and curvature parameters. The form of the equation of state in MIT bag model, [Formula: see text], where the constant [Formula: see text] is termed as bag constant, is implemented to investigate the relevant physical features of anisotropic strange quark stars containing a net amount of charge. The inclusion of higher dimensions effectively decreases the mass retained within a given radius of a compact object but increases its compactness. For a particular dimension, if one increases the value of [Formula: see text], the mass increases for a given value of radius. Determination of maximum radius and consequently, maximum mass have been obtained by equating the value of radial sound velocity as the extreme limit of causality [Formula: see text] at the center of the star. Both the maximum mass and radius of a given compact object are found to increase when both charge and pressure anisotropy increase and decrease for an increment of surface density or bag constant [Formula: see text]. The maximum mass attained in the model is [Formula: see text]. Prediction of the radius of some recently observed compact objects has also been done for different [Formula: see text], [Formula: see text], charge and pressure anisotropy parameters. Different energy conditions and stability criteria stand up throughout the compact object containing anisotropy in pressure and net charge. The tidal deformability of some compact objects has also been investigated using the present model.

In the present article a new generalised solution is obtained for anisotropic matter configuration using Karmarkar’s condition. The solution is used to model the interior structure of anisotropic relativistic objects as it satisfies all necessary physical conditions. The pressure, density and metric potentials are free from any singularities and exhibit well behaved nature inside the anisotropic fluid sphere. The TOV equation is well maintained within the stellar configuration and all energy conditions hold good. The causality condition is well satisfied for our stellar models and stability of compact star models is further verified via Herrera’s cracking method. Harrison-Zeldovich-Novikov criterion for stability is also satisfied by our model. The adiabatic index is greater than $\frac{4}{3}$ throughout the stellar interior and the compactification factor also lies within the Buchdahl limit i.e. $M/R \le 4/9$ . We investigate the models for two compact stars PSRJ0348+0432 and SAX J1808.4-3658 within the framework of the general theory of relativity. The estimated mass and radius are in close agreement with the observational data. we extensively study the solutions corresponding to compact star PSRJ0348+0432 for $ n = 0, 1, 2, 3, 4, 4.5$ and the detailed graphical analysis is provided to substantiate the viability of the compact star model. One specific feature of our solution is that for large values of n, i.e. for $ n > 5$ solution reduces to Finch and Skea type solution.

After a critical overview of the generalized uncertainty principle (GUP) applied to compact objects, we propose a texture of Heisenberg uncertainty principle in curved spacetimes (CHUP). CHUP allows to write down physically motivated STUR (spacetime uncertainty relations) in a generic background for a non commutative spacetime in terms of tetrad variables. In order to study possible quantum effects for compact astrophysical objects as white dwarf, neutron stars and black holes, an expression for quantum fluctuations is outlined. As a result, contrary to GUP-based claims, we found no evidence for quantum effects concerning equilibrium equation and critical mass M c for white dwarf and neutron stars. Conversely, our expression for CHUP confirms that general relativistic effects strongly reduce the Oppenheimer–Volkoff Newtonian limit for very compact astrophysical objects as neutron stars. In particular, we found that for a degenerate relativistic Fermi gas, the maximum mass decreases for increasing compactness of the star with a minimum critical mass M c ≃ 0.59M ⊙ at the Buchdahl limit. Finally, we study possible non commutative effects near the event horizon of a black hole.

We explore a class of compact charged spheres made of a charged perfect fluid with a polytropic equation of state. The charge density is chosen to be proportional to the energy density. The study is performed by solving the Tolman-Oppenheimer-Volkoff (TOV) equation which describes the hydrostatic equilibrium. We show the dependence of the structure of the spheres for several characteristic values of the polytropic exponent and for different values of the charge densities. We also study other physical properties of the charged spheres, such as the total mass, total charge, radius and sound speed and their dependence on the polytropic exponent. We find that for the polytropic exponent \gamma=4/3 the Chandrasekhar mass limit coincides with the Oppenheimer-Volkoff mass limit. We test the Oppenheimer-Volkoff limit for such compact objects. We also analyze the Buchdahl limit for these charged polytropic spheres, which happens in the limit of very high polytropic exponents, i.e., for a stiff equation of state. It is found that this limit is extremal and it is a quasiblack hole.

