General Relativistic Spacetimes Research Articles

The Physics of Accretion Discs, Winds and Jets in Tidal Disruption Events

Accretion onto black holes is an efficient mechanism in converting the gas mass-energy into energetic outputs as radiation, wind and jet. Tidal disruption events, in which stars are tidally torn apart and then accreted onto supermassive black holes, offer unique opportunities of studying the accretion physics as well as the wind and jet launching physics across different accretion regimes. In this review, we systematically describe and discuss the models that have been developed to study the accretion flows and jets in tidal disruption events. A good knowledge of these physics is not only needed for understanding the emissions of the observed events, but also crucial for probing the general relativistic space-time around black holes and the demographics of supermassive black holes via tidal disruption events.

P1-Curvature tensor in the space time of general relativity

The P1 - curvature tensor defined from W3 - curvature tensor has been studied in the space time of general relativity. The Bianchi like differential identity is satisfied by P1 - tensor if and only if the Ricci tensor is of Codazzi type. It is shown that Einstein like field equations can be expressed with the help of the contracted part of P1 - tensor, which is conserved if the energy momentum tensor is Codazzi type. Considering P1 -flat space time satisfying Einstein’s field equations with cosmological term, the existence of Killing vector field ξ is shown if and only if the Lie derivative of the energy-momentum tensor vanishes with respect to ξ, as well as admitting a conformal Killing vector field is established if and only if the energy-momentum tensor has the symmetry inheritance property. Finally for a P1 - flat perfect fluid space time satisfying Einstein’s equations with cosmological term, some results are obtained.

Pseudo-quasi-conformal curvature tensor and spacetimes of general relativity

In the present paper, we carried out a systematic investigation of pseudo-quasi-conformal curvature tensor has been made on the four-dimensional spacetime of general relativity. The spacetime fulfilling Einstein?s field equations with vanishing of pseudo-quasi-conformal curvature tensor is being considered and existence of Killing and conformal Killing vectors on such spacetime have been established. At last, we extend the similar case for the investigation of cosmological models with dust and perfect fluid spacetime.

Energy-Momentum Density of Non-Diagonal Bianchi Type Space-Time in General Relativity and Teleparallel Gravity

We calculated the energy-momentum density of non-diagonal Bianchi type space-time in two different theories of gravity, General relativity (GR) and the theory of Teleparallel gravity (TG). Firstly, by applying Einstein, Landau-Lifshitz, Bergmann-Thomson and Moller prescriptions, using double index complexes in GR. Secondly, in the frame work of TG, we used the energy momentum complexes of Einstein, Bergmann-Thomson and Landau-Lifshitz. We also study the spacial cases of non-diagonal Bianchi type space-time BII, BVIII and BIX. We obtained the same energy-momentum density components for Einstein and Bergmann-Thomson prescriptions for the above four mentioned space-times that we considered in our work. Also, we found that the energy density component in Moller prescription is zero for all Bianchi types space-times in GR. Furthermore, we show that if the metric components are functions of time t alone, then the total gravitational energy is identically zero.

Junction conditions and local spacetimes in general relativity

Junction conditions and local spacetimes in general relativity

Junction conditions and local spacetimes in general relativity

In the present work, a theoretical framework focussing on local geometric deformations is introduced in order to cope with the problem of how to join spacetimes with different geometries and physical properties. This framework is used to show that two Lorentzian manifolds can be matched by considering local deformations of the associated spacetime metrics. Based on the fact that metrics can be suitably matched in this way, it is shown that the underlying geometric approach allows the characterization of local spacetimes in general relativity. Furthermore, it is shown that said approach not only extends the conventional thin shell formalism, but also allows the treatment of geometric problems that cannot be treated with standard gluing techniques.

Ensemble from coarse graining: Reconstructing the interior of an evaporating black hole

In understanding the quantum physics of a black hole, nonperturbative aspects of gravity play important roles. In particular, huge gauge redundancies of a gravitational theory at the nonperturbative level, which are much larger than the standard diffeomorphism and relate even spaces with different topologies, allow us to take different descriptions of a system. While the physical conclusions are the same in any description, the same physics may manifest itself in vastly different forms in descriptions based on different gauge choices. In this paper, we explore the relation between two such descriptions, which we refer to as the global gauge and unitary gauge constructions. The former is based on the global spacetime of general relativity, in which understanding unitarity requires the inclusion of subtle nonperturbative effects of gravity. The latter is based on a distant view of the black hole, in which unitarity is manifest but the existence of interior spacetime is obscured. These two descriptions are complementary. In this paper, we initiate the study of learning aspects of one construction through the analysis of the other. We find that the existence of near empty interior spacetime manifest in the global gauge construction is related to the maximally chaotic, fast scrambling, and universal dynamics of the horizon in the unitary gauge construction. We use the complementarity of the gauge choices to understand the ensemble nature of the gravitational path integral in global spacetime in terms of coarse graining and thermality in a single unitary theory that does not involve any ensemble nature at the fundamental level. We also discuss how the interior degrees of freedom are related with those in the exterior in the two constructions. This relation emerges most naturally as entanglement wedge reconstruction and the effective theory of the interior in the respective constructions.

