Effective Gravitational Mass Research Articles

Shadows and quasinormal modes of rotating black holes in Horndeski theory: Parameter constraints using EHT observations of M87* and Sgr A*

One way to test the presence of scalar & vector fields in the spacetime of black holes is to get constraints on the fields and black hole parameters using astrophysical observations such as black hole shadow, quasiperiodic oscillations, etc. In this work, we aimed to investigate spacetime properties around black holes in Horndeski gravity. First, we obtain a rotating black hole solution using the Newman–Janis Algorithm (NJA), and we study the event horizon, statistic limits, and ergoregion of the black hole spacetime. In addition, we calculate the effective gravitational mass of the black hole. We derive equations for null geodesics and show the combined effects of the black hole spin and Horndeski gravity parameter on the shadow shape of the black hole and its radius distortion. We find that black hole spin and Horndeski parameters cause an increase in the values of shadow radius and its deformation. Next, we obtain constraints for the upper and lower values for black hole spin and Horndeski parameters using event horizon telescope (EHT) data from Sgr A* and M87*shadow sizes. Finally, we investigated the shadow radius, equatorial, and polar quasinormal modes using the geometric-optic relationship between the parameters of the quasinormal mode and the conserved values along the geodesics in the spacetime of the rotating Horndeski black hole.

Szekeres models: a covariant approach

We exploit the 1 + 1 + 2 formalism to covariantly describe the inhomogeneous and anisotropic Szekeres models. It is shown that an average scale length can be defined covariantly which satisfies a 2d equation of motion driven from the effective gravitational mass (EGM) contained in the dust cloud. The contributions to the EGM are encoded to the energy density of the dust fluid and the free gravitational field Eab. We show that the quasi-symmetric property of the Szekeres models is justified through the existence of 3 independent intrinsic Killing vector fields (IKVFs). In addition the notions of the apparent and absolute apparent horizons are briefly discussed and we give an alternative gauge-invariant form to define them in terms of the kinematical variables of the spacelike congruences. We argue that the proposed program can be used in order to express Sachs’ optical equations in a covariant form and analyze the confrontation of a spatially inhomogeneous irrotational overdense fluid model with the observational data.

Gravitationally induced phase shift on a single photon

The effect of the Earth’s gravitational potential on a quantum wave function has only been observed for massive particles. In this paper we present a scheme to measure a gravitationally induced phase shift on a single photon traveling in a coherent superposition along different paths of an optical fiber interferometer. To create a measurable signal for the interaction between the static gravitational potential and the wave function of the photon, we propose a variant of a conventional Mach–Zehnder interferometer. We show that the predicted relative phase difference of 10−5 rad is measurable even in the presence of fiber noise, provided additional stabilization techniques are implemented for each arm of a large-scale fiber interferometer. Effects arising from the rotation of the Earth and the material properties of the fibers are analysed. We conclude that optical fiber interferometry is a feasible way to measure the gravitationally induced phase shift on a single-photon wave function, and thus provides a means to corroborate the equivalence of the energy of the photon and its effective gravitational mass.

Effective gravitational mass of the Ayón-Beato and García metric

In this paper, we calculate the effective gravitational mass of Ayón-Beato and García (AG) regular (nonsingular) static spherically symmetric asymptotically Minkowskian metric that is a solution to Einstein’s equations coupled with a nonlinear electromagnetic field. The effective gravitational mass is negative, zero, or positive that depends on the ratio of magnitude of electric charge to the ADM mass and the ratio of the radial distance to the ADM mass. As expected, at large values of radial distance, our result gives effective gravitational mass of the Reissner–Nordström metric.

Energy distribution of a noncommutative Vaidya black hole background in Møller’s prescription

We compute Moller’s energy-momentum pseudotensor of a Vaidya black hole in the framework of a deformed spacetime. The computed energy is contained in a sphere of radius R which gives a taste of the effective gravitational mass that a neutral test particle experiences. Our results show a rich dynamical structure with a regular behavior at radial distances.

