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We suggest that the vacuum field equation in Finsler spacetime is equivalent to the vanishing of the Ricci scalar. The Schwarzschild metric can be deduced from a solution of our field equation if the spacetime preserves spherical symmetry. Supposing that the spacetime preserves the symmetry of the "Finslerian sphere," we find a non-Riemannian exact solution of the Finslerian vacuum field equation. The solution is similar to the Schwarzschild metric. It reduces to the Schwarzschild metric as the Finslerian parameter e vanishes. It is proven that the Finslerian covariant derivative of the geometrical part of the gravitational field equation is conserved. The interior solution is also given. We get solutions of the geodesic equation in such a Schwarzschild-like spacetime, and show that the geodesic equation returns to its counterpart in Newtonian gravity in the weak-field approximation. Celestial observations give a constraint on the Finslerian parameter ∈ < 10-4, and the recent Michelson-Morley experiment requires ∈ < 10-16. A counterpart of Birkhoff's theorem exists in the Finslerian vacuum. This shows that the Finslerian gravitational field with the symmetry of the "Finslerian sphere" in vacuum must be static. [ABSTRACT FROM AUTHOR]

Within the framework of the supergroup theory and by making use of the general Holstein–Primakoff transformation, we set up an infinite hierarchy of equations of motion in the Green's functions for the t-J model. A physical criterion involving self-consistency of the decoupling is presented. A Green's function method for the t-J model, approximately valid through the entire temperature range, is given for low doping case. At low temperatures, the sublattice magnetization is in good agreement with the neutron scattering experiments in the high-temperature superconductors. The Néel temperatures and features at the antiferromagnetic-metalic phase transition region are obtained by taking into account the doping effect. Copyright 1999 Academic Press.

Abstract: In papers [4] and [6], the Variation Diminition Property of Bernstein polynomials defined on a triangle was studied. It is well known that the sequence of Bezier nets $$\widehat{f_n }$$ obtained by elevation formula convergence to the polynomial itself when n goes to infinite. But the Sequence of variation of Bezier nets does not convergence to the variation of the polynomial. This means that variations are not compatible. In this paper, we give a new definition of variation of Bezier net and prove that the inequality of variation diminition holds and the variations are compatible.

We deal with the problem of the computation of amplitudes for the bosonic Polyakov string with boundaries and show that both conformal invariance and reparametrization invariance are maintained in critical dimensional as the case without boundaries. The amplitudes of the bosonic, closed oriented Polyakov string with boundaries are formulated as integral over moduli space with respect to the Weil-Petersson measure.

In a recent work on rotating black hole shadows [Z. Chang and Q.-H. Zhu, Phys. Rev. D 101, 084029 (2020)], we proposed a new approach for calculating size and shape of the shadows in terms of astrometrical observables with respect to finite-distance observers. In this paper, we introduce a distortion parameter for the shadow shapes and discuss the appearance of the shadows of static spherical black holes and Kerr black holes in a uniform framework. We show that the shape of the shadow of a spherical black hole is circular in the view of arbitrary observers, and the size of the shadows tends to be shrunk in the view of a moving observer. The diameter of the shadows is contracted even in the direction perpendicular to the observers' motion. This seems not to be understood as length contraction effect in special relativity. The shape of Kerr black holes is dependent on motional status of the observers located at finite distance. In spite of this, it is found that there is not a surrounding observer who could view the shape of the Kerr black hole shadows as circularity. These results could be helpful for observation of the Sagittarius A* in the center of the Milky Way, as our Solar System is moving around the center of the black hole. [ABSTRACT FROM AUTHOR]

Observations recently suggest 4.4σ discrepancy between Hubble constant measured locally and that inferred from cosmic microwave background in standard cosmology. Either standard cosmology or local measurement might expect something new. We investigate the possibility that the value of Hubble constants might be affected by the observers' motional status in the local measurement. Using adapted coordinates for geodesic observers in Friedmann-Lemaitre-Robertson-Walker space-time and constraints inferred from observation of cosmic shear, we find that the motional status of the reference frame could contribute to about 1.1±0.3% discrepancy of these Hubble constants. Namely, the difference is ΔH0=0.81±0.22 km s-1 Mpc-1, if the locally measured Hubble constant is 74 km s-1 Mpc-1. This effect seems not negligible as an uncertainty for local measurement of Hubble constant. [ABSTRACT FROM AUTHOR]

The first image of a black hole in the M87 galaxy taken by the Event Horizon Telescope shows that directed observation of supermassive black holes would be a promising way to test general relativity in strong gravity field regime. In order to calculate the shadow of rotating black holes with respect to observers located at finite distance, orthonormal tetrads have been introduced in previous works. However, it is noticed that a different choice of tetrads does not lead to the same shape of shadow for observers in near regions. In this paper, we alternatively use the formula of astrometric observables for calculating the shadow of a general rotating black hole with respect to these observers. For the sake of intuition, we also consider Kerr-de Sitter black holes as a representative example. In this space-time, size and shape of Kerr-de Sitter black hole shadows are expressed as functions of distance between the black hole and observer. It is forecasted that the distortion of the shadow would increase with distance. [ABSTRACT FROM AUTHOR]

As an attractive candidate for dark matter, the primordial black holes (PBHs) in the mass range (8×1014∼1016) g could be detected via their Hawking radiation, including neutrinos and antineutrinos of three flavors. In this paper, we investigate the possibility to constrain the PBHs as dark matter by measuring (anti)neutrino signals at the large liquid-scintillator detector of Jiangmen Underground Neutrino Observatory (JUNO). Among six available detection channels, the inverse beta decay ¯νe+p→e++n is shown to be most sensitive to the fraction fPBH of PBHs contributing to the dark matter abundance. Given the PBH mass MPBH=1015 g, we find that JUNO will be able to place an upper bound fPBH≲3×10-5, which is 20 times better than the current best limit fPBH≲6×10-4 from Super-Kamiokande. For heavier PBHs with a lower Hawking temperature, the (anti)neutrinos become less energetic, leading to a relatively weaker bound. [ABSTRACT FROM AUTHOR]