This work is devoted to present a new solution of field equations in the Rastall paradigm for isotropic matter content with quintessence field specified by the parameter $$\omega _q$$ with the condition $$-1<\omega _q<-\frac{1}{3}$$ . In order to obtain relativistic analytic solution, we used the Krori and Barua (KB) insatz in the static and spherically symmetric geometry. The obtained results analyzed analytically and graphically for the physical assessment. It is shown that for a suitable choice of coupling parameter, the original results in the standard general relativity (GR) can be retrieved. We provide a comparative study of acquired results in both the aspects, graphically and numerically with the observational evidences and GR counterpart. The comparative study shown that our obtained model is in good concurrence with the observational data in comparison with the GR. For this whole analysis, we considered five different compact stars namely, SAX J1808-3658 (SSI), Vela X-12, Her X-1, PSR J1416-2230 and 4U 1820-30 with radii 7.07 km, 9.99 km, 7.7 km, 10.3 km and 10 km, respectively. To check the viability of the presented model, we investigate different physical parameters such as energy conditions, stability analysis (via. sound speed and adiabatic index), Buchdahl limit, hydrostatic equilibrium of forces. We found that presented model is totally stable and well consistent with the plausible physical conditions.

A new exact solution of embedding class I is presented for a relativistic anisotropic massive fluid sphere. The new exact solution satisfies Karmarkar condition, is well-behaved in all respects, and therefore is suitable for the modelling of superdense stars. Consequently, using this solution, we have studied in detail two compact stars, namely, XTE J1739-289 (strange star $$1.51M_{\odot }$$ , 10.9 km) and PSR J1614-2230 (neutron star $$1.97M_{\odot }$$ , 14 km). The solution also satisfies all energy conditions with the compactness parameter lying within the Buchdahl limit.

In this paper, we explore anisotropic compact stellar models in the framework of general theory of relativity with [Formula: see text] component governed by Buchdahl ansatz. We choose the anisotropic factor such as to render the solution physically compatible for stellar modeling. We have analyzed the solution for different values of [Formula: see text] to demonstrate the profiles of thermodynamical variables. The stability of the proposed models has been verified using different stability criteria. The hydrostatic equilibrium condition is well retained by the models studied in this work. The Buchdahl limit is well obeyed by the proposed models. The models of four compact stars viz., PSR J1614-2230, Vela X-1, Cen X-3 and SMC X-4 are extensively analyzed in close agreement with their observational details.

In this paper, we generate a new generalized solution for modeling of compact anisotropic astrophysical configurations by using Karmarkar condition of embedded class 1 spacetime manifold. We demonstrate that the new solution satisfies all required physical conditions. We investigate several physical properties of compact star models, i.e. Vela X-1 (Mass [Formula: see text][Formula: see text], radius = [Formula: see text][Formula: see text]km), PSRJ [Formula: see text] (Mass [Formula: see text][Formula: see text], radius = [Formula: see text][Formula: see text]km) and PSRJ [Formula: see text] (Mass [Formula: see text][Formula: see text], radius = [Formula: see text][Formula: see text]km) in conformity with the observational data. The proposed solution is free from singularities, satisfies causality condition and displays well-behaved nature inside the anisotropic configurations. All energy conditions and hydrostatic equilibrium condition are well defined inside the anisotropic fluid spheres. The adiabatic index throughout the stellar interior is greater than [Formula: see text] and the compactification factor lies within the Buchdahl limit [Formula: see text]. We study the physical features of the solution in detail, analytically as well as graphically for compact star Vela X-1 with [Formula: see text] ranging from [Formula: see text] to [Formula: see text].

