General Relativity and Gravitation最新文献

Starting from the eigenvalue equation for the mass of a black hole derived by Mäkelä and Repo, we show that, by reparametrizing the radial coordinate and the wave function, it can be rewritten as the eigenvalue equation of a quantum harmonic oscillator. We then study the interior of a Schwarzschild black hole using two quantization approaches. In the standard quantization, the area and mass spectra are discrete, characterized by a quantum number (n), but the wave function is not square-integrable, limiting its physical interpretation. In contrast, a minimal-uncertainty quantization approach yields an area spectrum that grows as (n^2), and consequently the mass (M) also increases. In this framework, the wave function is finite and square-integrable, with convergence requiring that the deformation parameter (beta ) be regulated by a discrete quantum number (m). The wave function exhibits quantum tunneling connecting the black hole interior with both its exterior and a white hole region, effects that disappear in the limit (beta rightarrow 0). These results demonstrate how minimal-length effects both regularize the wave function and modify the semiclassical structure of the black hole.

The Schwarzschild-Melvin spacetime is an exact solution of the Einstein electrovacuum equations describing a black hole immersed in a magnetic field which is asymptotically aligned with the (z-)axis. It plays an important role in our understanding of the interplay between geometry and matter, and is often used as a proxy for astrophysical environments. Here, we construct the scalar counterpart to the Schwarzschild-Melvin spacetime: a non-asymptotically flat black hole geometry with an everywhere regular scalar field whose gradient is asymptotically aligned with the (z-)axis.

In this study, we investigate the thermodynamic law of accelerating and rotating black hole described by rotating C-metric, as well as holography properties in Nariai limit, which are related to Nariai-CFT and Kerr-CFT correspondence. In order to achieve this goal we define a regularized Komar mass with physical interpretation of varying the horizon area from spinless limit to general case, and derive the first law based on this construction through covariant phase space formalism. Serving for potential future studies, we also reduce the model to a 2-dimensional JT-type action and discuss some of its properties.

In this paper, we derive the entropy of Reissner-Nordström (RN) and Kerr black holes using the Hawking–Gibbons path integral method. We determine the periodicity of the Euclidean time coordinate using two approaches: first, by analyzing the near-horizon geometry, and second, by applying the Chern–Gauss–Bonnet (CGB) theorem. For non-extremal cases, both these methods yield a consistent and unique periodicity, which in turn leads to a well-defined expression for the entropy. In contrast, the extremal case exhibits a crucial difference. The absence of a conical structure in the near-horizon geometry implies that the periodicity of the Euclidean time is no longer uniquely fixed within the Hawking–Gibbons framework. The CGB theorem also fails to constrain the periodicity, as the corresponding Euler characteristic vanishes. As a result, the entropy cannot be uniquely determined using either method.

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.