We consider a spherically symmetric stellar model in general relativity whose interior consists of a pressureless fluid undergoing microscopic velocity diffusion in a cosmological scalar field. We show that the diffusion dynamics compel the interior to be spatially homogeneous, by which one can infer immediately that within our model, and in contrast to the diffusion-free case, no naked singularities can form in the gravitational collapse. We then study the problem of matching an exterior Bondi type metric to the surface of the star and find that the exterior can be chosen to be a modified Vaidya metric with variable cosmological constant. Finally, we study in detail the causal structure of an explicit, self-similar solution.
We apply the 1+1+2 covariant semi-tetrad approach to describe a general static and spherically symmetric relativistic stellar object which contains two fluids with anisotropic pressure. The corresponding Tolman-Oppenheimer-Volkoff equations are then obtained in covariant form for the anisotropic case. These equations are used to obtain new exact solutions using direct resolution and reconstruction techniques. Finally, we show that three of the generating theorems known for the single fluid case can also be used to obtain two-fluid solutions from single fluid ones.
We apply the 1+1+2 covariant approach to describe a general static and spherically symmetric relativistic stellar object which contains two interacting fluids. We then use the 1+1+2 equations to derive the corresponding Tolman-Oppenheimer-Volkoff (TOV) equations in covariant form in the isotropic, non-interacting case. These equations are used to obtain new exact solutions by means of direct resolution and reconstruction techniques. Finally, we show that the generating theorem known for the single fluid case can also be used to obtain two-fluid solutions from single fluid ones.
It is shown that the expressions for the tangential pressure, the anisotropy factor and the radial pressure in the Einstein equations may serve as generating functions for stellar models. The latter can incorporate an equation of state when the expression for the energy density is also used. Other generating functions are based on the condition for the existence of conformal motion (conformal flatness in particular) and the Karmarkar condition for embedding class one metrics. In all these cases the equations are linear first order differential equations for one of the metric components and Ric…
It is shown that the expressions for the tangential pressure, the anisotropy factor and the radial pressure in the Einstein - Maxwell equations may serve as generating functions for charged stellar models. The latter can incorporate an equation of state when the expression for the energy density is also used. Other generating functions are based on the condition for the existence of conformal motion (conformal flatness in particular) and the Karmarkar condition for embedding class one metrics, which do not depend on charge. In all these cases the equations are linear first order differential e…
We consider the observation of stellar-mass black holes binaries with the Laser Interferometer Space Antenna (LISA). Preliminary results based on Fisher information matrix analyses have suggested that gravitational waves from those sources could be very sensitive to possible deviations from the theory of general relativity and from the strong equivalence principle during the low-frequency binary inspiral. We perform a full Markov Chain Monte Carlo Bayesian analysis to quantify the sensitivity of these signals to two phenomenological modifications of general relativity, namely a putative gravit…
The iron line and the continuum-fitting methods are currently the two leading techniques for measuring black hole spins with electromagnetic radiation. They can be naturally extended for probing the spacetime geometry around black holes and testing general relativity in the strong field regime. In the past couple of years, there has been significant work to use the iron line method to test the nature of black holes. In this Letter, we use the continuum-fitting method and we show its capability of constraining the spacetime geometry around black holes by analyzing 17 RXTE data of the X-ray bina…
S-stars in the Galactic Center are excellent testbeds of various general relativistic effects. While previous works focus on modeling their orbital motion around Sgr A*--the supermassive black hole in the Galactic Center--here we explore the possibility of using the rotation of S-stars to test the de Sitter precession predicted by general relativity. We show that by reorienting the rotation axes of S-stars, de Sitter precession will change the apparent width of the absorption lines in the stellar spectra. Our numerical simulations suggest that the newly discovered S4714 and S62 are best suited…
In Riemannian geometry, the Ricci flow is the analogue of heat diffusion; a deformation of the metric tensor driven by its Ricci curvature. As a step towards resolving the problem of time in quantum gravity, we attempt to merge the Ricci flow equation with the Hamilton-Jacobi equation for general relativity.
