General Relativity and Gravitation最新文献

We give a brief review of the basic principles of inflationary theory and discuss the present status of the simplest inflationary models which can describe Planck/BICEP/Keck observational data by choice of a single model parameter. In particular, we discuss the Starobinsky model, Higgs inflation, and (alpha )-attractors, including the recently developed(alpha )-attractor models with (SL(2,mathbb {Z})) invariant potentials. We also describe inflationary models providing a good fit to the recent ACT data, as well as the polynomial chaotic inflation models with three parameters, which can account for any values of the three main CMB-related inflationary parameters (A_{s}), (n_{s}) and r.

We consider a class of exact solutions to the Einstein equations in the presence of a scalar field, recently introduced in [1, 2], and derive their generalized form with dyonic charges using Harrison transformations. For specific parameter values, this class of metrics includes the charged Fisher-Janis-Newman-Winicour (FJNW) and Zipoy-Voorhees (ZV) metrics. We then investigate the motion of neutral particles in the background of these metrics and derive the corresponding effective potential. Next, by applying Ehlers transformations, we introduce the NUT parameter into the Reissner-Nordström (RN) metric in the presence of the scalar field. We also examine gravitational lensing, focusing on the effects of dyonic and NUT charges, as well as the scalar field, on the deflection angle of light. Finally, we explore the quasi-normal modes associated with this class of metrics.

We investigate the influence of a minimal length and the accumulation of dark energy on the structure of black holes, for Schwarzschild and Kerr solutions. We show that near the event horizon the minimal length creates a region of negative temperature, resulting in a negative pressure, which counteracts a collapse. When dark energy is added, in addition the position of the event horizon will change and, depending on the size of the dark energy, stable dark stars are created. Our study ranges from standard black holes (no minimal length and no dark energy) to black holes with a minimal length and various radial intensities for the accumulation of dark energy. The dependence of the effects as a function of the black holes’s mass is studied. We find that a minimal length is possibly responsible for the suppression of primordial black holes.

In this work, we introduce a method for finding exact solutions to the vacuum Einstein field equations in higher dimensions from a given solution to the chiral equation. When considering a (n + 2)-dimensional spacetime with n commutative Killing vectors, the metric tensor can take the form (hat{g} = f ( rho , zeta ) ( d rho ^2 + d zeta ^2 ) + g_{mu nu } ( rho , zeta ) d x^mu d x^nu ). Then, the Einstein field equations in vacuum reduce to a chiral equation, (( rho g_{, z} g ^{-1} )_{, bar{z}} + ( rho g_{, bar{z}} g ^{-1} )_{, z} = 0), and two differential equations, (( ln f rho ^{1-1/n} )_{, Z} = frac{rho }{2} operatorname {tr} ( g_{, _Z} g^{-1} )^2), where (g in SL( n, mathbb {R} )) is the normalized matrix representation of (g_{mu nu }), (z = rho + i zeta ) and (Z = z, bar{z}). We use the ansatz (g = g ( xi ^a )), where the parameters (xi ^a) depend on z and (bar{z}) and satisfy a generalized Laplace equation, (( rho xi ^a _{, z} )_{, bar{z}} + ( rho xi ^a _{, bar{z}} )_{, z} = 0). The chiral equation to the Killing equation, (A_{a, xi ^b} + A_{b, xi ^a} = 0), where (A_a = g_{, xi ^a} g^{-1}). Furthermore, we assume that the matrices (A_a) commute with each other; in this way, they fulfill the Killing equation.

