Showing papers on "Gravitation published in 1997"

Exterior gravitation of a polyhedron derived and compared with harmonic and mascon gravitation representations of asteroid 4769 Castalia

Abstract: The exterior gravitation of a constant-density polyhedron is derived analytically in closed form. Expressions for potential, attraction, and gravity gradient matrix involve one logarithm term per edge and one arctangent term per face, The Laplacian can be used to determine whether a field point is inside or outside the polyhedron, This polyhedral method is well suited to evaluating the gravitational field of an irregularly shaped body such as an asteroid or comet, Conventional harmonic and mascon potential and attraction expressions suffer large errors when evaluated close to a polyhedral model of asteroid 4769 Castalia.

Axiomatic approach to electromagnetic and gravitational radiation reaction of particles in curved spacetime

Abstract: The problem of determining the electromagnetic and gravitational ``self-force'' on a particle in a curved spacetime is investigated using an axiomatic approach. In the electromagnetic case, our key postulate is a ``comparison axiom,'' which states that whenever two particles of the same charge $e$ have the same magnitude of acceleration, the difference in their self-force is given by the ordinary Lorentz force of the difference in their (suitably compared) electromagnetic fields. We thereby derive an expression for the electromagnetic self-force which agrees with that of DeWitt and Brehme as corrected by Hobbs. Despite several important differences, our analysis of the gravitational self-force proceeds in close parallel with the electromagnetic case. In the gravitational case, our final expression for the (reduced order) equations of motion shows that the deviation from geodesic motion arises entirely from a ``tail term,'' in agreement with recent results of Mino et al. Throughout the paper, we take the view that ``point particles'' do not make sense as fundamental objects, but that ``point particle equations of motion'' do make sense as means of encoding information about the motion of an extended body in the limit where not only the size but also the charge and mass of the body go to zero at a suitable rate. Plausibility arguments for the validity of our comparison axiom are given by considering the limiting behavior of the self-force on extended bodies.

Energy-momentum tensor for cosmological perturbations

Abstract: We study the effective energy-momentum tensor (EMT) for cosmological perturbations and formulate the gravitational back-reaction problem in a gauge-invariant manner. We analyze the explicit expressions for the EMT in the cases of scalar metric fluctuations and of gravitational waves and derive the resulting equations of state. The formalism is applied to investigate the back-reaction effects in chaotic inflation. We find that for long wavelength scalar and tensor perturbations, the effective energy density is negative and thus counteracts any preexisting cosmological constant. For scalar perturbations during an epoch of inflation, the equation of state is de Sitter-like.

Gravito-electromagnetism

Abstract: We develop and apply a fully covariant 1+3 electromagnetic analogy for gravity The free gravitational field is covariantly characterized by the Weyl gravito-electric and gravito-magnetic spatial tensor fields, whose dynamical equations are the Bianchi identities Using a covariant generalization of spatial vector algebra and calculus to spatial tensor fields, we exhibit the covariant analogy between the tensor Bianchi equations and the vector Maxwell equations We identify gravitational source terms, couplings and potentials with and without electromagnetic analogues The nonlinear vacuum Bianchi equations are shown to be invariant under covariant spatial duality rotation of the gravito-electric and gravito-magnetic tensor fields We construct the super-energy density and super-Poynting vector of the gravitational field as natural U(1) group invariants, and derive their super-energy conservation equation A covariant approach to gravito-electric/magnetic monopoles is also presented

On Formation and Evolution of Disk Galaxies: Cosmological Initial Conditions and the Gravitational Collapse

Abstract: We use a semianalytical approach and a CDM cosmological model to study the gravitational collapse and virialization, the structure, as well as the global and statistical properties of isolated dark matter galactic halos which emerge from primordial Gaussian fluctuations. From the statistical properties of the density fluctuation field the possible mass aggregation histories (MAHs) are generated, and these histories are used as the initial conditions of the gravitational collapse. To calculate the structure of the virialized systems we have generalized the secondary infall model. Although a range of halo structures is obtained, the average density profiles agree with the profile derived as a fitting formula to results of N-body cosmological simulations. The comparison of the density profiles with the observational data is disscused, and some possible solutions to the disagreement found in the inner regions are discussed. The results of our approach, after considering the gravitational dragging of the baryon matter that forms a central disk in centrifugal equilibrium, show that the Tully-Fisher relation and its scatter can be explained through the initial cosmological conditions. The sigma8=1 SCDM model produces galaxies with high velocities when compared to observations, but when the SCDM power spectrum is normalized to sigma8=0.57 an excellent agreement with the observable TF relation is found, suggesting that this relation is the natural extension to galactic scales of the observed galaxy distribution power spectrum. The theoretical TF scatter is close to the measured one. The slope of the TF relation is practically invariant with respect to the spin parameter lambda.