Application of Hyper-generalized Quasi-Einstein Spacetimes in General Relativity

In this paper, we study the hyper-generalized quasi-Einstein (HGQE) warped product spaces with non-positive scalar curvature. This note deals with investigating of some geometric and physical properties of $$(HGQE)_{n}$$ manifolds. Next, we study the general relativistic viscous fluid $$(HGQE)_{4}$$ spacetimes with some physical applications. Lastly, we show the existence of $$(HGQE)_{4}$$ spacetimes by constructing a non-trivial example.

Nothing really matters

We study non-perturbative instabilities of AdS spacetime in General Relativity with a cosmological constant in arbitrary dimensions. In this simple setup we explicitly construct a class of gravitational instantons generalizing Witten’s bubble of nothing. We calculate the corresponding Euclidean action and show that its change is finite. The expansion of these bubbles is described by a lower-dimensional de Sitter geometry within a non- compact foliation of the background spacetime. Moreover we discuss the existence of covariantly constant spinors as a possible topological obstruction for such decays to occur. This mechanism is further connected to the stability of supersymmetric vacua in string theory.

A Novel multidimensional Boltzmann neutrino transport scheme for core-collapse supernovae.

We introduce a new discrete-ordinate scheme for solving the general relativistic (GR) Boltzmann transport equation in the context of core-collapse supernovae (CCSNe). Our algorithm avoids the need to spell out the complicated advection terms in energy and angle that arise when the transport equation is formulated in spherical polar coordinates, in the comoving frame, or in a GR space-time. We instead approach the problem by calculating the advection of neutrinos across momentum space using an intuitive particle-like approach that has excellent conservation properties and fully accounts for Lorentz boosts, GR effects, and grid geometry terms. In order to avoid the need for a global implicit solution, time integration is performed using a locally implicit Lax-Wendroff scheme that correctly reproduces the diffusion limit. This will facilitate the use of our method on massively parallel distributed-memory architectures. We have verified the accuracy and stability of our scheme with a suite of test problems in spherical symmetry and axisymmetry. To demonstrate that the new algorithm works stably in CCSN simulations, we have coupled it to the GR hydrodynamics code coconut and present a first demonstration run of a [Formula: see text] progenitor with a reduced set of neutrino opacities.

Advancing Computational Methods to Understand the Dynamics of Ejection, Accretion, Winds, and Jets in Binary Neutron Star Mergers

AbstractWe introduce the HandOff, a set of computational tools to transfer general relativistic magnetohydrodynamic and spacetime data from the numerical code IllinoisGRMHD to Harm3d. While the former simulates binary neutron star (BNS) mergers in full dynamical General Relativity, the latter specializes in modeling accretion disks around black holes (BH) over long timescales. The HandOff, then, enables us to transfer the outcome of BNS mergers after BH formation from IllinoisGRMHD to Harm3d and to evolve the post-merger system efficiently over long timescales. We show our latest results in this respect, for matter modeled as a magnetized ideal-fluid, and discuss our future plans which involve incorporating advanced equations of state and neutrino physics into BNS simulations using the HandOff approach.

Loop quantum ontology: Spacetime and spin-networks

It is standardly claimed in loop quantum gravity (LQG) that spacetime both disappears, fundamentally, and emerges from spin-networks in the low energy regime. In this paper, I critically explore these claims and develop a variety of substantival and relational interpretations of LQG for which these claims are false. According to most of the interpretations I consider, including the “received interpretation”, it is in fact false that spacetime emerges from spin-networks. In the process of supporting these claims, I also explain why spacetime is thought to be missing from the theory's fundamental ontology and demonstrate how this conclusion depends on our interpretation of the theory. In fact, I will argue that for a variety of interpretations spacetime survives quantization just as the electromagnetic field survives quantization. The upshot of the following analysis is a much needed clarification of the ontology of LQG and how it relates, or fails to relate, to the spacetime of general relativity.

Energy-Momentum Distribution for Magnetically Charged Black Hole Metric

This work investigates the well known localization problem of energy and momentum. The purpose of this paper is two fold. First, we compute Einstein, Landau-Lifshitz and Bergmann's energy-momentum complexes for static spherically symmetric magnetically charged regular black hole spacetime in general relativity. We observe strong coincidences among the results obtained form the three descriptions. These resembling results from different energy-momentum prescriptions may offer some basis to explain a exclusive quantity which supports Virabhadra's viewpoint. Secondly, the problem is discussed in modified gravity. In particular, we use generalized Landau-Lifshitz prescription for the determination of energy-momentum with reference to $f(R)$ theory of gravity. We explicitly compute the energy-momentum complex for the static spherically symmetric magnetically consistent regular black hole metric for a well-known choice of the $f(R)$ gravity models.