Formation of redbacks via accretion-induced collapse

We examine the growing class of binary millisecond pulsars known as redbacks. In these systems, the pulsar's companion has a mass between 0.1 and about 0.5 M⊙ in an orbital period of less than 1.5 d. All show extended radio eclipses associated with circumbinary material. They do not lie on the period–companion mass relation expected from the canonical intermediate-mass X-ray binary evolution in which the companion filled its Roche lobe as a red giant and has now lost its envelope and cooled as a white dwarf. The redbacks lie closer to, but usually at higher period than, the period–companion mass relation followed by cataclysmic variables and low-mass X-ray binaries. In order to turn on as a pulsar mass accretion on to a neutron star must be sufficiently weak, considerably weaker than expected in systems with low-mass main-sequence companions driven together by magnetic braking or gravitational radiation. If a neutron star is formed by accretion-induced collapse of a white dwarf as it approaches the Chandrasekhar limit some baryonic mass is abruptly lost to its binding energy so that its effective gravitational mass falls. We propose that redbacks form when accretion-induced collapse of a white dwarf takes place during cataclysmic variable binary evolution because the loss of gravitational mass makes the orbit expand suddenly so that the companion no longer fills its Roche lobe. Once activated, the pulsar can ablate its companion and so further expand the orbit and also account for the extended eclipses in the radio emission of the pulsar that are characteristic of these systems. The whole period–companion mass space occupied by the redbacks can be populated in this way.

Entropic gravity versus gravitational pseudotensors in static spherically symmetric spacetimes

We present some well-known energy-momentum complexes and evaluate the gravitational energy associated with static spherically symmetric spacetimes. In fact, the energy distribution of the aforementioned gravitational background that is contained in a two-sphere of radius r shows that a test particle situated at a finite distance r experiences the gravitational field of the effective gravitational mass. In addition, we apply Verlinde’s entropic gravity to find the emergent gravitational energy on static spherically symmetric screens. In this setup, we find that the energy distribution in the prescription of Møller is similar to the energy derived from the emergent gravity, while other prescriptions give the different results. This result may confirm the argument of Lessner who argues that Møller’s definition of energy is a powerful concept of energy in General Relativity.

Nonstandard Approach to Gravity for the Dark Sector of the Universe

We summarize the present state of research on the darkon fluid as a model for the dark sector of the Universe. Nonrelativistic massless particles are introduced as a realization of the Galilei group in an enlarged phase space. The additional degrees of freedom allow for a nonstandard, minimal coupling to gravity respecting Einstein’s equivalence principle. Extended to a self-gravitating fluid the Poisson equation for the gravitational potential contains a dynamically generated effective gravitational mass density of either sign. The equations of motion (EOMs) contain no free parameters and are invariant w.r.t. Milne gauge transformations. Fixing the gauge eliminates the unphysical degrees of freedom. The resulting Lagrangian possesses no free particle limit. The particles it describes, darkons, exist only as fluid particles of a self-gravitating fluid. This darkon fluid realizes the zero-mass Galilean algebra extended by dilations with dynamical exponent z = 5/3 . We reduce the EOMs to Friedmann-like equations and derive conserved quantities and a unique Hamiltonian dynamics by implementing dilation symmetry. By the Casimir of the Poisson-bracket (PB)-algebra we foliate the phase space and construct a Lagrangian in reduced phase space. We solve the Friedmann-like equations with the transition redshift and the value of the Casimir as integration constants. We obtain a deceleration phase for the early Universe and an acceleration phase for the late Universe in agreement with observations. Steady state equations in the spherically symmetric case may model a galactic halo. Numerical solutions of a nonlinear differential equation for the gravitational potential lead to predictions for the dark matter (DM) part of the rotation curves (RCs) of galaxies in qualitative agreement with observational data. We also present a general covariant generalization of the model.

Gravitational energy of a noncommutative Vaidya black hole

In this paper we evaluate the components of the energy–momentum pseudotensors of Landau and Lifshitz for the noncommutative Vaidya space–time. The effective gravitational mass experienced by a neutral test particle present at any finite distance in the gravitational field of the noncommutative Vaidya black hole is derived. Using the effective mass parameter, one finds that the naked singularity is massless and this supports Seifert's conjecture.

