The secondary component of GW190814 has mass in the range $2.5$--$2.67{\rm M}_\odot$, placing it within the lower mass gap separating neutron stars from black holes. According to the predictions of general relativity and state-of-the-art nuclear equations of state, this object is too heavy to be a neutron star.~In this work, we explore the possibility that this object is a neutron star under the hypothesis that general relativity is modified to include screening mechanisms, and that the neutron star formed in an unscreened environment. We introduce a set of parameterized-post-Tolman-Oppenheimer-Volkoff (post-TOV) equations appropriate for screened modified gravity whose free parameters are environment-dependent. We find that it is possible that the GW190814 secondary could be a neutron star that formed in an unscreened environment for a range of reasonable post-TOV parameters.
We construct a covariant version of the Tolman-Oppenheimer-Volkoff equations in the case of isotropic sources. The new equations make evident the mathematical problems in the determination of interior solutions of relativistic stellar objects. Using a reconstruction algorithm we find two physically interesting generalisations of previously known stellar interior solutions. The variables that we use also allow an easier formulation of known generating theorems for solutions associated to relativistic stellar objects.
We generalise the covariant Tolman-Oppenheimer-Volkoff equations proposed in arXiv:1709.02818 [gr-qc] to the case of static and spherically symmetric spacetimes with anisotropic sources. The extended equations allow a detailed analysis of the role of the anisotropic terms in the interior solution of relativistic stars and lead to the generalisation of some well known solutions of this type. We show that, like in the isotropic case, one can define generating theorems for the anisotropic Tolman-Oppenheimer-Volkoff equations. We also find that it is possible to define a reconstruction algorithm a…
Based on a stringy inspired Gauss-Bonnet (GB) modification of classical gravity, we constructed a model for neutron stars. We derived the modified forms of Tolman-Oppenheimer-Volkoff (TOV) equations for a generic function of $f(G)$ gravity. The hydrostatic equations remained unchanged but the dynamical equations for metric functions are modified due to the effects of GB term.
The bulk properties of spherically symmetric stars in general relativity can be obtained by integrating the Tolman-Oppenheimer-Volkoff (TOV) equations. In previous work we developed a "post-TOV" formalism - inspired by parametrized post-Newtonian theory - which allows us to classify in a parametrized, phenomenological form all possible perturbative deviations from the structure of compact stars in general relativity that may be induced by modified gravity at second post-Newtonian order. In this paper we extend the formalism to deal with the stellar exterior, and we compute several potential as…
In this paper, we discuss the internal and external metric of the semi-realistic stars in relativistic MOND theory. We show the Oppenheimer-Volkoff equation in relativistic MOND theory and get the metric and pressure inside the stars to order of post-Newtonian corrections. We study the features of motion around the static, spherically symmetric stars by Hamilton-Jacobi mothod, and find there are only some small corrections in relativistic MOND theory.
We rewrite the Tolman -- Oppenheimer -- Volkoff (TOV) equations for four and higher dimensional static spherically symmetric stars so that they resemble the equations for anisotropic cosmology. This becomes possible by treating the curvature terms of the sphere as part of the matter sector. Comparing then with the effective equations in the Loop Quantum Cosmology -- inspired models, we propose analogous modifications to the TOV equations which contain one arbitrary function. A linear function gives the TOV equations. If the function and all its derivatives are finite then the solutions are non…
We connect two formalisms that describe deformations away from general relativity, one valid in the strong-field regime of neutrons stars and another valid in the radiative regime of gravitational waves: the post-Tolman-Oppenheimer-Volkoff and the parametrized-post-Einsteinian formalisms respectively. We find that post-Tolman-Oppenheimer-Volkoff deformations of the exterior metric of an isolated neutron star induce deformations in the orbital binding energy of a neutron star binary. Such a modification to the binding energy then percolates into the gravitational waves emitted by such a binary,…
We investigate in this paper the structures of neutron and quark stars in f(T) theory of gravity where T denotes the torsion scalar. Attention is attached to the TOV type equations of this theory and numerical integrations of these equations are performed with suitable EoS. We search for the deviation of the mass-radius diagrams for power-law and exponential type correction from the TT gravity. Our results show that for some values of the input parameters appearing in the considered models, f(T) theory promotes more the structures of the relativistic stars, in consistency with the observationa…
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 spee…
