General Relativity and Gravitation最新文献

Unifying quantum theory and gravity remains a fundamental challenge in physics. While most existing literature focuses on the ultraviolet modifications of quantum theory due to gravity, this work shows that generic infrared modifications arise when we describe quantum theory in curved spacetime. We explicitly demonstrate that the modifications to the position-momentum algebra are proportional to curvature invariants (such as the Ricci scalar and Kretschmann scalar). Our results, derived through a rigorous application of Dirac’s quantization procedure, demonstrate that infrared effects in quantum systems can be axiomatically derived. We study particle dynamics in an arbitrary curved spacetime by embedding them in a higher-dimensional flat geometry. Our approach, which involves embedding particle dynamics in a higher-dimensional flat geometry and utilizing Dirac’s quantization procedure, allows us to capture the dynamics of a particle in 4-dimensional curved spacetime through a modified position-momentum algebra. When applied to various spacetimes, this method reveals that the corrections due to the spacetime curvature are universal. We further compare our results with those derived using extended uncertainty principles. Finally, we discuss the implications of our work for black holes and entanglement.

This research deals with the impacts of Rastall parameter on the physical behavior of isotropic compact stars. For this purpose, the static spherically symmetric as well as perfect fluid distribution are taking into account. To examine the various aspects of some particular compact star models, the Durgapal-Fuloria metric functions are considered. The unknown parameters involved in Durgapal-Fuloria metric functions are computed via matching constraints with observed choices of masses and radii of few particular stellar objects. The viability of the endorsed functions is inspected through the graphical description of matter contents, energy constraints, equation of state factor, mass constituents, causality condition and stellar equation for certain values of Rastall parameter. It is determined that the stars under consideration manifest stable structures corresponding to Durgapal-Fuloria metric potentials in this framework. Further, it is exhibited that for Rastall factor equals to zero, the general results of theory of relativity can be achieved.

Black holes represent an ideal laboratory to test Einstein’s theory of general relativity and alternative theories of gravity. Among the latter, Einstein-scalar–Gauss–Bonnet Theories have received much attention in recent years. Depending on the coupling function of the scalar field, the resulting black holes may then differ significantly from their counterparts in general relativity. Focusing on the lowest modes, linear mode stability of the black holes is addressed for several types of coupling functions. When in addition to the coupling to the Gauss–Bonnet term a cosmologically motivated further term with coupling to the curvature scalar is included, a new set of instabilities arises: quadrupole and hexadecupole instabilities of spherically symmetric scalarized black holes, that are stable under radial perturbations.

The null-surface formulation (NSF) of general relativity differs markedly from the conventional approach. The conventional approach to general relativity is concerned with local fields such as the metric, whereas the NSF focuses on surfaces. The NSF has two distinct but mathematically equivalent interpretations: (a) Future-directed light rays leave a spacetime point and intersect future null-infinity. The resulting surface, known as a light-cone cut, encodes the properties of the spacetime; (b) The angular coordinates (Bondi coordinates) of null-infinity are used to label past light cones, thereby producing a family of null surfaces. These will satisfy the NSF field equations and a solution of these equations provides a description of spacetime. This paper features a new exact solution that, for the first time, directly links the two interpretations, thereby illustrating both approaches and demonstrating their equivalence. The solution and its properties are first explored in 2+1 dimensions, after which, the generalization to 3+1 is outlined.

A gravitational field can cause a rotation of the polarisation vector of light. This phenomenon is known as the gravitational Faraday effect. We study the gravitational Faraday effect of linearly polarised light propagating in the gravitational field of a weak plane gravitational wave (GW) with “(+)", “(times )", and elliptical polarisation modes. The corresponding gravitational Faraday rotation angle is proportional to the GW amplitude and to the squared distance traveled by the light and inversely proportional to the GW squared wavelength. The Faraday rotation is maximal if the light propagates along directions perpendicular to the GW propagation and tilted by (pi /4) to the directions of its polarisation. There is no a gravitational Faraday rotation when light and a GW propagate along the same directions, or when light propagates along directions of a GW polarisation. Helicity of an elliptically polarised GW gives cubic order contribution to the Faraday rotation.