The limiting mass of cold white dwarfs was first calculated by E. Stoner in an approximate model of a uniform star and was soon reduced by ~20% in papers by S. Chandrasekhar and L. D. Landau based on an exact solution of the equations for the stellar equilibrium. Here we examine uniform models of white dwarfs taking general relativity effects and the influence of finite temperature into account. Solutions are obtained in the form of finite analytic formulas and, for masses differing by no more than ~20% from the exact solutions, found by numerical integration of the differential equations for …
We present the first set of constant rest-mass ultra-massive oxygen/neon white dwarf cooling tracks with masses larger than 1.29 Msun which fully take into account the effects of general relativity on their structural and evolutionary properties. We have computed the full evolution sequences of 1.29, 1.31, 1.33, 1.35, and 1.369 Msun white dwarfs with the La Plata stellar evolution code, LPCODE. For this work, the standard equations of stellar structure and evolution have been modified to include the full effects of general relativity. For comparison purposes, the same sequences have been compu…
We revisit the analysis made by Hwang and Noh [JCAP 1310 (2013)] aiming the construction of a Newtonian set of equations incorporating pressure effects typical of the General Relativity theory. We explicitly derive the Hwang-Noh equations, comparing them with similar computations found in the literature. Then, we investigate $i)$ the cosmological expansion, $ii)$ linear cosmological perturbations theory and $iii)$ stellar equilibrium by using the new set of equations and comparing the results with those coming from the usual Newtonian theory, from the Neo-Newtonian theory and from the General …
Effective geometrostatics of spherical stars beyond general relativity
SISSA - International School for Advanced Studies（国际高等研究院）；IFPU - Institute for Fundamental Physics of the Universe（宇宙基础物理研究所）；INFN Sezione di Trieste（意大利国家核物理研究所的里雅斯特分部）；Instituto de Astrofísica de Andalucía (IAA-CSIC)（安达卢西亚天体物理研究所）；School of Mathematics and Statistics, Victoria University of Wellington（惠灵顿维多利亚大学数学与统计学院）
Gravitational light bending by compact stars is an important astrophysical phenomenon. The bending angle depends on the stellar compactness, which is the ratio of stellar mass $M$ to radius $R$. In this paper, we investigate the pulse profile of highly compact rotating neutron stars for which the bending angle exceeds $π/2$. When $M/R > 0.284$ (the bending angle becomes equal to $π/2$ for the stellar model with $M/R=0.284$), such a large bending happens, resulting in that a photon emitted from any position on the stellar surface can reach an observer. First, we classify the parameter plane of …
A tidal disruption event (TDE) ensues when a star passes too close to the supermassive black hole (SMBH) in a galactic center and is ripped apart by the tidal field of the SMBH. The gaseous debris produced in a TDE can power a bright electromagnetic flare as it is accreted by the SMBH; so far, several dozen TDE candidates have been observed. For SMBHs with masses above $\sim 10^7 M_\odot$, the tidal disruption of solar-type stars occurs within ten gravitational radii of the SMBH, implying that general relativity (GR) is needed to describe gravity. Three promising signatures of GR in TDEs are: …
In this Letter, we demonstrate that short-period stars orbiting around the supermassive black hole in our Galactic Center can successfully be used to probe the gravitational theory in a strong regime. We use 19 years of observations of the two best measured short-period stars orbiting our Galactic Center to constrain a hypothetical fifth force that arises in various scenarios motivated by the development of a unification theory or in some models of dark matter and dark energy. No deviation from General Relativity is reported and the fifth force strength is restricted to an upper 95% confidence…
This paper deals with the spherically symmetric self-gravitating star which is considered to be expansion free dissipative perfect fluids distribution. Some recent research reveals that expansion free dynamical star must be accelerating and dissipating. We adopted some conjectures to obtain the analytical solution for the dynamical model of such stars. Firstly, it has shown that density of dynamical star is homogeneous and \Lamada-dominated under quasi-static diffusion approximation. Secondly, the self-similar solution is also discussed to describe the dynamical model.