Besides their astrophysical interest, compact stars also provide an arena for understanding the properties of theories of gravity that differ from Einstein's general relativity. Numerous studies have shown that different modified theories of gravity can modify the bulk properties (such as mass and radius) of neutron stars for given assumptions on the microphysics. What is not usually stressed though is the strong degeneracy in the predictions of these theories for the stellar mass and radius. Motivated by this observation, in this paper we take an alternative route and construct a stellar stru…
Motivated by previous studies in literature about the potential importance of relativistic corrections to galaxy cluster hydrostatic masses, we calculate the masses of 12 relaxed clusters (with Chandra X-ray data) using the Tolman-Oppenheimer-Volkov (TOV) equation of hydrostatic equilibrium and the ideal gas equation of state. Analytical formulae for gas density and temperature profiles for these clusters, previously derived by Vikhlinin et al (astro-ph/0507092) were used to obtain these masses. We compare the TOV-based masses with those obtained using the corresponding Newtonian equation of h…
We investigate the Tolman-Oppenheimer-Volkoff equations for the generalized Chaplygin gas with the aim of extending the findings of V. Gorini, U. Moschella, A. Y. Kamenshchik, V. Pasquier, and A. A. Starobinsky [Phys. Rev. D {\bf 78}, 064064 (2008)]. We study both the standard case, where we reproduce some previous results, and the phantom case. In the phantom case we show that even a superluminal group velocity arising for $α> 1$ cannot prevent the divergence of the pressure at a finite radial distance. Finally, we investigate how a modification of the generalized Chaplygin gas equation of st…
The Tolman-Oppenheimer-Volkoff (TOV) equation admits singular solutions in addition to regular ones. Here, we prove the following theorem. For any equation of state that (i) is obtained from an entropy function, (ii) has positive pressure and (iii) satisfies the dominant energy condition, the TOV equation can be integrated from a boundary inwards to the center. Hence, thermodynamic consistency of the EoS precludes pathological solutions, in which the integration terminates at finite radius (because of horizons, or divergences / zeroes of energy density). At the center, the mass function either…
We investigate spherically symmetric perfect-fluid spacetimes and discuss the existence and stability of a dividing shell separating expanding and collapsing regions. We perform a 3+1 splitting and obtain gauge invariant conditions relating the intrinsic spatial curvature of the shells to the Misner-Sharp mass and to a function of the pressure that we introduce and that generalizes the Tolman-Oppenheimer-Volkoff equilibrium condition. We find that surfaces fulfilling those two conditions fit, locally, the requirements of a dividing shell and we argue that cosmological initial conditions should…
Recently, the covariant formulation of the Tolman-Oppenheimer-Volkoff (TOV) equations for studying the equilibrium structure of a spherically symmetric compact star in the presence of the pressure anisotropy in the interior of a star was presented in Phys. Rev. D \textbf{97} (2018) 124057. It was suggested there that the anisotropic solution of these equations can be obtained by finding, first, the solution of the common TOV equations for the isotropic pressure, and then by solving the differential equation for the anisotropic pressure whose particular form was established on the basis of the …
We investigate the existence of analytic solutions for the field equations in the Einstein-æther theory for a static spherically symmetric spacetime and provide a detailed dynamical system analysis of the field equations. In particular, we investigate if the gravitational field equations in the Einstein-æther model in the static spherically symmetric spacetime possesses the Painlevè property, so that an analytic explicit integration can be performed. We find that analytic solutions can be presented in terms of Laurent expansion only when the matter source consists of a perfect fluid with linea…
The torsion models have stood out among the proposals for an alternative description of gravity. The simplest of them, the Teleparallel theory, is equivalent to General Relativity and there are many studies that seek to study its extension to more general functions of the torsion $T$. The purpose of {our study } is to consider a family of $f(T)$ models and apply their corresponding Tolman-Oppenheimer-Volkof equations to compact objects such as neutron stars. Consequently, through a numerical analysis, calculate, among other things, the maximum mass allowed by the model for a neutron star, whic…
We study static solutions of the Tolman--Oppenheimer--Volkoff equations for spherically symmetric objects (stars) living in a space filled with the Chaplygin gas. Two cases are considered. In the normal case all solutions (excluding the de Sitter one) realize a three-dimensional spheroidal geometry because the radial coordinate achieves a maximal value (the "equator"). After crossing the equator, three scenarios are possible: a closed spheroid having a Schwarzschild-type singularity with infinite blue-shift at the "south pole", a regular spheroid, and a truncated spheroid having a scalar curva…
Non-local $f(R)$ gravity was proposed as a powerfull alternative to general relativity (GR) . This theory has potentially adverse implications for infrared (IR) regime as well as ultraviolent(UV) early epochs. However, there are a lot of powerful features, making it really user-friendly. A scalar-tensor frame comprising two auxiliary scalar fields, used to reduce complex action. However this is not the case for the modification complex which plays a distinct role in modified theories for gravity. In this work, we study the dynamics of a static, spherically symmetric object. The interior region…