Renewed relevance of new tests of the equivalence principle involving intrinsic properties of particles and antiparticles

The equivalence of the Shapiro delay for photons and (anti)neutrinos is the currently accepted lone test of the equivalence principle concerning intrinsic properties and quantum numbers of relativistic particles and seemingly constitute the only direct test for antiparticles. We show that due to the overwhelming contribution of the kinetic energy to the effective passive gravitational mass, Shapiro delay neither tests the equivalence principle nor anomalous long-range couplings related to the intrinsic properties and quantum numbers of the particles. In effect, the internal properties of the test particle are irrelevant in the context of weak equivalence principle (WEP) due to the relativistic suppression factor. The general result, independent of the nature of the long-range WEP-violating interaction assumed, underlines the potential significance of new tests.

The vertical oscillations of coupled magnets

The International Young Physicists' Tournament (IYPT) is a worldwide, annual competition for high school students. This paper is adapted from the winning solution to Problem 14, Magnetic Spring, as presented in the final round of the 23rd IYPT in Vienna, Austria. Two magnets were arranged on top of each other on a common axis. One was fixed, while the other could move vertically. Various parameters of interest were investigated, including the effective gravitational acceleration, the strength, size, mass and geometry of the magnets, and damping of the oscillations. Despite its simplicity, this setup yielded a number of interesting and unexpected relations. The first stage of the investigation was concerned only with the undamped oscillations of small amplitudes, and the period of small amplitude oscillations was found to be dependent only on the eighth root of important magnet properties such as its strength and mass. The second stage sought to investigate more general oscillations. A numerical model which took into account magnet size, magnet geometry and damping effects was developed to model the general oscillations. Air resistance and friction were found to be significant sources of damping, while eddy currents were negligible.

Black Holes and Photons with Entropic Force

We study the entropic force effects on black holes and photons. It is found that application of an entropic analysis restricts the radial change ΔR of a black hole of radius RH, due to a test particle of a Schwarzschild radius Rh moving towards the black hole by Δx near a black body surface, to be given by a relation RHΔR = RhΔx/2, or ΔR/M = Δx/2m. We suggest a new rule regarding entropy changes in different dimensions, ΔS = 2πkDΔl/, which unifies Verlinde's conjecture and the black hole entropy formula. We also propose the extension of the entropic force idea to massless particles such as photons. It is realized that there is an entropic force on a photon of energy Eγ, with F = GM(Eγ/c2)/R2, and therefore the photon has an effective gravitational mass mγ = Eγ/c2.

Generalized Swiss-cheese cosmologies: Mass scales

We generalize the Swiss-cheese cosmologies so as to include nonzero linear momenta of the associated boundary surfaces. The evolution of mass scales in these generalized cosmologies is studied for a variety of models for the background without having to specify any details within the local inhomogeneities. We find that the final effective gravitational mass and size of the evolving inhomogeneities depends on their linear momenta but these properties are essentially unaffected by the details of the background model.

THE CONNECTION BETWEEN THE HUBBLE AND UNIVERSAL CONSTANTS

Within the λ−member interpretation made on the basis of the physical vacuum quantization hypothesis the physical vacuum quantization parameters are obtained by using the universal macroscopic and microscopic constants. Also found are dimensions of physical vacuum elementary cells, their effective gravitational mass and lifetime as virtual elements of the environment. The physical vacuum is a virtual quantized lepton matter (dark energy) being the propagation medium for electromagnetic radiation. Using the macroscopic and microscopic constants allowed obtaining the relations between the Hubble constant and the basic parameters of the universe. The data obtained can be used in the study of evolutionary behavior of the universe.