Volterra distortions, spinning strings, and cosmic defects

Abstract: Cosmic strings, as topological spacetime defects, show striking resemblance to defects in solid continua: distortions, which can be classied into disclinations and dislocations, are linelike defects characterized by a delta function-valued curvature and torsion distribution giving rise to rotational and translational holonomy. We exploit this analogy and investigate how distortions can be adapted in a systematic manner from solid state systems to Einstein{Cartan gravity. As distortions are eciently described within the framework of a SO(3) T (3) gauge theory of solid continua with line defects, we are led in a straightforward way to a Poincar e gauge approach to gravity which is a natural framework for introducing the notion of distorted spacetimes. Constructing all ten possible distorted spacetimes, we recover, inter alia, the wellknown exterior spacetime of a spin-polarized cosmic string as a special case of such a geometry. In a second step, we search for matter distributions which, in Einstein{Cartan gravity, act as sources of distorted spacetimes. The resulting solutions, appropriately matched to the distorted vacua, are cylindrically symmetric and are interpreted as spin-polarized cosmic strings and cosmic dislocations.

A Simple Derivation of Canonical Structure and Quasi-local Hamiltonians in General Relativity

Abstract: A new method of variation of the gravitational Lagrangian is proposed. This method leads in a simple and straightforward way to the canonical description of the gravitational field dynamics in a finite volume V with boundary. No boundary terms are neglected or subtracted ad hoc. Two different forms of gravitational quasi-local energy are derived. Each of them is equal to the field Hamiltonian, corresponding to a specific way of controlling the field boundary data. They play the role of the “internal energy” and the “free energy” respectively. A relation with the boundary formula governing the thermodynamics of black holes is discussed.

Photoionization, numerical resolution, and galaxy formation

Abstract: Using cosmological simulations that incorporate gasdynamics and gravitational forces, we investigate the influence of photoionization by an ultraviolet radiation background on the formation of galaxies. In our highest resolution simulations, we find that photoionization has essentially no effect on the baryonic mass function of galaxies at z = 2, down to our resolution limit of ~5 × 109 M☉. We do, however, find a strong interplay between the mass resolution of a simulation and the microphysics included in the computation of heating and cooling rates. At low resolution, a photoionizing background can appear to suppress the formation of even relatively massive galaxies. However, when the same initial conditions are evolved with a factor of 8 improvement in mass resolution, this effect disappears. Our results demonstrate the need for care in interpreting the results of cosmological simulations that incorporate hydrodynamics and radiation physics. For example, we conclude that a simulation with limited resolution may yield more accurate results if it ignores some relevant physical processes, such as photoionization. At higher resolution, the simulated population of massive galaxies is insensitive to the treatment of photoionization or the inclusion of star formation in the simulations, but it does depend significantly on the amplitude of the initial density fluctuations. By z = 2, an Ω = 1 cold dark matter model normalized to produce the observed masses of present-day clusters has already formed galaxies with baryon masses exceeding 1011 M☉.

General relativistic energy conditions: The Hubble expansion in the epoch of galaxy formation

Abstract: The energy conditions of Einstein gravity (classical general relativity) are designed to extract as much information as possible from classical general relativity without enforcing a particular equation of state for the stress energy. This systematic avoidance of the need to specify a particular equation of state is particularly useful in a cosmological setting {emdash} since the equation of state for the cosmological fluid in a Friedmann-Robertson-Walker-type universe is extremely uncertain. I shall show that the energy conditions provide simple and robust bounds on the behavior of both the density and look-back time as a function of redshift. I shall show that current observations {ital suggest} that the so-called {ital strong energy condition} (SEC) is violated at some time between the epoch of galaxy formation and the present. This implies that no possible combination of {ital {open_quotes}normal{close_quotes}} matter is capable of fitting the observational data. {copyright} {ital 1997} {ital The American Physical Society}

Neutrino oscillations in curved spacetime: A heuristic treatment

Abstract: Author(s): Cardall, CY; Fuller, GM | Abstract: We discuss neutrino oscillations in curved spacetime. Our heuristic approach can accommodate matter effects and gravitational contributions to neutrino spin precession in the presence of a magnetic field. By way of illustration, we perform explicit calculations in the Schwarzschild geometry. In this case, gravitational effects on neutrino oscillations are intimately related to the redshift. We discuss how spacetime curvature could affect the resonance position and adiabaticity of matter-enhanced neutrino flavor conversion. © 1997 The American Physical Society.