There are many ways to probe alternative theories of gravity, namely, via: experimental tests at solar system scale, cosmological data and models, gravitational waves and compact objects. In the present paper we consider a model of gravity with torsion $f(T)$ applied to compact objects such as neutron stars (NSs) for a couple of realistic equations of state (EOS). To do so we follow our previous articles, in which we show how to model compact stars in this $f(T)$ gravity by obtaining its corresponding Tolman-Oppenheimer-Volkof equations and applying this prescription to model polytropic compac…
Corda, Mosquera Cuesta and Lorduy Gomez have shown that spherically symmetric stationary states can be used as a model for galaxies in the framework of the linearized R^2 gravity. Those states could represent a partial solution to the Dark Matter Problem. Here we discuss an improvement of this work. In fact, as the star density is a functional of the invariants of the associated Vlasov equation, we show that any of these invariants is in its turn a functional of the local energy and the angular momentum. As a consequence, the star density depends only on these two integrals of the Vlasov syste…
Stars are essentially gravitationally stabilised thermonuclear reactors in hydrostatic equilibrium. The fundamental differential equation for all Newtonian gaseous stars in equilibrium is \begin{align} \frac{dp(r)}{dr}=-\frac{\mathscr{G}\mathcal{M}(r)ρ(r)}{r^{2}}\nonumber \end{align} where $p(r),ρ(r)$ are the pressure, density at radius $r$ and $\mathcal{M}(r)$ is the mass contained within a shell of radius $r$ given by $\mathcal{M}(r)=\int_{0}^{r}4π\overline{r}^{2} ρ(\overline{r})d\overline{r}$, and $\mathscr{G}$ is Newton's constant. This simple but crucial differential equation for the pres…
The well-known equation for hydrostatic equilibrium in a static spherically symmetric spacetime supported by an isotropic perfect fluid is referred to as the Oppenheimer-Volkoff (OV) equation or the Tolman-Oppenheimer-Volkoff (TOV) equation in various General Relativity textbooks or research papers. We scrutinize the relevant original publications to argue that the former is the more appropriate terminology.
We argued previously that the well-known equation for hydrostatic equilibrium in a static spherically symmetric spacetime supported by an isotropic perfect fluid should be called the Oppenheimer-Volkoff (OV) equation, rather than the Tolman-Oppenheimer-Volkoff (TOV) equation, a later ArXiv manuscript has disagreed. Here we reply to that comment, reaffirming the original argument.
In a recent manuscript published in the Arxives (arXiv:1610.03049v1), it is claimed that it should be more appropriate to refer to the equation of hydrostatic equilibrium in a static spherically symmetric spacetime, supported by an isotropic perfect fluid, as the "Oppenheimer-Volkoff (OV) equation", instead of the "Tolman-Oppenheimer-Volkoff (TOV)", as is frequently done. As we shall see in this brief note, such a claim is not supported by the existing bibliography.
We consider a static self-gravitating system consisting of perfect fluid with isometries of an $(n-2)$-dimensional maximally symmetric space in Lovelock gravity theory. A straightforward analysis of the time-time component of the equations of motion suggests a generalized mass function. Tolman-Oppenheimer-Volkoff like equation is obtained by using this mass function and gravitational equations. We investigate the maximum entropy principle in Lovelock gravity, and find that this Tolman-Oppenheimer-Volkoff equation can also be deduced from the so called "maximum entropy principle" which is origi…
The Tolman-Oppenheimer-Snyder description gives exact analytical solutions for an Einstein-matter system describing total gravitational collapse of a zero-pressure perfect-fluid sphere, representing a massive star which has exhausted its nuclear fuel. The star collapses to a point of infinite density within a finite comoving proper time interval $[0,t_{*}]$, and the exterior metric matches the Schwarzchild black hole metric. The description is re-expressed in terms of a 'density function' $u(t)=(ρ(t)/ρ_{o}))^{1/3}=R^{-1}(t)$ for initial density $u_{0}=R^{-1}(0)=1$ and radius $R(0)$, whereby th…
Static thermal equilibrium of a quantum self-gravitating ideal gas in general relativity is studied at any temperature, taking into account the Tolman-Ehrenfest effect. Thermal contribution to the gravitational stability of static neutron cores is quantified. The curve of maximum mass with respect to temperature is reported. At low temperatures the Oppenheimer-Volkoff calculation is recovered, while at high temperatures the recently reported classical gas calculation is recovered. An ultimate upper mass limit $M = 2.43M_\odot$ of all maximum values is found to occur at Tolman temperature $ T =…
In this comment we discuss the application of homotopy perturbation method to a nonlinear differential mass equation that solves the Tolman-Oppenheimer-Volkoff equation for an isotropic and spherically symmetric system. We show that one obtains the same results, more easily and straightforwardly, by means of a textbook power-series method.