EFFECTIVE MASS OF A RADIATING CHARGED PARTICLE IN EINSTEIN'S UNIVERSE

The effective gravitational mass as well as the energy and momentum distributions of a radiating charged particle in Einstein's universe are evaluated. The Møller's energy–momentum complex is employed for this computation. The spacetime under study is a generalization of Bonnor and Vaidya spacetime in the sense that the metric is described in the cosmological background of Einstein's universe in lieu of the flat background. Several spacetimes are limiting cases of the one considered here. In particular for the Reissner–Nordström black hole background, our results are exactly the same as those derived by Cohen and Gautreau using Whittaker's theorem and by Cohen and de Felice using Komar's mass. Furthermore, the power output for the spacetime under consideration is obtained.

Freely Falling 2-Surfaces and the Effective Gravitational Mass

We derive an expression for the effectivegravitational mass for any closed spacelike 2-surface.This effective gravitational energy is defined directlythrough the geometrical quantity of the freely falling 2-surface and thus is well adapted to intuitiveexpectation that the gravitational mass should bedetermined by the motion of a test body moving freely inthe gravitational field. We find that this effective gravitational mass has a reasonable positivevalue for a small sphere in the non-vacuum space-timesand can be negative for the vacuum case. Further, thiseffective gravitational energy is compared with the quasi-local energy based on the (2 + 2)formalism of General Relativity. Although some gaugefreedoms exist, analytic expressions of the quasi-localenergy for vacuum cases are the same as the effective gravitational mass. Especially, we see that thecontribution from the cosmological constant is the samein general cases.

Dark Matter versus Mach's Principle

Empirical and theoretical evidence show that the astrophysical problem of dark matter might be solved by a theory of Einstein-Mayer type. In this theory, up to global Lorentz rotations, the reference system is determined by the motion of cosmic matter. Thus, one is led to a “Riemannian space with teleparallelism” realizing a geometric version of the Mach-Einstein doctrine. The field equations of this gravitational theory contain hidden matter terms, where the existence of hidden matter is inferred solely from its gravitational effects. It is argued that, in the nonrelativistic mechanical approximation, they provide an inertia-free mechanics, where the inertial mass of a body is induced by the gravitational action of the comic masses. Interpreted from the Newtonian point of view, this mechanics shows that the effective gravitational mass of astrophysical objects depends on r such that one expects the existence of dark matter.

On Gravitational Repulsion

The concepts of negative gravitational mass and gravitational repulsion are alien to general relativity. Still, we show here that small negative fluctuations - small dimples in the primordial density field - that act as if they have an effective negative gravitational mass, play a dominant role in shaping our Universe. These initially tiny perturbations repel matter surrounding them, expand and grow to become voids in the galaxy distribution. These voids - regions with a diameter of $40 \h$ Mpc which are almost devoid of galaxies - are the largest object in the Universe.

Limiting configurations allowed by the energy conditions

The energy conditions of general relativity are satisfied by all experimentally detected fields. We discuss their interpretation and application to charged spheres. It is found that they prevent the existence of naked singularities, and demand that the effective gravitational mass be everywhere non-negative. We focus on the emergence of limiting configurations-sources of the Reissner-Nordstrom field that have vanishing effective mass everywhere within the sphere. These configurations have a number of interesting features. Among them we find that, near the center, the limiting form of the equation of state isρ+3p=0. Notably this is the only equation of state consistent with the existence of zero-point electromagnetic field, and it has been considered in different contexts, in discussions of cosmic strings and in derivations of (3+1) properties of matter from (4+1) geometry. The consistency of these configurations with the Einstein-Maxwell equations is shown by means of explicit examples. These configurations can be interpreted as due to selfinteracting gravitational effects of the zero-point electromagnetic field.

Gravitational energy of a stringy charged black hole

It is known that a static, spherically symmetric stringy charged black hole has several different properties than that of the Reissner-Nordström black hole. In this letter we obtain the gravitational energy of the stringy charged black hole and observe that the total energy is positive and is confined to the interior of the black hole. This is in contrast to the result for the Reissner-Nordström black hole, where the total gravitational energy is positive but is shared by its interior as well as exterior. Consequently, unlike the case of the Reissner-Nordström black hole, the effective gravitational mass experienced by a neutral test particle situated at any finite distance in the gravitational field of the stringy charged black hole is positive.