Chandrasekaran, Penington and Witten (CPW) used the crossed product construction in modular theory to associate an entropy with the algebra of observables in the Schwarzschild black hole exterior. This entropy was shown to equal the generalized entropy modulo a constant. They also proved a version of the generalized second law (GSL) in Einstein gravity. We summarize these developments and our generalization of these results to static black holes in an arbitrary diffeomorphism invariant theory of gravity [1] — this article is a summary of that work and is based on a talk at the QGatRRI conference in Sep.2023. The algebra entropy again equals the generalized entropy modulo a constant where the generalized entropy now contains the Wald entropy. A version of the GSL follows by employing the arguments of CPW to this case.

Causal set theory offers a simple and elegant picture of discrete physics. But the vast majority of causal sets look nothing at all like continuum spacetimes, and must be excluded in some way to obtain a realistic theory. I describe recent results showing that almost all non-manifoldlike causal sets are, in fact, very strongly suppressed in the gravitational path integral. This does not quite demonstrate the emergence of a continuum—we do not yet understand the remaining unsuppressed causal sets well enough—but it is a significant step in that direction.

We consider a massless and minimally coupled self interacting quantum scalar field in the inflationary de Sitter spacetime. The scalar potential is taken to be a hybrid of cubic and quartic self interactions, (V(phi )= lambda phi ^4/4!+beta phi ^3/3!) ((lambda >0)). Compared to the earlier well studied (beta =0) case, the present potential has a rolling down effect due to the (phi ^3) term, along with the usual bounding effect due to the (phi ^4) term. We begin by constructing the Schwinger–Dyson equation for the scalar Feynman propagator up to two loop, at ({mathcal {O}}(lambda )), ({{mathcal {O}}}(beta ^2)), ({{mathcal {O}}}(lambda ^2)) and ({mathcal {O}}(lambda beta ^2)). Using this equation, we consider first the local part of the scalar self energy and compute the rest mass squared of the scalar field, dynamically generated via the late time non-perturbative secular logarithms, by resumming the daisy-like graphs. The logarithms associated here are sub-leading, compared to those associated with the non-local, leading terms. We also argue that unlike the quartic case, considering merely the one loop results for the purpose of resummation does not give us any sensible result here. We next construct the non-perturbative two particle irreducible effective action up to three loop and derive from it the Schwinger–Dyson equation once again. This equation is satisfied by the non-perturbative Feynman propagator. By series expanding this propagator, the resummed local part of the self energy is shown to yield the same dynamical mass as that of the above. We next use this equation to resum the effect of the non-local part of the scalar self energy in the Feynman propagator, and show that even though the perturbatively corrected propagator shows secular growth at late times, there exists one resummed solution which is vanishing for large spacelike separations, in qualitative agreement with the well known result found via the stochastic formalism.

In this paper, we delve into the study of thermodynamics and phase transition of charged Gauss–Bonnet black holes within the context of anti-de Sitter space, with particular emphasis on the central charge’s role within the dual conformal field theory (CFT). We employ a holographic methodology that interprets the cosmological constant and the Newton constant as thermodynamic variables, leading to the derivation of a modified first law of thermodynamics that incorporates the thermodynamic volume and pressure. Our findings reveal that the central charge of the CFT is intrinsically linked to the variation of these constants, and its stability can be ensured by simultaneous adjustment of these constants. We further explore the phase structures of the black holes, utilizing the free energy. Our research uncovers the existence of a critical value of the central charge, beyond which the phase diagram displays a first-order phase transition between small and large black holes. We also delve into the implications of our findings on the complexity of the CFT. Our conclusions underscore the significant role of the central charge in the holographic thermodynamics and phase transition of charged Gauss–Bonnet black holes. Furthermore, we conclude that while the central charge considered provides suitable and satisfactory solutions for this black hole in 4 and 5 dimensions, it becomes necessary to introduce a unique central charge for this structure of modified gravity. In essence, the central charge in holographic thermodynamics is not a universal value and requires modification in accordance with different modified gravities. Consequently, the physics of the problem will significantly deviate from the one discussed in this article, indicating a rich and complex landscape for future work.