Relativistic Diskoseismology. I. Analytical Results for “Gravity Modes”

Abstract: We generalize previous calculations to a fully relativistic treatment of adiabatic oscillations that are trapped in the inner regions of accretion disks by non-Newtonian gravitational effects of a black hole. We employ the Kerr geometry within the scalar potential formalism of Ipser and Lindblom, neglecting the gravitational field of the disk. This approach treats perturbations of arbitrary stationary, axisymmetric, perfect fluid models. It is applied here to thin accretion disks. Approximate analytic eigenfunctions and eigenfrequencies are obtained for the most robust and observable class of modes, which corresponds roughly to the gravity (internal) oscillations of stars. The dependence of the oscillation frequencies on the mass and angular momentum of the black hole is exhibited. These trapped modes do not exist in Newtonian gravity, and thus provide a signature and probe of the strong-field structure of black holes. Our predictions are relevant to observations that could detect modulation of the X-ray luminosity from stellar mass black holes in our Galaxy and the UV and optical luminosity from supermassive black holes in active galactic nuclei.

Cosmological Models with Variable Cosmological and Gravitational “Constants” and Bulk Viscous Models

Abstract: A viscous model with variable gravitational and cosmological constant has been considered. Several solutions are presented and some are shown to be equivalent to Berman, Kalligas et al. and Brans-Dicke solutions.

String Theory and Classical Absorption by Threebranes

Abstract: Low energy absorption cross-sections for various particles falling into extreme non-dilatonic branes are calculated using string theory and world-volume field theory methods. The results are compared with classical absorption by the corresponding gravitational backgrounds. For the self-dual threebrane, earlier work by one of us demonstrated precise agreement of the absorption cross-sections for the dilaton, and here we extend the result to Ramond-Ramond scalars and to gravitons polarized parallel to the brane. In string theory, the only absorption channel available to dilatons and Ramond-Ramond scalars at leading order is conversion into a pair of gauge bosons on the threebrane. For gravitons polarized parallel to the brane, scalars, fermions and gauge bosons all make leading order contributions to the cross-section, which remarkably add up to the value predicted by classical gravity. For the twobrane and fivebrane of M-theory, numerical coefficients fail to agree, signalling our lack of a precise understanding of the world-volume theory for large numbers of coincident branes. In many cases, we note a remarkable isotropy in the final state particle flux within the brane. We also consider the generalization to higher partial waves of minimally coupled scalars. We demonstrate agreement for the threebrane at l=1 and indicate that further work is necessary to understand l>1.

A stratified framework for scalar-tensor theories of modified dynamics

Abstract: Although the modified Newtonian dynamics (MOND) proposed by Milgrom successfully accounts for the systematics of galaxy rotation curves and cluster dynamics without invoking dark matter, the idea remains a largely ad hoc modification of Newtonian dynamics with no basis in deeper theory. Nonstandard scalar-tensor theories have been suggested as a theoretical basis for MOND; however, any such theory with the usual conformal relation between the Einstein and physical metrics fails to predict the degree of light deflection observed in distant clusters of galaxies. The prediction is that there should be no discrepancy between the detectable mass in stars and gas and the lensing mass, in sharp contradiction to the observations (Bekenstein & Sanders). In the present paper, I demonstrate that one can write down a framework for scalar-tensor theories that predict the MOND phenomenology for the low-velocity (v c) dynamics of galaxies and clusters of galaxies and are consistent with observations of extragalactic gravitational lenses, provided that one drops the requirement of the Lorentz invariance of gravitational dynamics. This leads to "preferred-frame" theories characterized by a nonconformal relation between the two metrics. I describe a toy theory in which the local environment (the solar system, binary pulsars) is protected from detectable preferred-frame effects by the very same nonstandard (aquadratic) scalar Lagrangian that gives rise to the MOND phenomenology. Although this particular theory is also contrived, it represents a limiting case for two-field theories of MOND and is consistent with a wide range of gravitational phenomena. Moreover, it is a cosmological effective theory which may explain the near numerical coincidence between the MOND acceleration parameter and the present value of the Hubble parameter multiplied by the speed of light.