Finch–Skea quintessence models in non-conservative theory of gravity

Very compact stars seem to be forbidden in General Relativity. While Buchdahl's theorem sets an upper bound on compactness, further no-go results rely on the existence of two light rings, the inner of which has been associated to gravitational instabilities. However, little is known about the role of quantum fields in these strong gravity regimes. Here, we consider the particularly simple model of a constant density star and we work in the probe approximation where the backreaction is ignored. We show that the trapping of modes inside the star leads the renormalized stress tensor of Conformal Field Theories to diverge faster than the classical source in the Buchdahl limit. This leads to the violation of the Null Energy Condition around the inner light ring. The backreaction of quantum fields in this regime therefore cannot be ignored. This happens as the star's surface approaches the Buchdahl radius 9GM/4 rather than the Schwarzschild radius. The results are independent of the details of the interactions, but contain an ambiguity associated to the renormalization scheme.

Regarding the strong magnetic field of neutron stars and the high-energy regime scenario that is based on the high-curvature region near the compact objects, one is motivated to study magnetic neutron stars in an energy-dependent spacetime. In this paper, we show that such a strong magnetic field and energy dependency of spacetime have considerable effects on the properties of neutron stars. We examine the variations of maximum mass and related radius, Schwarzschild radius, average density, gravitational redshift, Kretschmann scalar, and Buchdahl theorem due to the magnetic field and energy dependency of the metric. First, it will be shown that the maximum mass and radius of neutron stars are increasing functions of the magnetic field, while average density, redshift, strength of gravity, and Kretschmann scalar are decreasing functions of it. These results are due to a repulsive-like force behavior for the magnetic field. Next, the effects of gravity’s rainbow will be studied, and it will be shown that by increasing the rainbow function, the neutron stars could enjoy an expansion in their structures. Then, we obtain a new relation for the upper mass limit of a static spherical neutron star with uniform density in gravity’s rainbow (Buchdahl limit) in which such an upper limit is modified as . In addition, stability and energy conditions for the equation of state of neutron star matter are investigated, and a comparison with empirical results is done. It is notable that the numerical study in this paper is conducted by using the lowest-order constrained variational approach in the presence of a magnetic field employing AV 18 potential.

We study equilibrium configurations of a homogenous ball of matter in a bootstrapped description of gravity which includes a gravitational self-interaction term beyond the Newtonian coupling. Both matter density and pressure are accounted for as sources of the gravitational potential for test particles. Unlike the general relativistic case, no Buchdahl limit is found and the pressure can in principle support a star of arbitrarily large compactness. By defining the horizon as the location where the escape velocity of test particles equals the speed of light, like in Newtonian gravity, we find a minimum value of the compactness for which this occurs. The solutions for the gravitational potential here found could effectively describe the interior of macroscopic black holes in the quantum theory, as well as predict consequent deviations from general relativity in the strong field regime of very compact objects.

In this paper we used the theory of adiabatic radial oscillations developed by Chandrasekhar to study the conditions for dynamical stability of constant energy-density stars, or Schwarzschild stars, in the unstudied ultra compact regime beyond the Buchdahl limit, that is, for configurations with radius R in the range , where is the Schwarzschild radius of the star. These recently found analytical solutions exhibit a negative pressure region in their centre and, in the limit when , the full interior region of the star becomes filled with negative pressure. Here we present a systematic analysis of the stability of these configurations against radial perturbations. We found that, contrary to the usual expectation found in many classical works, the ultra compact Schwarzschild star is stable against radial oscillations. We computed values of the critical adiabatic index for several stellar models with varying radius and found that it also approaches a finite value as .

One of the macroscopically measurable effects of gravity is the tidal deformability of astrophysical objects, which can be quantified by their tidal Love numbers. For planets and stars, these numbers measure the resistance of their material against the tidal forces, and the resulting contribution to their gravitational multipole moments. According to general relativity, nonrotating deformed black holes, instead, show no addition to their gravitational multipole moments, and all of their Love numbers are zero. In this paper we explore different configurations of nonrotating compact and ultracompact stars to bridge the compactness gap between black holes and neutron stars and calculate their Love number k 2. We calculate k 2 for the first time for uniform density ultracompact stars with mass M and radius R beyond the Buchdahl limit (compactness M/R > 4/9), and we find that k 2 → 0+ as M/R → 1/2, i.e., the Schwarzschild black hole limit. Our results provide insight on the zero tidal deformability limit and we use current constraints on the binary tidal deformability from GW170817 (and future upper limits from binary black hole mergers) to propose tests of alternative models.