Strong cosmic censorship conjecture in higher curvature gravity

Deterministic nature of general relativity is ensured by the strong cosmic censorship conjecture, which asserts that spacetime cannot be extended beyond Cauchy horizon with square integrable connection. Although this conjecture holds true for asymptotically flat black hole spacetimes in general relativity, a potential violation of this conjecture occurs in charged asymptotically de Sitter spacetimes. Since it is expected that Einstein-Hilbert action will involve higher curvature corrections, in this article we have studied whether one can restore faith in the strong cosmic censorship when higher curvature corrections to general relativity are considered. Contrary to our expectations, we have explicitly demonstrated that not only a violation to the conjecture occurs near extremality, but the violation appears to become stronger as the strength of the higher curvature term increases.

Spacetimes with different forms of energy–momentum tensor

The object of the present paper is to characterize spacetimes with different types of energy–momentum tensor. At first we consider spacetimes with pseudo symmetric energy–momentum tensor T. We obtain a necessary and sufficient condition for a spacetime with pseudo symmetric energy–momentum tensor to be a pseudo Ricci symmetric spacetime. Next we consider the spacetimes with Codazzi type of energy–momentum tensor and several interesting results are pointed out. Moreover, some results related to perfect fluid spacetimes with different forms of energy–momentum tensors have been obtained. We study spacetimes with quadratic Killing energy–momentum tensor T and show that a GRW spacetime with quadratic Killing energy–momentum tensor is an Einstein space. Finally, we have considered general relativistic spacetimes with semisymmetric energy–momentum tensor and obtained some important results.

Different instances of time as different quantum modes: quantum states across space-time for continuous variables

Space-time is one of the most essential, yet most mysterious concepts in physics. In quantum mechanics it is common to understand time as a marker of instances of evolution and define states around all the space but at one time; while in general relativity space-time is taken as a combinator, curved around mass. Here we present a unified approach on both space and time in quantum theory, and build quantum states across spacetime instead of only on spatial slices. We no longer distinguish measurements on the same system at different times with measurements on different systems at one time and construct spacetime states upon these measurement statistics. As a first step towards non-relativistic quantum field theory, we consider how to approach this in the continuous-variable multi-mode regime. We propose six possible definitions for spacetime states in continuous variables, based on four different measurement processes: quadratures, displaced parity operators, position measurements and weak measurements. The basic idea is to treat different instances of time as different quantum modes. They are motivated by the pseudo-density matrix formulation among indefinite causal structures and the path integral formalism. We show that these definitions lead to desirable properties, and raise the differences and similarities between spatial and temporal correlations. An experimental proposal for tomography is presented, construing the operational meaning of the spacetime states.

String clouds and radiation flows as sources of gravity in static or rotating cylinders

Static and stationary cylindrically symmetric space-times in general relativity are considered, supported by distributions of cosmic strings stretched in the azimuthal ([Formula: see text]), longitudinal ([Formula: see text]) or radial ([Formula: see text]) directions or and by pairs of mutually opposite radiation flows in any of these directions. For such systems, exact solutions are obtained and briefly discussed, except for radial strings (a stationary solution for them is not found); it is shown that static solutions with [Formula: see text]- and [Formula: see text]-directed radiation flows do not exist while for [Formula: see text]-directed strings a solution is only possible with negative energy density. Almost all solutions under discussion contain singularities, and all stationary solutions have regions with closed timelike curves, hence, most probably, only their well-behaved regions admit application to real physical situations.

Emergence of Spacetime from Structural Interpretations

In recent discussions as to emergence of spacetime, spacetime is said to be not fundamental in quantum regions, which we must apply quantum gravity’s theory to and to be derived from fundamental entities. This is a very strange picture not only from philosophically but also commonsensically. As to classical regions, there have been already many discussions from structural realists about spacetime in General Relativity regarding how “curved spacetime” exists and where it does. But most papers on emergence of spacetime in quantum gravity’s theory are independent from details of these structural interpretations, namely traditional discussions about ontology of spacetime. This paper tries to connect classical structural spacetime and quantum spacetime’s atoms called “spinnetwork” in loop quantum gravity as one of the examples of fundamental entities through the quantization of gravitational fields. And I check from ontological viewpoints whether there are some structural discontinuities between classical and quantum regions based on “isomorphism”, comparing the quantization of electromagnetic fields.

Semiconformal curvature tensor and perfect fluid spacetimes in general relativity

The semiconformal curvature tensor and its divergence have been studied for perfect fluid spacetimes. It is seen, apart from other results, that the perfect fluid spacetimes with divergence-free semiconformal curvature tensor either satisfy the vacuum-like equation of state or represent FLRW cosmological model.

A Newman Penrose approach to Bertrand spacetime in general relativity

Newman Penrose (NP) formalism is a new approach to general relativity was presented. In various geometrical groups are estimate on a chosen null tetrad basis for tetrad formalism. This approach widely used in analytical and numerical studies of Einstein’s equations. The reasonable utilization of explicit complex straight emulsions of Ricci rotation coefficients which present, in the product, the spinor relative association. And we construct a null tetrad for general case and special attension for Bertrand’s space-time type-1 metric for special case k=0.