Behavior of cosmological models with varying G

Abstract: We provide a detailed analysis of Friedmann-Robertson-Walker universes in a wide range of scalar-tensor theories of gravity. We apply solution-generating methods to three parametrized classes of scalar-tensor theory which lead naturally to general relativity in the weak-field limit. We restrict the parameters which specify these theories by the requirements imposed by the weak-field tests of gravitation theories in the solar system and by the requirement that viable cosmological solutions be obtained. We construct a range of exact solutions for open, closed, and flat isotropic universes containing matter with equation of state p{le}(1)/(3){rho} and in vacuum. We study the range of early- and late-time behaviors displayed, examine when there is a {open_quotes}bounce{close_quotes} at early times, and expansion maxima in closed models. {copyright} {ital 1997} {ital The American Physical Society}

Review of Matrix Theory

Abstract: In this article we present a self contained review of the principles of Matrix Theory including the basics of light cone quantization, the formulation of 11 dimensional M-Theory in terms of supersymmetric quantum mechanics, the origin of membranes and the rules of compactification on 1,2 and 3 tori. We emphasize the unusual origins of space time and gravitation which are very different than in conventional approaches to quantum gravity. Finally we discuss application of Matrix Theory to the quantum mechanics of Schwarzschild black holes. This work is based on lectures given by the second author at the Cargese ASI 1997 and at the Institute for Advanced Study in Princeton.

Saturated-cascade similitude theory of gravity wave spectra

Abstract: A theory is presented, which is based mainly on dimensional analysis (but also on gravity wave theory), that attempts to explain all the types of gravity wave power spectral densities (PSDs) now being measured. This theory is based on two concepts, namely, wave saturation and wave cascade. The immediate result of the simultaneous presence of these two processes is that there should exist a unique relation between the vertical (or horizontal) wavelength of a gravity wave and its period (provided the Brunt Period and dissipation rate are given and Doppler effects are omitted). This relation provides a way to derive all of the intrinsic spectra from the fundamental one which is the vertical wavenumber PSD of the horizontal winds. The most important suggestion to emerge from this theory is that e, the dissipation rate, is the main controlling independent variable for the amplitude of all but 3 of the 12 spectra predicted. It would also control the wavelength-period relations. Comparisons are made between observations and theory, and important experimental tests are proposed. This model presently appears to be useful in the analysis of gravity wave data obtained by means of lidars, radars, interferometers, and imagers. In addition, it raises a number of new scientific issues for future research.

Two-wavelength-difference measurement of gravitationally induced quantum interference phases

Abstract: One of the significant successes in the field of neutron interferometry has been the experimental observation of the phase shift of a neutron de Broglie wave due to the action of the Earth's gravitational field. Past experiments have clearly demonstrated the effect and verified the quantum-mechanical equivalence of gravitational and inertial masses to a precision of about 1%. In this experiment the gravitationally induced phase shift of the neutron is measured with a statistical uncertainty of order 1 part in 1000 in two different interferometers. Nearly harmonic pairs of neutron wavelengths are used to measure and compensate for effects due to the distortion of the interferometer as it is tilted about the incident beam direction. A discrepancy between the theoretically predicted and experimentally measured values of the phase shift due to gravity is observed at the 1% level. Extensions to the theoretical description of the shape of a neutron interferogram as a function of tilt in a gravitational field are discussed and compared with experiment.

Belated Decision in the Hilbert-Einstein Priority Dispute

Abstract: According to the commonly accepted view, David Hilbert completed the general theory of relativity at least 5 days before Albert Einstein submitted his conclusive paper on this theory on 25 November 1915. Hilbert's article, bearing the date of submission 20 November 1915 but published only on 31 March 1916, presents a generally covariant theory of gravitation, including field equations essentially equivalent to those in Einstein's paper. A close analysis of archival material reveals that Hilbert did not anticipate Einstein. The first set of proofs of Hilbert's paper shows that the theory he originally submitted is not generally covariant and does not include the explicit form of the field equations of general relativity.