Pulsar timing observations precisely test general relativity. Recently, the hierarchical triple system PSR J0337+1715 has placed new constraints on the existence of a fifth force from violation in the strong equivalence principle. Many alternative gravity theories exist with massive (pseudo-)scalar fields to explain a variety of phenomena from the accelerating expansion of the universe at large scales to the QCD strong CP problem at small scales. We here develop a generic formalism for the fifth force effect in theories involving massive scalar fields arising from e.g. string theory. With PSR …
Amongst a number of modified theories of gravity, the Rastall theory has been propounded to address some shortcomings of the standard theory of general relativity. Our purpose is to investigate this framework's capacity to analyse stellar structure in the context of elementary requirements for physical plausibility such as positive definite functions for the energy density and pressure, conformity to the causality criterion and the existence of an equation of state. We consider the analogue of the Saslaw \textit{et al} \cite{saslaw} isothermal model of general relativity and show that the Rast…
Stellar rotation of S301 as a macroscopic gyroscope to test general relativity
Universitat Politècnica de València（瓦伦西亚理工大学）；Max Planck Institute for Extraterrestrial Physics（马克斯·普朗克地外物理研究所）；Kavli Institute for Astronomy and Astrophysics at Peking University（北京大学 Kavli 天体物理学与天文研究所）；Astronomy Department, School of Physics, Peking University（北京大学物理学院天文学系）；Beijing Institute of Mathematical Sciences and Applications（北京应用数学与物理研究所）；University of California, Berkeley（加州大学伯克利分校）；Technical University of Munich（慕尼黑工业大学）
Eddington-inspired Born-Infeld gravity is an important modification of Einstein's general relativity, which can give rise to non-singular cosmologies at the classical level, and avoid the end-stage singularity in a gravitational collapse process. In the Newtonian limit, this theory gives rise to a modified Poisson's equation, as a consequence of which stellar observables acquire model dependent corrections, compared to the ones computed in the low energy limit of general relativity. This can in turn be used to establish astrophysical constraints on the theory. Here, we obtain such a constraint…
Thermodynamic acceptability of spherically symmetric perfect-fluid solutions in general relativity
Al-Farabi Kazakh National University（阿拉伯·法拉比哈萨克国立大学）；Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México（墨西哥国立自治大学核科学研究所）；Dipartimento di Fisica and ICRA, Università di Roma “La Sapienza”（罗马第一大学物理系及ICRA）
Some pairs of neutron star models can intuitively be thought of as being `closer' together than others, in the sense that more precise observations might be required to distinguish between them than would be necessary for other pairs. In this paper, borrowing ideas from the study of geometrodynamics, we introduce a mathematical formalism to define a geometric distance between stellar models, to provide a quantitative meaning to this notion of closeness. In particular, it is known that the set of all metrics on a Riemannian manifold itself admits the structure of a Riemannian manifold (`configu…
In this work we present an exact solution of the Einstein-Maxwell field equations describing compact, charged objects within the framework of classical general relativity. Our model is constructed by embedding a four-dimensional spherically symmetric static metric into a five dimensional flat metric. The source term for the matter field is composed of a perfect fluid distribution with charge. We show that our model obeys all the physical requirements and stability conditions necessary for a realistic stellar model. Our theoretical model approximates observations of neutron stars and pulsars to…
University of Bologna（博洛尼亚大学）；University of Pennsylvania（宾夕法尼亚大学）；University of California, Los Angeles（加利福尼亚大学洛杉矶分校）
Stochastic gradient descent (SGD) is a key ingredient in the training of deep neural networks and yet its geometrical significance appears elusive. We study a deterministic model in which the trajectories of our dynamical systems are described via geodesics of a family of metrics arising from the diffusion matrix. These metrics encode information about the highly non-isotropic gradient noise in SGD. We establish a parallel with General Relativity models, where the role of the electromagnetic field is played by the gradient of the loss function. We compute an example of a two layer network.