Models of neutron stars (NSs) with hyperon cores are constructed with an effective chiral model in mean-field approximation. The hyperon couplings are fixed by reproducing their experimentally determined binding energies. The impact of these couplings on population of different particles and the equation of state (EoS) are studied in this work. The global properties of NSs like gravitational mass, radius, baryonic mass and central density are calculated using parameterized Tolman-Oppenheimer-Volkoff equations (PTOV) with special emphasis on two effects of pressure - one contributing to total m…
We present interesting aspects of neutron stars (NSs) from the standpoint of a modified theory of gravity called Hořava-Lifshitz (HL) gravity. A deviation from general relativity (GR) in HL gravity can change typical features of the NS structure. In this study, we investigate the NS structure by deriving the Tolman-Oppenheimer-Volkoff equation in HL gravity. We find that a NS in HL gravity with a larger radius and heavier mass than a NS in GR remains stable without collapsing into a black hole.
We formulate the generalized Tolman-Oppenheimer-Volkoff equations for the $f(\hat{R})$ Palatini gravity in the case of static and spherical symmetric geometry. We also show that a neutron star is a stable system independently of the form of the functional $f(\hat{R})$
Neutron stars are ideal astrophysical sources to probe general relativity due to their large compactnesses and strong gravitational fields. For example, binary pulsar and gravitational wave observations have placed stringent bounds on certain scalar-tensor theories in which a massless scalar field is coupled to the metric through matter. A remarkable phenomenon of neutron stars in such scalar-tensor theories is spontaneous scalarization, where a normalized scalar charge remains order unity even if the matter-scalar coupling vanishes asymptotically far from the neutron star. While most works on…
The modified gravity (MOG) theory is applied to the gravitational wave binary merger GW190814 to demonstrate that the modified Tolman-Oppenheimer-Volkoff equation for a neutron star can produce a mass $M=2.6 -2.7 M_\odot$, allowing for the binary secondary component to be identified as a heavy neutron star in the hypothesized mass gap $2.5 - 5 M_\odot$.
In the present work we study the gravitational effects of condensed dark matter on strange stars. We consider self-interacting dark matter particles with properties consistent with current observational constraints, and dark matter inside the star is modelled as a Bose-Einstein condensate. We integrate numerically the Tolman-Oppenheimer-Volkoff equations in the two-fluid formalism assuming that strange stars are made of up to 4 per cent of dark matter. It is shown that for a mass of the dark matter particles in the range $50 MeV-160 MeV$ strange stars are characterized by a maximum mass and ra…
In this paper, we consider the mimetic gravitational theory to derive a novel category of anisotropic star models. To end and to put the resulting differential equations into a closed system, the form of the metric potential $g_{rr}$ as used by Tolman (Tolman 1939) is assumed as well as a linear form of the equation-of-state. The resulting energy-momentum components, energy-density, and radial and tangential pressures contain five constants; three of these are determined through the junction condition, matching the interior with the exterior Schwarzschild solution the fourth is constrained by …
We study relativistic non-rotating stars in the framework of Lovelock gravity. In particular, we consider the Gauss-Bonnet term in a five-dimensional spacetime, and we investigate the impact of the Gauss-Bonnet parameter on properties of the stars, both isotropic and anisotropic. For matter inside the star, we assume a relativistic gas of de-confined massless quarks. We integrate the modified Tolman-Oppenheimer-Volkoff equations numerically, and we obtain the mass-to-radius profile, the compactness of the star as well as the gravitational red-shift for several values of the Gauss-Bonnet parame…
