International Journal of Geometric Methods in Modern Physics最新文献

The purpose of this paper is to investigate the existence of Ricci solitons and the nature of curvature inheritance as well as collineations on the Robinson–Trautman (briefly, RT) spacetime. It is shown that under certain conditions RT spacetime admits almost-Ricci soliton, almost-$\eta$-Ricci soliton, almost-gradient $\eta$-Ricci soliton. As a generalization of curvature inheritance [K. L. Duggal, Curvature inheritance symmetry in Riemannian spaces with applications to fluid space times, J. Math. Phys.33(9) (1992) 2989–2997] and curvature collineation [G. H. Katzin, J. Livine and W. R. Davis, Curvature collineations: A fundamental symmetry property of the space-times of general relativity defined by the vanishing Lie derivative of the Riemann curvature tensor, J. Math. Phys.10(4) (1969) 617–629], in this paper, we introduce the notion of generalized curvature inheritance and examine if RT spacetime admits such a notion. It is shown that RT spacetime also realizes the generalized curvature (resp., Ricci, Weyl conformal, concircular, conharmonic, Weyl projective) inheritance. Finally, several conditions are obtained, under which RT spacetime possesses curvature (resp., Ricci, conharmonic, Weyl projective) inheritance as well as curvature (resp., Ricci, Weyl conformal, concircular, conharmonic, Weyl projective) collineation, and we have also introduced the concept of generalized Lie inheritance and showed that RT spacetime realizes such a notion.

The goal of this paper is to analyze sharp-type inequalities including the scalar and Ricci curvatures of bi-slant Riemannian submersions in complex space forms. Then, for bi-slant Riemannian submersion between a complex space form and a Riemannian manifold, we give inequalities involving the Casorati curvature of the space ker ${\phi }_{\ast }.$ Also, we mention some examples.

In this paper, we obtain a Lichnerowicz-type formula for $J$-Witten deformation and give the proof of the Kastler–Kalau–Walze-type theorems associated with $J$-Witten deformation on four-dimensional and six-dimensional almost product Riemannian manifold with (respectively, without) boundary. We give an explanation of the Einstein–Hilbert action for $J$-Witten deformation on four-dimensional manifold with boundary.

In this paper, we study the tunneling radiation from a charged-accelerating AdS black hole with gauge potential under the impact of quantum gravity. Using the semi-classical phenomenon known as the Hamilton–Jacobi ansatz, it is studied that tunneling radiation occurs via the horizon of a black hole and also employs the Lagrangian equation using the generalized uncertainty principle. Furthermore, we investigate the impact of charge, gauge potential, and first order correction parameters on the temperature as well as the stable and unstable states of the black hole. We also compute thermodynamic properties such as entropy, internal energy, Helmholtz free energy, enthalpy, specific heat, and Gibbs free energy under the impact of the correction parameter for the black hole. We calculate the logarithmic modification terms for entropy around the equilibrium state to analyze the impacts of logarithmic correction. In the presence of the correction terms, we also check the validity of the thermodynamics. It examines the graphical representation of the influence of logarithmic correction on the thermodynamic properties of black hole stability as well as charged, accelerating, and gauge potential parameters.

Dabrowski et al. [Spectral metric and Einstein functionals for Hodge–Dirac operator, preprint (2023), arXiv:2307.14877] gave spectral Einstein bilinear functionals of differential forms for the Hodge–Dirac operator $d+\delta$ on an oriented even-dimensional Riemannian manifold. In this paper, we generalize the results of Dabrowski et al. to the cases of 4-dimensional oriented Riemannian manifolds with boundary. Furthermore, we give the proof of Dabrowski–Sitarz–Zalecki-type theorems associated with the Hodge–Dirac operator for manifolds with boundary.

We develop a notion of causal order on a generic manifold as independent of the underlying differential and topological structure. We show that sufficiently regular causal orders can be recovered from a distinguished algebra of sets, which plays a role analogous to that of topologies and $\sigma$ algebras. We then discuss how a natural notion of measure can be associated to the algebra of causal sets.

We review some recent results on the mathematical foundations of a quantum theory over a scalar field that is a quadratic extension of the non-Archimedean field of $p$-adic numbers. In our approach, we are inspired by the idea — first postulated in [I. V. Volovich, $p$-adic string, Class. Quantum Grav.4 (1987) L83–L87] — that space, below a suitably small scale, does not behave as a continuum and, accordingly, should be modeled as a totally disconnected metrizable topological space, ruled by a metric satisfying the strong triangle inequality. The first step of our construction is a suitable definition of a $p$-adic Hilbert space. Next, after introducing all necessary mathematical tools — in particular, various classes of linear operators in a $p$-adic Hilbert space — we consider an algebraic definition of physical states in $p$-adic quantum mechanics. The corresponding observables, whose definition completes the statistical interpretation of the theory, are introduced as SOVMs, a $p$-adic counterpart of the POVMs associated with a standard quantum system over the complex numbers. Interestingly, it turns out that the typical convex geometry of the space of states of a standard quantum system is replaced, in the $p$-adic setting, with an affine geometry; therefore, a symmetry transformation of a $p$-adic quantum system may be defined as a map preserving this affine geometry. We argue that, as a consequence, the group of all symmetry transformations of a $p$-adic quantum system has a richer structure with respect to the case of standard quantum mechanics over the complex numbers.