This paper is based upon the observation that the translation operator D in a curved space–time must depend upon the position of the particle and thus one must allow the [D, X] commutator to be a function of position X in a generalized Lie algebra. This work consists of two parts; In a purely mathematical development, we first reframe Riemannian geometry (RG) as a Generalized Lie algebra (GLA) by allowing the structure constants to be functions of an Abelian subalgebra as is necessary when translations in a space of n variables depend upon the position in the space. In the second part we show that Einstein’s equations for General Relativity (GR) can now be written as commutation relations in this GLA framework including relativistic Quantum Theory (QT) and the Standard Model (SM) with novel predictions. We begin with an Abelian Lie algebra of n “position” operators, X, whose simultaneous eigenvalues, y, define a real n-dimensional space R(n) with a Hilbert space representation. Then with n new operators defined as independent functions, X^′(X), we define contravariant and covariant tensors in terms of their eigenvalues, y and y^′ with Dirac notation. We then define n additional operators, D, whose exponential map is, by definition, to translate X in a noncommutative algebra of operators (observables) where the “structure constants” are shown to be the metric functions of the X operators to allow for spatial curvature. The D operators then have a Hilbert space position-diagonal representation as a generalized differential operator plus a Christoffel symbol, Γ^µ (y), an arbitrary vector function A^µ (y), and the derivative of a scalar function g^µn∂ϕ(y)/∂yⁿ. One can then express the Christoffel symbols, and the Riemann, Ricci, and other tensors as commutators in this representation thereby framing RG as a GLA. We then show that this GLA provides a more general framework for RG to support GR, QT, the SM with novel predictions.

We investigate the evolution of cosmological anisotropies within the framework of (fleft( Gright) )-gravity. Specifically, we consider a locally rotationally symmetric geometry in four-dimensional spacetime that describes the Bianchi I, Bianchi III, and the Kantowski-Sachs spacetimes. Within this context, we introduce a Lagrange multiplier which allows us to reformulate the geometric degrees of freedom in terms of a scalar field. The resulting theory is dynamically equivalent to an Einstein-Gauss-Bonnet scalar field model. We normalize the field equations by introducing dimensionless variables. The dynamics of our system is then explored by solving the resulting nonlinear differential equations numerically for various sets of initial conditions. Our analysis reveals the existence of two finite attractors: the Minkowski universe and an isotropic, spatially flat solution capable of describing accelerated expansion. Although de Sitter expansion may be recovered, it appears only as an unstable solution. In addition, the theory suffers from the existence of Big Rip singularities.

In recent decades, the precision of gravitational constant measurements has signifi-cantly improved. In this letter, we propose a method that takes advantage of the improved precision to measure in the laboratory whether leptons generate gravity in the same way as baryons. If leptons did not generate gravity, there would be a fractional difference in the value of the gravitational constant G expected for two different materials with different (frac{Z}{A}) ratios, where A and Z represent the mass and atomic number, respectively. We propose suitable pairs of materials where such a difference could be detected at about (4 sigma ) level given the precision in the present measurements of G.

The Moon is our future. It may seem like a chimera with a projected cost in excess of 100 billion$, and counting, dispensed on ARTEMIS with little to show to date. However it is the ideal site for the largest telescopes that we can dream about, at wavelengths spanning decimetric radio through optical to terahertz FIR. And it is these future telescopes that will penetrate the fundamental mysteries of the first hydrogen clouds, the first stars, the first galaxies, the first supermassive black holes, and the nearest habitable exoplanets. Nor does it stop there. Our lunar telescopes will take us back to the first months of the Universe, and even back to the first 10(^{-36}) second after the Big Bang when inflation most likely occurred. Our lunar telescopes will provide high resolution images of exoplanets that are nearby Earth-like ’twins’ and provide an unrivalled attempt to answer the ultimate cosmic question of whether we are alone in the universe. Here I will set out my vision of the case for lunar astronomy over the next several decades.

We consider configurations consisting of a gravitating nonlinear spinor field and a massless ghost scalar field providing a nontrivial spacetime topology. For such a mixed system, we have constructed families of asymptotically flat asymmetric solutions describing Dirac stars with wormhole topology. The physical properties of such systems are completely determined by the values of three input quantities: the nonlinearity parameter of the spinor field, the spinor frequency, and the throat parameter. Depending on the specific values of these parameters, the configurations may be regular or singular and possess one or two throats, as well as they may contain possible horizons of different kinds. Furthermore, because of the asymmetry, masses and sizes of the configurations observed at the two asymptotic ends of the wormhole may differ considerably. For large negative values of the nonlinearity parameter, it is possible to obtain configurations whose masses are comparable to the Chandrasekhar mass and effective radii are of the order of kilometers.