Complex actions in two-dimensional topology change

Abstract: We investigate topology change in (1 + 1) dimensions by analysing the scalar-curvature action at the points of metric-degeneration that (with minor exceptions) any non-trivial Lorentzian cobordism necessarily possesses. In two dimensions any cobordism can be built up as a combination of only two elementary types, the `yarmulke' and the `trousers.' For each of these elementary cobordisms, we consider a family of Morse-theory inspired Lorentzian metrics that vanish smoothly at a single point, resulting in a conical-type singularity there. In the yarmulke case, the distinguished point is analogous to a cosmological initial (or final) singularity, with the spacetime as a whole being obtained from one causal region of Misner space by adjoining a single point. In the trousers case, the distinguished point is a `crotch singularity' that signals a change in the spacetime topology (this being also the fundamental vertex of string theory, if one makes that interpretation). We regularize the metrics by adding a small imaginary part, whose sign is fixed to be positive by the condition that it lead to a convergent scalar field path integral on the regularized spacetime. As the regulator is removed, the scalar density approaches a delta-function, whose strength is complex: for the yarmulke family the strength is , where is the rapidity parameter of the associated Misner space; for the trousers family it is simply . This implies that in the path integral over spacetime metrics for Einstein gravity in three or more spacetime dimensions, topology change via a crotch singularity is exponentially suppressed, whereas appearance or disappearance of a universe via a yarmulke singularity is exponentially enhanced. We also contrast these results with the situation in a vielbein-cum-connection formulation of Einstein gravity.

Stability analysis of spherically symmetric star in scalar - tensor theories of gravity

Abstract: A stability analysis of a spherically symmetric star in scalar-tensor theories of gravity is given in terms of the frequencies of quasi-normal modes. The scalar-tensor theories have a scalar field which is related .to gravitation. There is an arbitrary function, the so-called coupling function, which determines the strength of the coupling between the gravitational scalar field and matter. Instability is induced by the scalar field for some ranges of the value of the first derivative of the coupling function. This instability leads to significant discrepancies with the results of binary-pulsar-timing experiments and hence, by the stability analysis, we can exclude the ranges of the lirst derivative of the coupling function in which the instability sets in. In this article, the constraint on the first derivative of the coupling function from the stability of relativistic stars is found. Analysis in terms of the quasi­ normal mode frequencies accounts for the parameter dependence of the wave form of the scalar gravitational waves emitted from the Oppenheimer-Snyder collapse. The spontaneous scalarization is also discussed.

Gravitational collapse with non-vanishing tangential stresses: a generalization of the Tolman - Bondi model

Abstract: The gravitational dynamics of anisotropic elastic spheres supported only by tangential stresses and satisfying an equation of state is analysed, and a fairly large class of non-static, spherically symmetric solutions of the Einstein field equations is found by quadratures. The solutions contain three arbitrary functions. Two such functions are immediately recognized as the initial distributions of mass and energy, familiar from the Tolman - Bondi (dust) models, while the third is the elastic internal energy per unit volume. If this function is a constant, the energy density becomes proportional to the matter density and therefore the metric reduces to the Tolman - Bondi one. In the general case, however, the solutions contain oscillating models as well as finite-bouncing models.

On the newtonian cosmology equations with pressure

Abstract: The basic equations describing a Newtonian universe with uniform pressure are reexamined. We argue that in the semi-classical formulation adopted in the literature the continuity equation has a misleading pressure gradient term. When this term is removed, the resulting equations give the same homogeneous background solutions with pressure and the same evolution equation for the density contrast as are obtained using the full relativistic approach.

Equations of Motion of Spinning Relativistic Particle in External Fields

Abstract: We consider the motion of a spinning relativistic particle in external electromagnetic and gravitational fields, to first order in the external field, but to an arbitrary order in spin. The correct account for the spin influence on the particle trajectory is obtained with the noncovariant description of spin. Concrete calculations are performed up to second order in spin included. A simple derivation is presented for the gravitational spin-orbit and spin-spin interactions of a relativistic particle. We discuss the gravimagnetic moment (GM), a specific spin effect in general relativity. It is demonstrated that for the Kerr black hole the gravimagnetic ratio, i.e., the coefficient at the GM, equals to unity (as well as for the charged Kerr hole the gyromagnetic ratio equals to two). The equations of motion obtained for relativistic spinning particle in external gravitational field differ essentially from the Papapetrou equations.

Scale-relativity and quantization of the universe I. Theoretical framework

Abstract: The theory of scale relativity extends Einstein's prin- ciple of relativity to scale transformations of resolutions. It is based on the giving up of the axiom of differentiability of the space-time continuum. The new framework generalizes the standard theory and includes it as a special case. Three conse- quences arise from this withdrawal: (i) The geometry of space- time must be fractal, i.e., explicitly resolution-dependent. This allows us to include resolutions in the denition of the state of the reference system, and to require scale-covariance of the equa- tions of physics under scale transformations. (ii) The geodesics of the non-differentiable space-time are themselves fractal and in innite number. This divergence strongly suggests we un- dertake a statistical, non-deterministic description. (iii) Time reversibility is broken at the innitesimal level. This can be described in terms of a two-valuedness of the time derivative, which we account by using complex numbers. We nally com- bine these three effects by constructing a new tool, the scale- covariant derivative, which transforms classical mechanics into a generalized, quantum-like mechanics. Scale relativity was initially developed in order to re-found quantum mechanics on rst principles (while its present foun- dation is axiomatic). However, the scale-relativistic approach is expected to apply not only at small scales, but also at very large space- and time-scales, although with a different interpre- tation. Indeed, we nd that the scale symmetry must be broken at two (relative) scales, so that the scale axis is divided in three domains: (i) the quantum, scale-dependent microphysical do- main, (ii) the classical, intermediate, scale-independent domain, (iii) but also the macroscopic, cosmological domain which be- comes scale-dependent again and may then be described on very large time-scales (beyond a predictability horizon) in terms of a non-deterministic, statistical, quantum-like theory. In the new framework, we denitively give up the hope to predict indi- vidual trajectories on very large time scales. This leads us to describing their virtual families in terms of complex probabil- ity amplitudes, which are solutions of generalized Schr¨ odinger equations. The squared modulus of these probability amplitudes yields probability densities, whose peaks are interpreted as a Send offprint requests to: L. Nottale tendency for the system to make structures. Since the quantiza- tions in quantum mechanics appear as a direct consequence of the limiting conditions and of the shape of the input eld, the theory thus naturally provides self-organization of the system it describes, in connection with its environment. In the present rst paper of this series, we rst recall the structure of the scale-relativity theory, then we apply our scale- covariant procedure to various equations of classical physics that are relevant to astrophysical processes, including the equation of motion of a particle in a gravitational eld (Newtonian and Einsteinian), in an electromagnetic eld, the Euler and Navier- Stokes equations, the rotational motion of solids, dissipative systems, and rst hints on eld equations themselves. In all these cases, we obtain new generalized Schr¨ odinger equations which allow quantized solutions. In scale-relativity therefore, the underlying fractal geometry of space-time plays the role of a universal structuring \eld". In subsequent papers of this series, we shall derive the solutions of our equations, then show that several new theoretical predictions can be made, and that they can be successfully checked by an analysis of the observational data.

The intrinsic derivative and centrifugal forces in general relativity: i. theoretical foundations

Abstract: Everyday experience with centrifugal forces has always guided thinking on the close relationship between gravitational forces and accelerated systems of reference. Once spatial gravitational forces and accelerations are introduced into general relativity through a splitting of spacetime into space-plus-time associated with a family of test observers, one may further split the local rest space of those observers with respect to the direction of relative motion of a test particle world line in order to define longitudinal and transverse accelerations as well. The intrinsic covariant derivative (induced connection) along such a world line is the appropriate mathematical tool to analyze this problem, and by modifying this operator to correspond to the observer measurements, one understands more clearly the work of Abramowicz et al. who derine an "optical centrifugal force" in static axisymmetric spacetimes and attempt to generalize it and other inertial forces to arbitrary spacetimes. In a companion article the application of this framework to some familiar stationary axisymmetric spacetimes helps give a more intuitive picture of their rotational features including spin precession effects, and puts related work of de Felice and others on circular orbits in black hole spacetimes into a more general context.

Einstein pseudotensor and total energy of the universe

Abstract: The total energy of the universe has been calculated assuming that it is the sum of the contributions from the matter part and gravitational part. The calculations involve the use of Einstein pseudotensor. Calculations have been carried out in some specific examples of spacetime geometries. In some cases the total energy is indeed zero confirming previous results but in other cases the total energy is nonzero. So Rosen’s idea that the pseudotensorial calculations will lead to the result that the total energy of the universe is zero, is very much model dependent.